Articles de revues : « Similarity measure and multi-Criteria »

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Yang, Qing Bo, et Ruo Juan Xue. « Similarity Measure between Vague Sets Based on Products ». Applied Mechanics and Materials 667 (octobre 2014) : 85–88. http://dx.doi.org/10.4028/www.scientific.net/amm.667.85.

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A new method for measure similarity between vague sets is proposed in this paper. Multi-criteria evaluation problems are used in decision-making constantly. Vague sets model is used to describe multi-criteria evaluation problems in this paper. And the similarity measure method based on products is used in sorting alternatives. The proposed method can solve the multi-criteria evaluation problems in a reasonable and objective way.

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Nisha, Dr B., et Dr S. Vijayalaksmi. « Hesitant Fuzzy Soft Sets with Similarity Measure ». International Journal for Research in Applied Science and Engineering Technology 12, n^o 1 (31 janvier 2024) : 1549–54. http://dx.doi.org/10.22214/ijraset.2024.58205.

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Abstract: Molodtsov’s soft set theory is a newly emerging mathematical tool to handle uncertainty. Babitha and John defined another important soft set, as hesitant fuzzy soft sets. This paper gives a methodology to solve the multi-criteria decision making problems using similarity measures on Hesitant fuzzy soft sets. A decision making problem was solved with the help of similarity measure on hesitant fuzzy soft set.

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Duong, Truong Thi Thuy, et Nguyen Xuan Thao. « TOPSIS model based on entropy and similarity measure for market segment selection and evaluation ». Asian Journal of Economics and Banking 5, n^o 2 (22 juin 2021) : 194–203. http://dx.doi.org/10.1108/ajeb-12-2020-0106.

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PurposeThe paper aims to propose a practical model for market segment selection and evaluation. The paper carries out a technique of order preference similarity to the ideal solution (TOPSIS) approach to make an operation systematic dealing with multi-criteria decision- making problem.Design/methodology/approachIntroducing a multi-criteria decision-making problem based on TOPSIS approach. A new entropy and new similarity measure under neutrosopic environment are proposed to evaluate the weights of criteria and the relative closeness coefficient in TOPSIS model.FindingsThe outcomes show that the TOPSIS model based on new entropy and similarity measure is effective for evaluation and selection market segment. Profitability, growth of the market, the likelihood of sustainable differential advantages are the most important insights of criteria.Originality/valueThis paper put forward an effective multi-criteria decision-making dealing with uncertain information.

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Wang, Lunyan, Qing Xia, Huimin Li et Yongchao Cao. « Multi-criteria decision making method based on improved cosine similarity measure with interval neutrosophic sets ». International Journal of Intelligent Computing and Cybernetics 12, n^o 3 (12 août 2019) : 414–23. http://dx.doi.org/10.1108/ijicc-05-2019-0047.

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Purpose The fuzziness and complexity of evaluation information are common phenomenon in practical decision-making problem, interval neutrosophic sets (INSs) is a power tool to deal with ambiguous information. Similarity measure plays an important role in judging the degree between ideal and each alternative in decision-making process, the purpose of this paper is to establish a multi-criteria decision-making method based on similarity measure under INSs. Design/methodology/approach Based on an extension of existing cosine similarity, this paper first introduces an improved cosine similarity measure between interval neutosophic numbers, which considers the degrees of the truth membership, the indeterminacy membership and the falsity membership of the evaluation values. And then a multi-criteria decision-making method is established based on the improved cosine similarity measure, in which the ordered weighted averaging (OWA) is adopted to aggregate the neutrosophic information related to each alternative. Finally, an example on supplier selection is given to illustrate the feasibility and practicality of the presented decision-making method. Findings In the whole process of research and practice, it was realized that the application field of the proposed similarity measure theory still should be expanded, and the development of interval number theory is one of further research direction. Originality/value The main contributions of this paper are as follows: this study presents an improved cosine similarity measure under INSs, in which the weights of the three independent components of an interval number are taken into account; OWA are adopted to aggregate the neutrosophic information related to each alternative; and a multi-criteria decision-making method using the proposed similarity is developed under INSs.

