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Bogomolnaia, Anna, and Jean-François Laslier. "Euclidean preferences." Journal of Mathematical Economics 43, no. 2 (2007): 87–98. http://dx.doi.org/10.1016/j.jmateco.2006.09.004.
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Luaces, Oscar, Jorge Díez, Thorsten Joachims, and Antonio Bahamonde. "Mapping preferences into Euclidean space." Expert Systems with Applications 42, no. 22 (2015): 8588–96. http://dx.doi.org/10.1016/j.eswa.2015.07.013.
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Conroy-Beam, Daniel. "Euclidean Mate Value and Power of Choice on the Mating Market." Personality and Social Psychology Bulletin 44, no. 2 (2017): 252–64. http://dx.doi.org/10.1177/0146167217739262.
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Three studies tested the hypothesis that human mate choice psychology uses a Euclidean algorithm to integrate mate preferences into estimates of mate value. In Study 1, a series of agent-based models identify a pattern of results relatively unique to mating markets where individuals high in Euclidean mate value experience greater power of choice: strong preference fulfillment overall and correlations between mate value and (a) preference fulfillment, (b) ideal standards, and (c) partner mate value. Studies 2 and 3 demonstrated that this pattern of results that emerges in human romantic relationships, is specific to mate value as a long-term partner, and is not accounted for by participant biases. These results suggest that human mate choice psychology uses a Euclidean algorithm to integrate mate preferences in mate choice, providing insight into the computational design of human mating psychology and validating this algorithm as a useful tool for future research.
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Bordes, Georges, Gilbert Laffond, and Michel Le Breton. "Euclidean preferences, option sets and strategyproofness." SERIEs 2, no. 4 (2011): 469–83. http://dx.doi.org/10.1007/s13209-011-0075-2.
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Richter, Michael, and Ariel Rubinstein. "Convex preferences: A new definition." Theoretical Economics 14, no. 4 (2019): 1169–83. http://dx.doi.org/10.3982/te3286.
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We suggest a concept of convexity of preferences that does not rely on any algebraic structure. A decision maker has in mind a set of orderings interpreted as evaluation criteria. A preference relation is defined to be convex when it satisfies the following condition: If, for each criterion, there is an element that is both inferior to b by the criterion and superior to a by the preference relation, then b is preferred to a. This definition generalizes the standard Euclidean definition of convex preferences. It is shown that under general conditions, any strict convex preference relation is represented by a maxmin of utility representations of the criteria. Some economic examples are provided.
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Mutlu, Güneş, and Ahmet Mete Çilingirtürk. "Social Network of Faculties According to Student Preferences in Transition to Higher Education." Lietuvos statistikos darbai 51, no. 1 (2012): 51–56. http://dx.doi.org/10.15388/ljs.2012.13905.
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In social network analysis, the studies on weighted adjacency matrix of nodes are increasing day by day. In thispaper, a method is proposed by including node properties to neighbourhood matrix, in order to see the structures of weightedadjacency matrix that defines the relationship between the nodes. In accordance with this proposal, the relationship betweenthe faculties of Turkish universities is studied according to student preferences. Weighted adjacency matrix between facultiesis composed based on the frequency of faculty preference of students. By using the properties of faculties, this matrix ismultiplied by the adjacency matrix, calculated by Squared Euclidian Distance. The weighted adjacency matrix of the facultiesis compared with the re-calculated weighted adjacency matrix. It is observed that the relations between faculties are turnedout to be more meaningful in new weighted neighbourhood matrix which is multiplied by Squared Euclidean Distance.
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Liu, Chunyang, Chao Liu, Haiqiang Xin, Jian Wang, Jiping Liu, and Shenghua Xu. "Joint Geosequential Preference and Distance Metric Factorization for Point-of-Interest Recommendation." Mathematical Problems in Engineering 2020 (October 30, 2020): 1–14. http://dx.doi.org/10.1155/2020/6582676.
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Point-of-interest (POI) recommendation is a valuable service to help users discover attractive locations in location-based social networks (LBSNs). It focuses on capturing users’ movement patterns and location preferences by using massive historical check-in data. In the past decade, matrix factorization has become a mature and widely used technology in POI recommendation. However, the inner product of latent vectors adopted in matrix factorization methods does not satisfy the triangle inequality property, which may limit the expressiveness and lead to suboptimal solutions. Besides, the extreme sparsity of check-in data makes it challenging to capture users’ movement preferences accurately. In this paper, we propose a joint geosequential preference and distance metric factorization framework, called GeoSeDMF, for POI recommendation. First, we introduce a distance metric factorization method that is capable of learning users’ personalized preferences from a position and distance perspective in the metric space. Specifically, we convert the user-POI interaction matrix into a distance matrix and factorize it into user and POI dense embeddings. Additionally, we measure users’ personalized preference for the POI by using the Euclidean distance metric instead of the inner product. Then, we model the users’ geospatial preference by applying a geographic weight coefficient and model the users’ sequential preference by using the Euclidean distance of continuous check-in locations. Moreover, a pointwise loss strategy and AdaGrad algorithm are adopted to optimize the positions and relationships of users and POIs in a metric space. Finally, experimental results on three large-scale real-world datasets demonstrate the effectiveness and superiority of the proposed method.
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Azrieli, Yaron. "Axioms for Euclidean preferences with a valence dimension." Journal of Mathematical Economics 47, no. 4-5 (2011): 545–53. http://dx.doi.org/10.1016/j.jmateco.2011.07.004.
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Henry, Marc, and Ismael Mourifié. "EUCLIDEAN REVEALED PREFERENCES: TESTING THE SPATIAL VOTING MODEL." Journal of Applied Econometrics 28, no. 4 (2011): 650–66. http://dx.doi.org/10.1002/jae.1276.
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Blasco, Xavier, Gilberto Reynoso-Meza, Enrique A. Sánchez-Pérez, Juan Vicente Sánchez-Pérez, and Natalia Jonard-Pérez. "A Simple Proposal for Including Designer Preferences in Multi-Objective Optimization Problems." Mathematics 9, no. 9 (2021): 991. http://dx.doi.org/10.3390/math9090991.