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Talukdar, Pranjal, et Palash Dutta. « An Advanced Entropy Measure of IFSs via Similarity Measure ». International Journal of Fuzzy System Applications 12, n^o 1 (10 mars 2023) : 1–23. http://dx.doi.org/10.4018/ijfsa.319712.

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The Entropy measure of an intuitionistic fuzzy set (IFS) plays a significant role in decision making sciences, for instance, medical diagnosis, pattern recognition, criminal investigation, etc. The inadequate nature of an entropy measure may lead to some invalid results. Therefore, it is significant to use an efficient entropy measure for studying various decision-making problems under IFS environment. This paper first proposes a novel similarity measure for IFS. Based on the proposed similarity measure, an advanced entropy measure is defined with a different axiomatic approach. This axiomatic approach allows us to measure an IFS's entropy with the help of a similarity measure. To show the efficiency of the proposed similarity measure, a comparative study is performed with the existing similarity measures. Some structural linguistic variables are taken as examples to show the validity and consistency of the proposed entropy measure along with the existing entropy measures. Finally, based on the proposed entropy measure, a multi-criteria decision-making problem is performed.

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Peng, Xindong, et Huiyong Yuan. « Pythagorean Fuzzy Multi-Criteria Decision Making Method Based on Multiparametric Similarity Measure ». Cognitive Computation 13, n^o 2 (17 janvier 2021) : 466–84. http://dx.doi.org/10.1007/s12559-020-09781-x.

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Wagh, Rupali S., et Deepa Anand. « Legal document similarity : a multi-criteria decision-making perspective ». PeerJ Computer Science 6 (23 mars 2020) : e262. http://dx.doi.org/10.7717/peerj-cs.262.

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The vast volume of documents available in legal databases demands effective information retrieval approaches which take into consideration the intricacies of the legal domain. Relevant document retrieval is the backbone of the legal domain. The concept of relevance in the legal domain is very complex and multi-faceted. In this work, we propose a novel approach of concept based similarity estimation among court judgments. We use a graph-based method, to identify prominent concepts present in a judgment and extract sentences representative of these concepts. The sentences and concepts so mined are used to express/visualize likeness among concepts between a pair of documents from different perspectives. We also propose to aggregate the different levels of matching so obtained into one measure quantifying the level of similarity between a judgment pair. We employ the ordered weighted average (OWA) family of aggregation operators for obtaining the similarity value. The experimental results suggest that the proposed approach of concept based similarity is effective in the extraction of relevant legal documents and performs better than other competing techniques. Additionally, the proposed two-level abstraction of similarity enables informative visualization for deeper insights into case relevance.

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Mohamed, Saida, Areeg Abdalla et Robert John. « New Entropy-Based Similarity Measure between Interval-Valued Intuitionstic Fuzzy Sets ». Axioms 8, n^o 2 (18 juin 2019) : 73. http://dx.doi.org/10.3390/axioms8020073.

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In this paper, we propose a new approach to constructing similarity measures using the entropy measure for Interval-Valued Intuitionistic Fuzzy Sets. In addition, we provide several illustrative examples to demonstrate the practicality and effectiveness of the proposed formula. Finally, we use the new proposed similarity measure to develop a new approach for solving problems of pattern recognition and multi-criteria fuzzy decision-making.

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Gvozdev, O. G., A. V. Materuhin et A. A. Maiorov. « Adaptive geofields similarity measure based on binary similarity measures generalization ». Geodesy and Cartography 1002, n^o 12 (20 janvier 2024) : 38–48. http://dx.doi.org/10.22389/0016-7126-2023-1002-12-38-48.