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Including designer preferences in every phase of the resolution of a multi-objective optimization problem is a fundamental issue to achieve a good quality in the final solution. To consider preferences, the proposal of this paper is based on the definition of what we call a preference basis that shows the preferred optimization directions in the objective space. Associated to this preference basis a new basis in the objective space—dominance basis—is computed. With this new basis the meaning of dominance is reinterpreted to include the designer’s preferences. In this paper, we show the effect of changing the geometric properties of the underlying structure of the Euclidean objective space by including preferences. This way of incorporating preferences is very simple and can be used in two ways: by redefining the optimization problem and/or in the decision-making phase. The approach can be used with any multi-objective optimization algorithm. An advantage of including preferences in the optimization process is that the solutions obtained are focused on the region of interest to the designer and the number of solutions is reduced, which facilitates the interpretation and analysis of the results. The article shows an example of the use of the preference basis and its associated dominance basis in the reformulation of the optimization problem, as well as in the decision-making phase.
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Nermend, Kesra. "Multi-Criteria Preference Vector Method (PVM) as a Tool Supporting the Decision Making Process." Przegląd Statystyczny 62, no. 1 (2015): 93–116. http://dx.doi.org/10.5604/01.3001.0014.1706.
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The paper presents the theoretical foundations of Preference Vector Method (PVM). It is the development of methods used by the Polish school and can be used in the decision making process. The ranking of objects according to a decision-maker preferences is performed on the basis of a combination of two methods for construction aggregate measures: Hellwig method, in which the Euclidean distance is used and the vector measures construction method (VMCM), which uses a vector projection.
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Milyo, Jeffrey. "A problem with Euclidean preferences in spatial models of politics." Economics Letters 66, no. 2 (2000): 179–82. http://dx.doi.org/10.1016/s0165-1765(99)00220-7.
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Schofield, Norman, and Craig A. Tovey. "Probability and convergence for supra-majority rule with Euclidean preferences." Mathematical and Computer Modelling 16, no. 8-9 (1992): 41–58. http://dx.doi.org/10.1016/0895-7177(92)90086-z.
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Delemazure, Théo, Jérôme Lang, and Grzegorz Pierczyński. "Independence of Irrelevant Alternatives under the Lens of Pairwise Distortion." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 9 (2024): 9645–52. http://dx.doi.org/10.1609/aaai.v38i9.28821.
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We give a quantitative analysis of the independence of irrelevant alternatives (IIA) axiom. IIA says that the society's preference between x and y should depend only on individual preferences between x and y: we show that, in several contexts, if the individuals express their preferences about additional (``irrelevant'') alternatives, this information helps to estimate better which of x and y has higher social welfare. Our contribution is threefold: (1) we provide a new tool to measure the impact of IIA on social welfare (pairwise distortion), based on the well-established notion of voting distortion, (2) we study the average impact of IIA in both general and metric settings, with experiments on synthetic and real data and (3) we study the worst-case impact of IIA in the 1D-Euclidean metric space.
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Jameel, Mohammed, and Mohamed Abouhawwash. "A Reference Point-Based Evolutionary Algorithm Solves Multi and Many-Objective Optimization Problems: Method and Validation." Computational Intelligence and Neuroscience 2023 (January 25, 2023): 1–26. http://dx.doi.org/10.1155/2023/4387053.
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The integration of a decision maker’s preferences in evolutionary multi-objective optimization (EMO) has been a common research scope over the last decade. In the published literature, several preference-based evolutionary approaches have been proposed. The reference point-based non-dominated sorting genetic (R-NSGA-II) algorithm represents one of the well-known preference-based evolutionary approaches. This method mainly aims to find a set of the Pareto-optimal solutions in the region of interest (ROI) rather than obtaining the entire Pareto-optimal set. This approach uses Euclidean distance as a metric to calculate the distance between each candidate solution and the reference point. However, this metric may not produce desired solutions because the final minimal Euclidean distance value is unknown. Thus, determining whether the true Pareto-optimal solution is achieved at the end of optimization run becomes difficult. In this study, R-NSGA-II method is modified using the recently proposed simplified Karush–Kuhn–Tucker proximity measure (S-KKTPM) metric instead of the Euclidean distance metric, where S-KKTPM-based distance measure can predict the convergence behavior of a point from the Pareto-optimal front without prior knowledge of the optimum solution. Experimental results show that the algorithm proposed herein is highly competitive compared with several state-of-the-art preference-based EMO methods. Extensive experiments were conducted with 2 to 10 objectives on various standard problems. Results show the effectiveness of our algorithm in obtaining the preferred solutions in the ROI and its ability to control the size of each preferred region separately at the same time.
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Chen, Chien-Hsiung, and Xiao Li. "Spatial Knowledge Acquisition with Mobile Maps: Effects of Map Size on Users’ Wayfinding Performance with Interactive Interfaces." ISPRS International Journal of Geo-Information 9, no. 11 (2020): 614. http://dx.doi.org/10.3390/ijgi9110614.
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Restricted by the small screen size, it is challenging for users to obtain all the wayfinding content they need when utilizing mobile devices. This study investigated the effects of map size and interactive interface on users’ wayfinding performance and preference when using mobile devices. Two types of interactive interfaces (i.e., panning and peephole interfaces) and three different map sizes (i.e., small, medium, and large) were examined. The experiment was a 2 × 3 between-subjects design. Sixty participants were invited to complete five wayfinding tasks (i.e., Euclidean distance judgment, route distance judgment, landmark recognition, map section rotation, and route recognition), a system usability scale (SUS) questionnaire, and the subjective preference questionnaire. The results showed that: (1) The participants’ wayfinding performance was affected by the map size and interactive interface; (2) the peephole interface was superior for the Euclidean distance judgment and the route recognition tasks; (3) it does not always take a significantly longer time to complete the task with the larger map when performing the map section rotation task with the panning interface; and (4) the usability scores of the peephole interface were considered above average, and it had a positive impact on the participants’ preferences.
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Escoffier, Bruno, Olivier Spanjaard, and Magdaléna Tydrichová. "Weighted majority tournaments and Kemeny ranking with 2-dimensional Euclidean preferences." Discrete Applied Mathematics 318 (September 2022): 6–12. http://dx.doi.org/10.1016/j.dam.2022.05.009.
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Godziszewski, Michał T., Paweł Batko, Piotr Skowron, and Piotr Faliszewski. "An Analysis of Approval-Based Committee Rules for 2D-Euclidean Elections." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 6 (2021): 5448–55. http://dx.doi.org/10.1609/aaai.v35i6.16686.
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We study approval-based committee elections for the case where the voters' preferences come from a 2D-Euclidean model. We consider two main issues: First, we ask for the complexity of computing election results. Second, we evaluate election outcomes experimentally, following the visualization technique of Elkind et al., (AAAI-2017). Regarding the first issue, we find that many NP-hard rules remain intractable for 2D-Euclidean elections. For the second one, we observe that the behavior and nature of many rules strongly depends on the exact protocol for choosing the approved candidates.