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The authors discuss the task of geofield similarity measurement. The local and global approaches to it are reviewed. The rationale of inapplicability of measures, originally developed for images, for general case of geofields is given. The adaptive function family based on generalization of binary similarity measures is proposed. It assumes adaptation to specific scales, tasks and subject domain. The software implementation of this functions family is discussed. Its applicability for detection of similarities and difference of several geofield special cases is considered. The computational performance of the proposed mechanism different use is studied. It is shown that MT-IoU one (Multi-threshold Intersection-over-Union) is flexible and performant framework for building specialized geofield similarity measure functions

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Dong, Yuanxiang, Xiaoting Cheng, Weijie Chen, Hongbo Shi et Ke Gong. « A cosine similarity measure for multi-criteria group decision making under neutrosophic soft environment ». Journal of Intelligent & ; Fuzzy Systems 39, n^o 5 (19 novembre 2020) : 7863–80. http://dx.doi.org/10.3233/jifs-201328.

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In actual life, uncertain and inconsistent information exists widely. How to deal with the information so that it can be better applied is a problem that has to be solved. Neutrosophic soft sets can process uncertain and inconsistent information. Also, Dempster-Shafer evidence theory has the advantage of dealing with uncertain information, and it can synthesize uncertain information and deal with subjective judgments effectively. Therefore, this paper creatively combines the Dempster-Shafer evidence theory with the neutrosophic soft sets, and proposes a cosine similarity measure for multi-criteria group decision making. Different from the previous studies, the proposed similarity measure is utilized to measure the similarity between two objects in the structure of neutrosophic soft set, rather than two neutrosophic soft sets. We also propose the objective degree and credibility degree which reflect the decision makers’ subjective preference based on the similarity measure. Then parameter weights are calculated by the objective degree. Additionally, based on credibility degree and parameter weights, we propose the modified score function, modified accuracy function, and modified certainty function, which can be employed to obtain partial order relation and make decisions. Later, we construct an aggregation algorithm for multi-criteria group decision making based on Dempster’s rule of combination and apply the algorithm to a case of medical diagnosis. Finally, by testing and comparing the algorithm, the results demonstrate that the proposed algorithm can solve the multi-criteria group decision making problems effectively.

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Aghababaei, H., G. Ferraioli et V. Pascazio. « RATIO-BASED SIMILARITY CRITERIA FOR POLARIMETRIC SAR IMAGE ». ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-3/W12-2020 (6 novembre 2020) : 483–86. http://dx.doi.org/10.5194/isprs-archives-xlii-3-w12-2020-483-2020.

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Abstract. Dealing with multi-look polarimetric synthetic aperture radar (PolSAR) images requires averaging several independent looks to generate a sample covariance matrix of similar target scattering vectors. Along this, estimation of optimal similarity between target scattering vectors is still an open issue. In the literature, this intrinsic task has been mainly addressed in the information-based, geometric-based and detection-based frameworks. However, the derived measures mainly rely on the model assumption such as fully developed speckle and circular complex Gaussian distribution of the scattering vectors, which may not be held in high-resolution images of urban environments. To cope with this possible issue a discriminative model-free measure is proposed, where the similarity of target scattering is computed in the framework of non-local or patch based algorithm. In particular, the discriminative measure is constructed using the ratio between two pre-estimated covariance matrices of the scattering vectors. Experimental validation of the proposed measure is provided using ALOS-PALSAR image and compared with existing criterions in the literature.

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Thao, Nguyen Xuan, et Truong Thi Thuy Duong. « SELECTING TARGET MARKET BY SIMILAR MEASURES IN INTERVAL INTUITIONISTIC FUZZY SET ». Technological and Economic Development of Economy 25, n^o 5 (21 juin 2019) : 934–50. http://dx.doi.org/10.3846/tede.2019.10290.

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The selection of the target market plays vital role in promoting the marketing strategies of companies. We presented is a method for target market selection. We introduce some novel similarity measures between intuitionistic fuzzy sets and the novel similarity measures between interval-valued intuitionistic fuzzy sets. They are constructed by combining exponential and other functions. Finally, we introduce a multi-criteria decision making model to select target market by using the novel similarity measure of interval intuitionistic fuzzy sets.

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Hussain, Zahid, Sahar Abbas et Miin-Shen Yang. « Distances and Similarity Measures of Q-Rung Orthopair Fuzzy Sets Based on the Hausdorff Metric with the Construction of Orthopair Fuzzy TODIM ». Symmetry 14, n^o 11 (21 novembre 2022) : 2467. http://dx.doi.org/10.3390/sym14112467.

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In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater accuracy than intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The characterization of a measure of similarity between q-ROFSs is important, as they have applications in different areas, including pattern recognition, clustering, image segmentation and decision making. Therefore, this article is dedicated to the construction of a measure of similarity between q-ROFSs based on the Hausdorff metric. This is a very useful tool for establishing the similarity between two objects. Furthermore, some axiomatic definitions of the distances and similarity measures of q-ROFSs are also presented. In this article, we first present a novel method to calculate the distance between q-ROFSs based on the Hausdorff metric. We then utilize our proposed distance measure to construct the degree of similarity between q-ROFSs. We provide some properties for the proposed similarity measures. We offer several numerical examples related to pattern recognition and characterization linguistic variables to demonstrate the usefulness of the proposed similarity measures. We construct an algorithm for orthopair fuzzy TODIM (interactive and multi-criteria decision making, in Portuguese) based on our proposed methods. Finally, we use the constructed orthopair fuzzy TODIM method to address problems related to daily life settings involving multi-criteria decision making (MCDM). The numerical results show that the proposed similarity measures are suitable, applicable and well-suited to the contexts of pattern recognition, queries with fuzzy linguistic variables and MCDM.

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Su, Limin, Tianze Wang, Lunyan Wang, Huimin Li et Yongchao Cao. « Project Procurement Method Selection Using a Multi-Criteria Decision-Making Method with Interval Neutrosophic Sets ». Information 10, n^o 6 (5 juin 2019) : 201. http://dx.doi.org/10.3390/info10060201.

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Project procurement method (PPM) selection influences the efficiency of project implementation. Owners are presented with different options for project delivery. However, selecting the appropriate PPM poses great challenges to owners, given the existence of ambiguous information. The interval neutrosophic set (INS) shows power to handle imprecise and ambiguous information. This paper aims to develop a PPM selection model under an interval neutrosophic environment for owners. The main contributions of this paper are as follows: (1) The similarity measure is innovatively introduced with interval neutrosophic information to handle the PPM selection problem. (2) The similarity measure based on minimum and maximum operators is applied to construct a decision-making model for PPM selection, through considering the truth, falsity, and indeterminacy memberships simultaneously. (3) This study establishes a PPM selection method with INS by applying similarity measures, that takes account into the determinacy, indeterminacy, and hesitation from the decision experts when giving an evaluation value. A case study on selecting PPM is made to show the applicability of the proposed approach. Finally, the results of the proposed method are compared with those of existing methods, which exhibit the superiority of the proposed PPM selection method.

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Dinesh et Satish Kumar. « A new exponential knowledge and similarity measure with application in multi-criteria decision-making ». Decision Analytics Journal 10 (mars 2024) : 100407. http://dx.doi.org/10.1016/j.dajour.2024.100407.

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Li, Hongyan, Peng Wu, Ligang Zhou et Huayou Chen. « A new multi-criteria group decision-making method based on consensus mechanism in an interval type-2 fuzzy environment ». Journal of Intelligent & ; Fuzzy Systems 40, n^o 6 (21 juin 2021) : 10935–53. http://dx.doi.org/10.3233/jifs-201979.