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Chung, Hun, and John Duggan. "Directional equilibria." Journal of Theoretical Politics 30, no. 3 (2018): 272–305. http://dx.doi.org/10.1177/0951629818775515.
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We propose the solution concept of directional equilibrium for the multidimensional model of voting with general spatial preferences. This concept isolates alternatives that are stable with respect to forces applied by all voters in the directions of their gradients, and it extends a known concept from statistics for Euclidean preferences. We establish connections to the majority core, Pareto optimality, and existence and closed graph, and we provide non-cooperative foundations in terms of a local contest game played by voters.
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Vásquez, Johanna, and Sergio Botero. "Hybrid Methodology to Improve Health Status Utility Values Derivation Using EQ-5D-5L and Advanced Multi-Criteria Techniques." International Journal of Environmental Research and Public Health 17, no. 4 (2020): 1423. http://dx.doi.org/10.3390/ijerph17041423.
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This paper presented a new approach to the calculation of quality-adjusted life years (QALY) based on multi-criteria decision-making (MCDM) methods and using the EQ-5D-5L questionnaire. The health status utility values were calculated through a hybrid methodology. We combined the analytic hierarchy process (AHP), the AHP with a D-number extended fuzzy preference relation (D-AHP), the fuzzy analytic hierarchy process (F-AHP), and the technique for order preference by similarity to the ideal solution (TOPSIS) to obtain individual and aggregated utility values. The preference data were elicited using a sample of individuals from a Colombian university. In all tested methods, the ordinal preferences were consistent, and the weights were compared using the Euclidean distance criterion (EDC). We identified F-AHP-TOPSIS as the optimal method; its benefits were associated with modeling the response options of the EQ-5D in linguistic terms, it gave the best approximation to the initial preferences according to EDC, and it could be used as an alternative to the known prioritization method. This hybrid methodology was particularly useful in certain medical decisions concerned with understanding how a specific person values his or her current health or possible health outcomes from different interventions in small population samples and studies carried out in low- and middle-low-income countries.
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Arslan, Turan. "A Weighted Euclidean Distance based TOPSIS Method for Modeling Public Subjective Judgments." Asia-Pacific Journal of Operational Research 34, no. 03 (2017): 1750004. http://dx.doi.org/10.1142/s021759591750004x.
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Public involvement in transportation planning and decision-making process is a key component for ensuring that decisions are made with consideration of public needs and preferences. In this paper, a weighted Euclidean distance based TOPSIS method (WEDTOPSIS) is developed for modeling such a public decision-making process. The Weber–Fechner psycho-physical law is adopted for behavioral modeling of human judgments. Distances to the positive-ideal and negative-ideal solutions of TOPSIS are converted to value measurement models using the Weber–Fechner law. The proposed method is applied on a case where public approval of two different types of public bus operation systems considering six criteria is sought. A numerical illustration is also provided to demonstrate the applicability of the approach. The method provides plausible results in terms of preferences, and shows a high agreement with the ordinary TOPSIS in terms of rankings. Another example showing disagreement on ranking is further analyzed to outline the discrepancies between the TOPSIS and WEDTOPSIS and to indicate the proposed model’s consistency with the behavioral theory. The results are also compared with the results of the additive multi-attribute value (MAVT) method for assessing the performance of the model. Based on the findings, using the proposed method as a decision support tool can be useful, particularly where public input is needed.
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Stoetzer, Lukas F., and Steffen Zittlau. "Multidimensional Spatial Voting with Non-separable Preferences." Political Analysis 23, no. 3 (2015): 415–28. http://dx.doi.org/10.1093/pan/mpv013.
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In most multidimensional spatial models, the systematic component of agent utility functions is specified as additive separable. We argue that this assumption is too restrictive, at least in the context of spatial voting in mass elections. Here, assuming separability would stipulate that voters do not care about how policy platforms combine positions on multiple policy dimensions. We present a statistical implementation of Davis, Hinich, and Ordeshook's (1970) Weighted Euclidean Distance model that allows for the estimation of the direction and magnitude of non-separability from vote choice data. We demonstrate in a Monte-Carlo experiment that conventional separable model specifications yield biased and/or unreliable estimates of the effect of policy distances on vote choice probabilities in the presence of non-separable preferences. In three empirical applications, we find voter preferences on economic and socio-cultural issues to be non-separable. If non-separability is unaccounted for, researchers run the risk of missing crucial parts of the story. The implications of our findings carry over to other fields of research: checking for non-separability is an essential part of robustness testing in empirical applications of multidimensional spatial models.
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Pan, N., K. C. Yen, S. J. Zhao, and S. R. Yang. "A New Approach to the Objective Evaluation of Fabric Handle from Mechanical Properties." Textile Research Journal 58, no. 8 (1988): 438–44. http://dx.doi.org/10.1177/004051758805800802.
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The existing problems of the current methods for fabric handle evaluation are analyzed and as an alternative, a new measure, the weighted Euclidean distance (WD) value, of total handle is proposed. Using this method, one can specify the preferences of fabric handle. The whole process for deriving and calculating this measure is also introduced. Through illustration and comparison with Kawabata's THV value, the advantages and applicability of the WD value to fabric handle evaluation are demonstrated.
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Schmitt, Thomas, Matthias Hoffmann, Tobias Rodemann, and Jürgen Adamy. "Incorporating Human Preferences in Decision Making for Dynamic Multi-Objective Optimization in Model Predictive Control." Inventions 7, no. 3 (2022): 46. http://dx.doi.org/10.3390/inventions7030046.
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We present a new two-step approach for automatized a posteriori decision making in multi-objective optimization problems, i.e., selecting a solution from the Pareto front. In the first step, a knee region is determined based on the normalized Euclidean distance from a hyperplane defined by the furthest Pareto solution and the negative unit vector. The size of the knee region depends on the Pareto front’s shape and a design parameter. In the second step, preferences for all objectives formulated by the decision maker, e.g., 50–20–30 for a 3D problem, are translated into a hyperplane which is then used to choose a final solution from the knee region. This way, the decision maker’s preference can be incorporated, while its influence depends on the Pareto front’s shape and a design parameter, at the same time favorizing knee points if they exist. The proposed approach is applied in simulation for the multi-objective model predictive control (MPC) of the two-dimensional rocket car example and the energy management system of a building.
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Golubin, A. Y. "A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences." Journal of Optimization Theory and Applications 166, no. 3 (2014): 791–803. http://dx.doi.org/10.1007/s10957-014-0698-0.