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The consensus problem is a very important aspect of group decision making (GDM). In order to deal with the multiple criteria group decision consensus problem in the interval type-2 fuzzy environment, a consensus measure based on similarity measurement is proposed in this paper. In this paper, first, a new similarity measure of two interval type-2 fuzzy sets (IT2FSs) is defined and the consensus measure is defined by the similarity measure between two IT2FSs. Then, a new consensus feedback mechanism is proposed. In the stage of alternatives selection, the entropy of IT2FSs is defined, and the entropy weight method is used to determine the weights of the criteria. Finally, the feasibility of the method proposed in this paper is illustrated by a comprehensive evaluation of old-age institutions.

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Sahoo, Laxminarayan. « Similarity measures for Fermatean fuzzy sets and its applications in group decision-making ». Decision Science Letters 11, n^o 2 (2022) : 167–80. http://dx.doi.org/10.5267/j.dsl.2021.11.003.

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The intention of this paper is to propose some similarity measures between Fermatean fuzzy sets (FFSs). Firstly, we propose some score based similarity measures for finding similarity measures of FFSs and also propose score based cosine similarity measures between FFSs. Furthermore, we introduce three newly scored functions for effective uses of Fermatean fuzzy sets and discuss some relevant properties of cosine similarity measure. Fermatean fuzzy sets introduced by Senapati and Yager can manipulate uncertain information more easily in the process of multi-criteria decision making (MCDM) and group decision making. Here, we investigate score based similarity measures of Fermatean fuzzy sets and scout the uses of FFSs in pattern recognition. Based on different types of similarity measures a pattern recognition problem viz. personnel appointment is presented to describe the use of FFSs and its similarity measure as well as scores. The counterfeit results show that the proposed method is more malleable than the existing method(s). Finally, concluding remarks and the scope of future research of the proposed approach are given.

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Shao, Songtao, et Xiaohong Zhang. « Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes ». Mathematics 7, n^o 7 (19 juillet 2019) : 649. http://dx.doi.org/10.3390/math7070649.

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Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming that will result in an inaccurate decision conclusion. Thus, based on the definition of a probabilistic neutrosophic hesitant fuzzy set (PNHFS), as an extended theory of fuzzy set, the basic definition of distance, similarity and entropy measures of PNHFS are established. Next, the interconnection among the distance, similarity and entropy measures are studied. Simultaneously, a novel measure model is established based on the PNHFSs. In addition, the new measure model is compared by some existed measures. Finally, we display their applicability concerning the investment problems, which can be utilized to avoid redundant evaluation processes.

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Roy, Subhadip, Jeong-Gon Lee, Anita Pal et Syamal Kumar Samanta. « Similarity Measures of Quadripartitioned Single Valued Bipolar Neutrosophic Sets and Its Application in Multi-Criteria Decision Making Problems ». Symmetry 12, n^o 6 (16 juin 2020) : 1012. http://dx.doi.org/10.3390/sym12061012.

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In this paper, a definition of quadripartitioned single valued bipolar neutrosophic set (QSVBNS) is introduced as a generalization of both quadripartitioned single valued neutrosophic sets (QSVNS) and bipolar neutrosophic sets (BNS). There is an inherent symmetry in the definition of QSVBNS. Some operations on them are defined and a set theoretic study is accomplished. Various similarity measures and distance measures are defined on QSVBNS. An algorithm relating to multi-criteria decision making problem is presented based on quadripartitioned bipolar weighted similarity measure. Finally, an example is shown to verify the flexibility of the given method and the advantage of considering QSVBNS in place of fuzzy sets and bipolar fuzzy sets.

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Selvaraj, Jeevaraj, et Melfi Alrasheedi. « A Few Similarity Measures on the Class of Trapezoidal-Valued Intuitionistic Fuzzy Numbers and Their Applications in Decision Analysis ». Mathematics 12, n^o 9 (25 avril 2024) : 1311. http://dx.doi.org/10.3390/math12091311.