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Al-Shamiri, Mohammed M. Ali, Adeel Farooq, Muhammad Nabeel, Ghous Ali, and Dragan Pamučar. "Integrating TOPSIS and ELECTRE-Ⅰ methods with cubic $ m $-polar fuzzy sets and its application to the diagnosis of psychiatric disorders." AIMS Mathematics 8, no. 5 (2023): 11875–915. http://dx.doi.org/10.3934/math.2023601.
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<abstract><p>Many real-world decision-making issues frequently involve competing sets of criteria, uncertainty, and inaccurate information. Some of these require the involvement of a group of decision-makers, where it is necessary to reduce the various available individual preferences to a single collective preference. To enhance the effectiveness of multi-criteria decisions, multi-criteria decision-making is a popular decision-making technique that makes the procedure more precise, reasonable, and efficient. The "Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)" and "Elimination and Choice Transforming Reality (ELECTRE)" are prominent ranking methods and widely used in the multi-criteria decision-making to solve complicated decision-making problems. In this study, two $ m $-polar fuzzy set-based ranking methods are proposed by extending the ELECTRE-Ⅰ and TOPSIS approaches equipped with cubic $ m $-polar fuzzy (C$ m $PF) sets, where the experts provide assessment results on feasible alternatives through a C$ m $PF decision matrix. The first proposed method, C$ m $PF-TOPSIS, focuses on the alternative that is closest to a C$ m $PF positive ideal solution and farthest away from the C$ m $PF negative ideal solution. The Euclidean and normalized Euclidean distances are used to determine the proximity of an alternative to ideal solutions. In contrast, the second developed method is C$ m $PF-ELECTRE-Ⅰ which uses an outranking directed decision graph to determine the optimal alternative, which entirely depends on the C$ m $PF concordance and discordance sets. Furthermore, a practical case study is carried out in the diagnosis of impulse control disorders to illustrate the feasibility and applicability of the proposed methods. Finally, a comparative analysis is performed to demonstrate the veracity, superiority, and effectiveness of the proposed methods.</p></abstract>
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Agyapong, Kingsley. "Students’ Perspectives on Satisfaction with Distance Education in Ghana: A Cluster Analysis." African Journal of Teacher Education 10, no. 1 (2021): 365–91. http://dx.doi.org/10.21083/ajote.v10i1.6287.
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This study sought to categorise students based on the preferences that influenced their choice of distance education program in Ghana. Questionnaires were used to collect data from 120 students taking part in the University of Education, Winneba (UEW) distance education (DE) programme at the Kumasi Girls Senior High School [SHS] Study Center. Respondents were segmented into three clusters (highly, moderately, and least satisfied) based on four preferences (price, quality, packaging, and social boding) that influenced their satisfaction with the distance education programme. Results from both hierarchical and non-hierarchical cluster analysis with squared Euclidean distance and Ward’s method showed that the highly satisfied cluster was driven by the quality of service and the competitive fees structure of the UEW distance education programme. Further analysis of the differences between the clusters indicated that satisfaction with the UEW distance programme significantly differs across the three segments.
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Saeki, Manabu. "Gridlock in the Government of the United States: Influence of Divided Government and Veto Players." British Journal of Political Science 39, no. 3 (2009): 587–607. http://dx.doi.org/10.1017/s0007123408000550.
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David Mayhew’s Divided We Govern significantly challenged the conventional wisdom of the adversarial effect of divided government on government effectiveness in the United States. While the post-Mayhewian literature has been centred on legislative productivity as a measure of gridlock, gridlock is here defined as an ‘inability to change policy’. In this study, the preferences of the legislators, such as the filibuster, override and House median veto players are plotted in Euclidean space. The analysis focuses on the influence of the area of the winset, which is an intersection overlapped by the veto players’ indifference curves. There is a substantial impact of the area of the winset on the change in policy output point, which is measured by the ADA scores and by Poole’s Mean Winning Coordinate. Yet divided government has marginal or no effect on policy swing. The conclusion is that the preferences of veto players, but not party control of the government, have a substantial impact on gridlock in the United States.
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Gershkov, Alex, Benny Moldovanu, and Xianwen Shi. "Voting on multiple issues: What to put on the ballot?" Theoretical Economics 14, no. 2 (2019): 555–96. http://dx.doi.org/10.3982/te3193.
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We study a multidimensional collective decision under incomplete information. Agents have Euclidean preferences and vote by simple majority on each issue (dimension), yielding the coordinate‐wise median. Judicious rotations of the orthogonal axes—the issues that are voted upon—lead to welfare improvements. If the agents' types are drawn from a distribution with independent marginals, then under weak conditions, voting on the original issues is not optimal. If the marginals are identical (but not necessarily independent), then voting first on the total sum and next on the differences is often welfare superior to voting on the original issues. We also provide various lower bounds on incentive efficiency: in particular, if agents' types are drawn from a log‐concave density with independently and identically distributed marginals, a second‐best voting mechanism attains at least 88 % of the first‐best efficiency. Finally, we generalize our method and some of our insights to preferences derived from distance functions based on inner products.
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Stoykov, Stanislav, and Ivan Kostov. "Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior." Games 14, no. 2 (2023): 24. http://dx.doi.org/10.3390/g14020024.
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A numerical procedure capable of obtaining the equilibrium states of oligopoly markets under several assumptions is presented. Horizontal and vertical product differentiation were included by taking into account Euclidean distance in a two-dimensional space and quality characteristics of the product. Different quality preferences of consumers were included in the model. Firms implement two strategies in the market: profit maximization and market share maximization. Numerical discretization of a two-dimensional area was performed for computing the equilibrium prices which allows one to consider any market area and any location of the firms. Four scenarios of oligopoly markets were developed by combining both strategies from one side and competitive behavior and a partial cartel agreement from another side. The main differences between the scenarios are outlined. Profits, market shares and equilibrium prices are presented and compared. The influence of collusion, the existence of participants with a market share maximization strategy and consumer preferences on the firm’s profits and equilibrium prices were examined. Cases whereby firms prefer to leave the cartel were investigated. Best locations for the setting of a new store for profit maximization are shown and discussed.
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Qin, Peng, and Lina Wang. "PPVC: Towards a Personalized Local Differential Privacy-Preserving Scheme for V2G Charging Networks." Mathematics 11, no. 20 (2023): 4257. http://dx.doi.org/10.3390/math11204257.