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Similarity measures on trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are functions that measure the closeness between two TrVIFNs, which has a lot of applications in the area of pattern recognition, clustering, decision-making, etc. Researchers around the world are proposing various similarity measures on the generalizations of fuzzy sets. However, many such measures do not satisfy the condition that “the similarity between two fuzzy numbers is equal to 1 implies that both the fuzzy numbers are equal” and this gives a pathway for the researchers to introduce different similarity measures on various classes of fuzzy sets. Also, all of them try to find out the similarity by using a single function, and in the present study, we try to propose a combined similarity measure principle by using four functions (four similarity measures). Thus, the main aim of this work is to introduce a few sets of similarity measures on the class of TrVIFNs and propose a combined similarity measure principle on TrVIFNs based on the proposed similarity measures. To do this, in this paper, firstly, we propose four distance-based similarity measures on TrVIFNs using score functions on TrVIFNs and study their mathematical properties by establishing various propositions, theorems, and illustrations, which is achieved by using numerical examples. Secondly, we propose the idea of a combined similarity measure principle by using the four proposed similarity measures sequentially, which is a first in the literature. Thirdly, we compare our combined similarity measure principle with a few important similarity measures introduced on various classes of fuzzy numbers, which shows the need for and efficacy of the proposed similarity measures over the existing methods. Fourthly, we discuss the trapezoidal-valued intuitionistic fuzzy TOPSIS (TrVIF-TOPSIS) method, which uses the proposed combined similarity measure principle for solving a multi-criteria decision-making (MCDM) problem. Then, we discuss the applicability of the proposed modified TrVIF-TOPSIS method by solving a model problem. Finally, we discuss the sensitivity analysis of the proposed approaches by using various cases.

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Şenel, Güzide, Jeong-Gon Lee et Kul Hur. « Distance and Similarity Measures for Octahedron Sets and Their Application to MCGDM Problems ». Mathematics 8, n^o 10 (1 octobre 2020) : 1690. http://dx.doi.org/10.3390/math8101690.

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In this paper, in order to apply the concept of octahedron sets to multi-criteria group decision-making problems, we define several similarity and distance measures for octahedron sets. We present a multi-criteria group decision-making method with linguistic variables in octahedron set environment. We give a numerical example for multi-criteria group decision-making problems.

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Arora, H. D., et Anjali Naithani. « Multi-Criteria Decision Making to Logarithmic Pythagorean Fuzzy Entropy Measure Under TOPSIS Approach ». International Journal of Fuzzy System Applications 11, n^o 4 (1 octobre 2022) : 1–23. http://dx.doi.org/10.4018/ijfsa.312237.

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One of the most essential ideas for tracing the best objects among a set of possible ones is decision-making theory. We make decisions to gain a wide range of advantages from them based on our previous experiences. The concept of Pythagorean fuzzy sets (PFS) was first established by Yager to provides a new technique to describe ambiguity with great precision when compared to intuitionistic fuzzy sets (IFS) and fuzzy sets (FS). The study of PFS is recently gaining importance due to its wide application in situations involving ambiguity. It can easily be merged with MADM techniques to solve real-life problems. However, many of these measures for PFS are ineffective in the sense that they have fundamental shortcomings that restrict them from providing reliable and consistent results. This paper provides a novel Pythagorean fuzzy entropy measure and its application to decision-making problem using technique for order preference by similarity of ideal solution (TOPSIS) on some real-life environment. Comparative study is also done for validation of the proposed measure.

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Beg, Ismat, et Tabasam Rashid. « Modelling Uncertainties in Multi-Criteria Decision Making using Distance Measure and TOPSIS for Hesitant Fuzzy Sets ». Journal of Artificial Intelligence and Soft Computing Research 7, n^o 2 (1 avril 2017) : 103–9. http://dx.doi.org/10.1515/jaiscr-2017-0007.

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Abstract A notion for distance between hesitant fuzzy data is given. Using this new distance notion, we propose the technique for order preference by similarity to ideal solution for hesitant fuzzy sets and a new approach in modelling uncertainties. An illustrative example is constructed to show the feasibility and practicality of the new method.