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The rapid development of electric vehicles provides users with convenience of life. When users enjoy the V2G charging service, privacy leakage of their charging location is a crucial security issue. Existing privacy-preserving algorithms for EV access to charging locations suffer from the problem of nondefendable background knowledge attacks and privacy attacks by untrustworthy third parties. We propose a personalized location privacy protection scheme (PPVC) based on differential privacy to meet users’ personalized EV charging requirements while protecting their privacy. First, by constructing a decision matrix, PPVC describes recommended routes’ utility and privacy effects. Then, a utility model is constructed based on the multiattribute theory. The user’s privacy preferences are integrated into the model to provide the route with the best utility. Finally, considering the privacy preference needs of users, the Euclidean distance share is used to assign appropriate privacy budgets to users and determine the generation range of false locations to generate the service request location with the highest utility. The experimental results show that the proposed personalized location privacy protection scheme can meet the service demands of users while reasonably protecting their privacy to provide higher service quality. Compared with existing solutions, PPVC improves the charging efficiency by up to 25%, and 8% at the same privacy protection level.
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Imber, Aviram, Jonas Israel, Markus Brill, Hadas Shachnai, and Benny Kimelfeld. "Spatial Voting with Incomplete Voter Information." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 9 (2024): 9790–97. http://dx.doi.org/10.1609/aaai.v38i9.28838.
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We consider spatial voting where candidates are located in the Euclidean d-dimensional space, and each voter ranks candidates based on their distance from the voter's ideal point. We explore the case where information about the location of voters' ideal points is incomplete: for each dimension, we are given an interval of possible values. We study the computational complexity of finding the possible and necessary winners for positional scoring rules. Our results show that we retain tractable cases of the classic model where voters have partial-order preferences. Moreover, we show that there are positional scoring rules under which the possible-winner problem is intractable for partial orders, but tractable in the one-dimensional spatial setting. We also consider approval voting in this setting. We show that for up to two dimensions, the necessary-winner problem is tractable, while the possible-winner problem is hard for any number of dimensions.
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Kim, Tae-Yeun, Hoon Ko, Sung-Hwan Kim, and Ho-Da Kim. "Modeling of Recommendation System Based on Emotional Information and Collaborative Filtering." Sensors 21, no. 6 (2021): 1997. http://dx.doi.org/10.3390/s21061997.
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Emotion information represents a user’s current emotional state and can be used in a variety of applications, such as cultural content services that recommend music according to user emotional states and user emotion monitoring. To increase user satisfaction, recommendation methods must understand and reflect user characteristics and circumstances, such as individual preferences and emotions. However, most recommendation methods do not reflect such characteristics accurately and are unable to increase user satisfaction. In this paper, six human emotions (neutral, happy, sad, angry, surprised, and bored) are broadly defined to consider user speech emotion information and recommend matching content. The “genetic algorithms as a feature selection method” (GAFS) algorithm was used to classify normalized speech according to speech emotion information. We used a support vector machine (SVM) algorithm and selected an optimal kernel function for recognizing the six target emotions. Performance evaluation results for each kernel function revealed that the radial basis function (RBF) kernel function yielded the highest emotion recognition accuracy of 86.98%. Additionally, content data (images and music) were classified based on emotion information using factor analysis, correspondence analysis, and Euclidean distance. Finally, speech information that was classified based on emotions and emotion information that was recognized through a collaborative filtering technique were used to predict user emotional preferences and recommend content that matched user emotions in a mobile application.
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Chirikjian, G., S. Sajjadi, D. Toptygin, and Y. Yan. "Mathematical aspects of molecular replacement. III. Properties of space groups preferred by proteins in the Protein Data Bank." Acta Crystallographica Section A Foundations and Advances 71, no. 2 (2015): 186–94. http://dx.doi.org/10.1107/s2053273314024358.
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The main goal of molecular replacement in macromolecular crystallography is to find the appropriate rigid-body transformations that situate identical copies of model proteins in the crystallographic unit cell. The search for such transformations can be thought of as taking place in the coset space Γ\Gwhere Γ is the Sohncke group of the macromolecular crystal andGis the continuous group of rigid-body motions in Euclidean space. This paper, the third in a series, is concerned with viewing nonsymmorphic Γ in a new way. These space groups, rather than symmorphic ones, are the most common ones for protein crystals. Moreover, their properties impact the structure of the space Γ\G. In particular, nonsymmorphic space groups contain both Bieberbach subgroups and symmorphic subgroups. A number of new theorems focusing on these subgroups are proven, and it is shown that these concepts are related to the preferences that proteins have for crystallizing in different space groups, as observed in the Protein Data Bank.
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Chukwuka, Azubuike Victor, Adedeji Hameed Adebowale, and Oloyede Adeyemi Adekolurejo. "Morphological Differences and Trophic Niche Breadth of Sarotherodon galilaeus and Oreochromis niloticus from the Freshwater Lake Geriyo, North-Eastern Nigeria." Croatian Journal of Fisheries 77, no. 1 (2019): 19–32. http://dx.doi.org/10.2478/cjf-2019-0003.
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Abstract The relationship between morphological traits and feeding ecology of the only two tilapiine cichlids (Sarotherodon galilaeus and Oreochromis niloticus) in Lake Geriyo, northeastern Nigeria, was examined. Stomach contents of 504 individuals were examined and analyzed to relate morphological differences of each species to its dietary preferences. Eleven ecological relevant morphological variables, including total length, standard length, head length, body depth, eye diameter, pectoral spine length, pelvic spine length, dorsal fin ray count, dorsal spine count and anal fin ray count, were also measured and subjected to Principal coordinate analysis (PCoA) to relate morphological differences of each species to its dietary preferences. The PCoA (using Euclidean distance) revealed a large morphological distance between species indicating adaptation for different spatial and vertical distributions within the lake. Furthermore, the correlation of these morphological differences with particular diet categories suggests a potential for specialized trophic tendencies, however, the high occurrence of two major food types (macrophytes and plankton) in stomach contents of both species indicate generalist trophic tendencies. While a high trophic overlap index (0.98) was recorded for both species, the trophic niche breadth was higher for S. galilaeus (4.18±0.32), compared to O. niloticus (3.33±0.24). Despite the large morphological differences of both tilapias, the high trophic overlaps indicate limited food options within Lake Geriyo. In addition, the successful coexistence of the tilapias in the face of limited food resources indicates suitable partitioning of food resources in the lake.
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Sidorchuk, Roman, Sergey Vladimirovich Mkhitaryan, Boris Vladimirovich Musatov, Aleksey Aleksandrovich Meshkov, and Timur Alekseevich Tultaev. "The influence of high level values on brand preferences of student youth in Russia." International Journal of Retail & Distribution Management 46, no. 7 (2018): 638–56. http://dx.doi.org/10.1108/ijrdm-01-2018-0006.
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Purpose The share of student youth, as consumers, is quite significant in the world. Considering that retailers view young consumers (including student audience) an important segment of the market, a substantial question is to study the effect of values on motivation consumer behavior. The purpose of this paper is to fill the lack of studies on motivational influence of “high-level values” (HLV) on young consumers. This research paper examines the motivational influence of HLV on brands in certain product categories-markers, to develop a methodology for segmenting consumers based on their clustering by values and evaluating brand preferences in different segments. Design/methodology/approach The sample was formed by the “snowball” method from first-year undergraduate students. The sample size involves 239 respondents. The research was carried out by the online survey method on the basis of a structured questionnaire. To obtain segments, the authors used hierarchical cluster analysis by the Ward method and the Euclidean distance method. The statistical significance of the differences in brand preferences between segments was checked in the conjugacy tables using the χ2 test at different significance levels. Findings Findings show clearly the possibility on the basis of HLV to identify segments of consumers, which allows obtaining the distribution of the perception of the brand. For a student audience received segments were: “Become a successful leader,” “become successful in a harmonious world,” “ascetic,” “the Hedonist,” Frequency analysis revealed an uneven distribution of preferences between the examined brands. At the same time, revealed the differences in the motivational significance HLV for brands in different product categories. Practical implications Retailers should use segmentation based on motivation influence of HLV for improving the effectiveness of communication of young consumers with brands. The solution of this problem will allow forming particular strategic behaviors of retailers occurring in the sphere of shaping relationships with young consumers. Originality/value It is one of the rare studies that investigate motivational influence of a complex of ten HLV on the young consumers. In this paper, the authors propose to use a methodology for young consumers segmentation based on clustering for HLV, and assessing brands preferences in different segments.
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Elkind, Edith, Abheek Ghosh, and Paul Goldberg. "Complexity of Deliberative Coalition Formation." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 5 (2022): 4975–82. http://dx.doi.org/10.1609/aaai.v36i5.20428.
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Elkind et al. (AAAI'21) introduced a model for deliberative coalition formation, where a community wishes to identify a strongly supported proposal from a space of alternatives, in order to change the status quo. In their model, agents and proposals are points in a metric space, agents' preferences are determined by distances, and agents deliberate by dynamically forming coalitions around proposals that they prefer over the status quo. The deliberation process operates via k-compromise transitions, where agents from k (current) coalitions come together to form a larger coalition in order to support a (perhaps new) proposal, possibly leaving behind some of the dissenting agents from their old coalitions. A deliberation succeeds if it terminates by identifying a proposal with the largest possible support. For deliberation in d dimensions, Elkind et al. consider two variants of their model: in the Euclidean model, proposals and agent locations are points in R^d and the distance is measured according to ||...||_2; and in the hypercube model, proposals and agent locations are vertices of the d-dimensional hypercube and the metric is the Hamming distance. They show that in the Euclidean model 2-compromises are guaranteed to succeed, but in the hypercube model for deliberation to succeed it may be necessary to use k-compromises with k >= d. We complement their analysis by (1) proving that in both models it is hard to find a proposal with a high degree of support, and even a 2-compromise transition may be hard to compute; (2) showing that a sequence of 2-compromise transitions may be exponentially long; (3) strengthening the lower bound on the size of the compromise for the d-hypercube model from d to 2^Ω(d).
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Izmailov, Alexey, Alexey Kurennoy, and Petr Stetsyuk. "Levenberg–Marquardt method for unconstrained optimization." Tambov University Reports. Series: Natural and Technical Sciences, no. 125 (2019): 60–74. http://dx.doi.org/10.20310/1810-0198-2019-24-125-60-74.
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We propose and study the Levenberg–Marquardt method globalized by means of linesearch for unconstrained optimization problems with possibly nonisolated solutions. It is well-recognized that this method is an efficient tool for solving systems of nonlinear equations, especially in the presence of singular and even nonisolated solutions. Customary globalization strategies for the Levenberg–Marquardt method rely on linesearch for the squared Euclidean residual of the equation being solved. In case of unconstrained optimization problem, this equation is formed by putting the gradient of the objective function equal to zero, according to the Fermat principle. However, these globalization strategies are not very adequate in the context of optimization problems, as the corresponding algorithms do not have “preferences” for convergence to minimizers, maximizers, or any other stationary points. To that end, in this work we considers a different technique for globalizing convergence of the Levenberg–Marquardt method, employing linesearch for the objective function of the original problem. We demonstrate that the proposed algorithm possesses reasonable global convergence properties, and preserves high convergence rate of the Levenberg–Marquardt method under weak assumptions.
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Tomlinson, Kiran, Johan Ugander, and Jon Kleinberg. "The Moderating Effect of Instant Runoff Voting." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 9 (2024): 9909–17. http://dx.doi.org/10.1609/aaai.v38i9.28852.
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Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. We develop a theory of exclusion zones, derived from properties of the voter distribution, which serve to show how moderate and extreme candidates interact during IRV vote tabulation. The theory allows us to prove that if voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can and validate our results computationally. Our methods provide new frameworks for the analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.
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Yao, Jing Wen, Royston C. B. Copley, Judith A. K. Howard, Frank H. Allen, and W. D. Samuel Motherwell. "General method for the description, visualization and comparison of metal coordination spheres: geometrical preferences, deformations and interconversion pathways." Acta Crystallographica Section B Structural Science 57, no. 3 (2001): 251–60. http://dx.doi.org/10.1107/s0108768101004141.
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The coordination sphere geometry of metal atoms (M) in their complexes with organic and inorganic ligands (L) is often compared with the geometry of archetypal forms for the appropriate coordination number, n in MLn species, by use of the k = n( n− 1)/2 L—M—L valence angles subtended at the metal centre. Here, a Euclidean dissimilarity metric, Rc (x), is introduced as a one-dimensional comparator of these k-dimensional valence-angle spaces. The computational procedure for Rc (x), where x is an appropriate archetypal form (e.g. an octahedron in ML 6 species), takes account of the atomic permutational symmetry inherent in MLn systems when no distinction is made between the individual ligand atoms. It is this permutational symmetry, of order n!, that precludes the routine application of multivariate analytical techniques, such as principal component analysis (PCA), to valence angle data for all but the lowest metal coordination numbers. It is shown that histograms of Rc (x) values and, particularly, scatterplots of Rc (x) values computed with respect to two or more different appropriate archetypal forms (e.g. tetrahedral and square-planar four-coordinations), provide information-rich visualizations of the observed geometrical preferences of metal coordination spheres retrieved from, e.g. the Cambridge Structural Database. These mappings reveal the highly populated clusters of similar geometries, together with the pathways that map their geometrical interconversions. Application of Rc (x) analysis to the geometry of four- and seven-coordination spheres provides information that is at least comparable to, and in some cases is more complete than, that obtained by PCA.
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Wang, Yanyan. "Multiperiod Optimal Allocation of Emergency Resources in Support of Cross-Regional Disaster Sustainable Rescue." International Journal of Disaster Risk Science 12, no. 3 (2021): 394–409. http://dx.doi.org/10.1007/s13753-021-00347-5.
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AbstractCross-regional allocation is necessary for the rational utilization and optimal allocation of resources. It is also the key to effective and sustainable disaster relief. Existing research, however, generally centers on emergency resource allocation only within territories or regions. This article proposes a multiperiod allocation optimization model for emergency resources based on regional self-rescue and cross-regional collaborative rescue efforts. The model targets the shortest delivery time and lowest allocation costs as its efficiency goals and the maximum coverage rate of resource allocation in the disaster-affected locations as its equity goal. An objective weighting fuzzy algorithm based on two-dimensional Euclidean distance is designed to solve the proposed model. A case study based on the Wenchuan Earthquake of 12 May 2008 was conducted to validate the proposed model. The results indicate that our proposed model allows for optimal, multiperiod cross-regional resource allocation by combining interterritorial and nearby allocation principles. Cross-regional relief makes resource allocation more equitable, minimizes dissatisfaction, and prevents losses. Different decision preferences appear to significantly affect the choice of resource allocation scheme employed, which provides flexibility for decision making in different emergencies.
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Son, Se-Hwan, Soon-Jik Kwon, Ji-Hyeok Im, Seong-Ki Kim, Dongsoo Kong, and Jong-Yun Choi. "Aquatic Macrophytes Determine the Spatial Distribution of Invertebrates in a Shallow Reservoir." Water 13, no. 11 (2021): 1455. http://dx.doi.org/10.3390/w13111455.
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Aquatic macrophytes determine the physical structure of many microhabitats in water and strongly influence the distribution of various aquatic animals. In this study, we analyzed the main microhabitat characteristics that affected the spatial distribution of invertebrates in shallow wetlands of South Korea (Jangcheok Reservoir). Environmental variables, macrophyte biomass, and invertebrate groups were used to analyze invertebrate distribution using a self-organizing map (SOM). Thirteen invertebrate groups were mapped onto the SOM, and each group was compared with the distribution of environmental variables and macrophyte biomass. Based on a U-matrix, five clusters were categorized according to Euclidean distance on the SOM. Invertebrate groups were closely related to macrophyte biomass. In particular, Lymnaeidae, Physidae, Viviparidae, Ecnomidae, and Hydrophilidae were abundant in quadrats with a high cover of Paspalum distichum and Nelumbo nucifera. Bithyniidae and Coenagrionidae were strongly associated with Trapa japonica and Hydrocharis dubia, whereas Planorbidae, Corduliidae, and Hydrophilidae were abundant with a high cover of Typha orientalis. Similar habitat preferences were found in a survey of gastropod distribution on the surface of each macrophyte species. The results clearly indicated that invertebrate distribution clusters were related to the spatial distribution of aquatic macrophytes in a shallow wetland.
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Li, Wenchao. "Morphologic, Syntactic, and Phonologic Distance Between Japanese and Altaic, Dravidian, Austronesian, and Korean Languages." European Journal of Theoretical and Applied Sciences 1, no. 2 (2023): 11–33. http://dx.doi.org/10.59324/ejtas.2023.1(2).02.
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The present study measures the resemblances of Japanese with Altaic languages (Turkic; Tungstic; Mongolic; Nivkh); the Dravidian language Tamil; Austronesian languages (Western Malayo-Polynesian; Malayo-Sumbawan; Central Luzon; Central Malayo-Polynesian), and Korean, in an effort to pin down the genealogy of Japanese. Morphologic, syntactic, and phonologic distance are calculated using data from corpora. The chi-square homogeneity test and Euclidean distances are used for statistical analysis. The finding brings to light, morphologically, in the light of preferences of causative/inchoative verb alternation patterning and morphemes that convey the alternation, that Japanese and Korean are close for the most part. Syntactically, Altaics and Tamil convey case via suffixes; case in Austronesian languages is marked by prefixes. Japanese and Korean share a similarity in rendering case with particles. Phonologically, the Tamil and Austronesian languages share a resemblance in the harmony of vowel height. The Korean, Altaic languages, and Austronesian languages show similarities in the harmony of vowel backness. Japanese, the Altaic languages, and the Austronesian language Madurese display vowel-consonant harmony. Pulling these strands together, a conclusion is thus drawn that Japanese is most closely related to Korean.
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Li, Zihao, Hui Chen, and Wentao Yan. "Exploring Spatial Distribution of Urban Park Service Areas in Shanghai Based on Travel Time Estimation: A Method Combining Multi-Source Data." ISPRS International Journal of Geo-Information 10, no. 9 (2021): 608. http://dx.doi.org/10.3390/ijgi10090608.
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Due to a growing appreciation for the ecological and recreational benefits of public green spaces, the evaluation of urban parks’ service efficiency, as well as citizens’ behavioral preferences for daily recreation, have become an increasing academic focus. However, due to the lack of empirical approaches, existing research on exploring park service areas has been simplified by their use of Euclidean distance or buffer sets by simulation, ignoring the fact that the likelihood of citizens visiting urban parks is time sensitive. Utilizing mobile signaling data and web map services, this study proposes an approach to estimating the travel times of park visitors and analyzing the characteristics of park service areas from the perspective of actual time consumption. Taking Shanghai as a case study, this research firstly identified the time–cost decay of parks with different areas and locations. A comparison analysis was then used to examine the spatial relationship between park service areas and their accessibility defined by time consumption. The results show that (1) urban parks in Shanghai have larger mean service radii than existing planning guidelines, and park service areas were significantly influenced by park locations; (2) people have a great preference for urban parks whose travel times by public transit are under 40 min, and they have no desire to visit parks located within or outside the Middle Ring Road when the travel times reach 60 min and 75 min, respectively; (3) the shapes of park service areas are consistent with the high-accessibility districts defined by time thresholds, in spite of some differences caused by citizens’ choices. These findings provide an effective tool for evaluating the actual characteristics of park recreational services, along with direct implications for policymakers aiming to establish effective strategies for improving the accessibility and vitality of urban parks.
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Kuzelewska, Urszula. "Clustering Algorithms in Hybrid Recommender System on MovieLens Data." Studies in Logic, Grammar and Rhetoric 37, no. 1 (2014): 125–39. http://dx.doi.org/10.2478/slgr-2014-0021.
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AbstractDecisions are taken by humans very often during professional as well as leisure activities. It is particularly evident during surfing the Internet: selecting web sites to explore, choosing needed information in search engine results or deciding which product to buy in an on-line store. Recommender systems are electronic applications, the aim of which is to support humans in this decision making process. They are widely used in many applications: adaptive WWW servers, e-learning, music and video preferences, internet stores etc. In on-line solutions, such as e-shops or libraries, the aim of recommendations is to show customers the products which they are probably interested in. As input data the following are taken: shopping basket archives, ratings of the products or servers log files.The article presents a solution of recommender system which helps users to select an interesting product. The system analyses data from other customers' ratings of the products. It uses clustering methods to find similarities among the users and proposed techniques to identify users' profiles. The system was implemented in Apache Mahout environment and tested on a movie database. Selected similarity measures are based on: Euclidean distance, cosine as well as correlation coefficient and loglikehood function.
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Guo, Shunsheng, Yuji Gao, Jun Guo, Zhijie Yang, Baigang Du, and Yibing Li. "A multi-stage group decision making for strategic supplier selection based on prospect theory with interval-valued q-rung orthopair fuzzy linguistic sets." Journal of Intelligent & Fuzzy Systems 40, no. 5 (2021): 9855–71. http://dx.doi.org/10.3233/jifs-202415.
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With the aggravation of market competition, strategic supplier is becoming more and more critical for the success of manufacturing enterprises. Suppler selection, being the critical and foremost activity must ensure that selected suppliers are capable of supporting the long-term development of organizations. Hence, strategic supplier selection must be restructures considering the long-term relationships and prospects for sustainable cooperation. This paper proposes a novel multi-stage multi-attribute group decision making method under an interval-valued q-rung orthopair fuzzy linguistic set (IVq-ROFLS) environment considering the decision makers’ (DMs) psychological state in the group decision-making process. First, the initial comprehensive fuzzy evaluations of DMs are represented as IVq-ROFLS. Subsequently, two new operators are proposed for aggregating different stages and DMs’ preferences respectively by extending generalized weighted averaging (GWA) to IVq-ROFLS context. Later, a new hamming distance based linear programming method based on entropy measure and score function is introduced to evaluate the unknown criteria weights. Additionally, the Euclidean distance is employed to compute the gain and loss matrix, and objects are prioritized by extending the popular Prospect theory (PT) method to the IVq-ROFLS context. Finally, the practical use of the proposed decision framework is validated by using a strategic supplier selection problem, as well as the effectiveness and applicability of the framework are discussed by using comparative analysis with other methods.
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Alves, Marcos Antonio, Ivan Reinaldo Meneghini, António Gaspar-Cunha, and Frederico Gadelha Guimarães. "Machine Learning-Driven Approach for Large Scale Decision Making with the Analytic Hierarchy Process." Mathematics 11, no. 3 (2023): 627. http://dx.doi.org/10.3390/math11030627.
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The Analytic Hierarchy Process (AHP) multicriteria method can be cognitively demanding for large-scale decision problems due to the requirement for the decision maker to make pairwise evaluations of all alternatives. To address this issue, this paper presents an interactive method that uses online learning to provide scalability for AHP. The proposed method involves a machine learning algorithm that learns the decision maker’s preferences through evaluations of small subsets of solutions, and guides the search for the optimal solution. The methodology was tested on four optimization problems with different surfaces to validate the results. We conducted a one factor at a time experimentation of each hyperparameter implemented, such as the number of alternatives to query the decision maker, the learner method, and the strategies for solution selection and recommendation. The results demonstrate that the model is able to learn the utility function that characterizes the decision maker in approximately 15 iterations with only a few comparisons, resulting in significant time and cognitive effort savings. The initial subset of solutions can be chosen randomly or from a cluster. The subsequent ones are recommended during the iterative process, with the best selection strategy depending on the problem type. Recommendation based solely on the smallest Euclidean or Cosine distances reveals better results on linear problems. The proposed methodology can also easily incorporate new parameters and multicriteria methods based on pairwise comparisons.
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Campbell, Donald E. "Euclidean individual preference and continuous social preference." European Journal of Political Economy 9, no. 4 (1993): 541–50. http://dx.doi.org/10.1016/0176-2680(93)90038-v.
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Chen, Jiehua, and Sven Grottke. "Small one-dimensional Euclidean preference profiles." Social Choice and Welfare 57, no. 1 (2021): 117–44. http://dx.doi.org/10.1007/s00355-020-01301-y.
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AbstractWe characterize one-dimensional Euclidean preference profiles with a small number of alternatives and voters. We show that every single-peaked preference profile with two voters is one-dimensional Euclidean, and that every preference profile with up to five alternatives is one-dimensional Euclidean if and only if it is both single-peaked and single-crossing. By the work of Chen et al. (Social Choice and Welfare 48(2):409–432, 2017), we thus obtain that the smallest single-peaked and single-crossing preference profiles that are not one-dimensional Euclidean consist of three voters and six alternatives.
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C.V., Sunil Kumar, and Srikanta Routroy. "An approach for measuring a manufacturer’s preferred supplier status." Asia Pacific Journal of Marketing and Logistics 28, no. 5 (2016): 939–63. http://dx.doi.org/10.1108/apjml-12-2015-0194.
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Purpose The purpose of this paper is to assist a manufacturer with a process to measure the level of preferred supplier status (PSS) of its key suppliers along the timeline. Design/methodology/approach In measuring the PSS, the prominent preferred supplier enablers (PSEs) were identified and were broadly categorized under manufacturer’s interest component, common interest component and supplier’s characteristic component. These PSEs were further analyzed by using fuzzy analytic hierarchy process, Euclidean distance measurement and grey relation analysis methods. In order to demonstrate the application and utility of the proposed approach, a case study conducted in an Indian automotive component manufacturing company has been presented. Findings By applying the proposed methodology in a case company, the PSSs of five of its key suppliers were measured and then the suppliers’ characteristic scores were determined. Based on these scores, a preferential status plot of the suppliers was developed. Through the status plot, the manufacturer was suggested with whom the proposed initiatives can be productive and with whom the manufacturer has to appeal for improvement strategies. Research limitations/implications Since the methodology was tried in the Indian manufacturing environment, the emphasis laid on the PSEs and in turn the measurement of PSS may not address the concern at large. Practical implications Measuring PSS would not only earn competitive advantages for the manufacturers but also facilitate the evolution of competitive suppliers. Originality/value Measuring PSS along the time would assist a manufacturer to effectively manage the preferences given to its suppliers and thereby enhance the supply base contribution in the value addition process.