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Choudhary, Priyankar, Vibhor Kant et Pragya Dwivedi. « Handling Natural Noise in Multi Criteria Recommender System utilizing effective similarity measure and Particle Swarm Optimization ». Procedia Computer Science 115 (2017) : 853–62. http://dx.doi.org/10.1016/j.procs.2017.09.168.

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Dou, Yaling, Lichun Zhu et Ho Simon Wang. « Solving the fuzzy shortest path problem using multi-criteria decision method based on vague similarity measure ». Applied Soft Computing 12, n^o 6 (juin 2012) : 1621–31. http://dx.doi.org/10.1016/j.asoc.2012.03.013.

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Liu, Donghai, Guangyan Liu et Zaiming Liu. « Some Similarity Measures of Neutrosophic Sets Based on the Euclidean Distance and Their Application in Medical Diagnosis ». Computational and Mathematical Methods in Medicine 2018 (28 novembre 2018) : 1–9. http://dx.doi.org/10.1155/2018/7325938.

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Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of single-valued neutrosophic sets (SVNSs) and interval-valued neutrosophic sets (IVNSs) are defined based on the Euclidean distance measure, respectively, and the proposed similarity measures satisfy the axiom of the similarity measure. Furthermore, we apply the proposed similarity measures to medical diagnosis decision problem; the numerical example is used to illustrate the feasibility and effectiveness of the proposed similarity measures of SVNSs and IVNSs, which are then compared to other existing similarity measures.

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Yi-Ting Huang, Yi-Ting Huang, Wan-Hui Lee Yi-Ting Huang et Jen-Hui Tsai Wan-Hui Lee. « A New Approach to Multiple Criteria Decision-Making Using the Dice Similarity Measure under Fermatean Fuzzy Environments ». 網際網路技術學刊 24, n^o 4 (juillet 2023) : 849–60. http://dx.doi.org/10.53106/160792642023072404003.

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<p>Many contemporary multiple criteria decision-making (MCDM) problems are rather complicated and uncertain to manage. MCDM problems can be complex because they involve making decisions based on multiple conflicting criteria, and they can be uncertain because they often involve incomplete or subjective information. This can make it difficult to determine the optimal solution to the problem. Over the last decades, tens of thousands MCDM methods have been proposed based on fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). In this paper, we propose a new MCDM method based on Fermatean fuzzy sets (FFSs) and improved Dice similarity measure (DSM) and generalized Dice similarity measures (GDSM) between two FFSs with completely unknown weights of criteria. When a decision matrix is given, we calculate the weights of criteria using a normalized entropy measure while the weights of criteria are not given by the decision-maker. Then, we use the proposed improved DSM and GDSM between two FFSs that take the hesitancy degree of elements of FFSs into account and develop a new MCDM method. Finally, we use the values of the proposed improved DSM and GDSM between two FFSs to get the preference order of the alternatives. The proposed method can overcome the drawbacks and limitations of some existing methods that they cannot get the preference order of the alternatives under Fermatean fuzzy (FF) environments.</p> <p> </p>

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Donghai, Liu, Liu Yuanyuan et Chen Xiaohong. « The new similarity measure and distance measure between hesitant fuzzy linguistic term sets and their application in multi-criteria decision making ». Journal of Intelligent & ; Fuzzy Systems 37, n^o 1 (9 juillet 2019) : 995–1006. http://dx.doi.org/10.3233/jifs-181886.

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Kaltwasser, P., F. Boschetti et P. Hornby. « Measure of similarity between geological sections accounting for subjective criteria ». Computers & ; Geosciences 31, n^o 1 (février 2005) : 29–34. http://dx.doi.org/10.1016/j.cageo.2004.09.004.

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Xu, Changlin, et Juhong Shen. « Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets ». Journal of Intelligent & ; Fuzzy Systems 41, n^o 6 (16 décembre 2021) : 5847–63. http://dx.doi.org/10.3233/jifs-201557.

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Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

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Ren, Haiping, Shixiao Xiao et Hui Zhou. « A Chi-square Distance-based Similarity Measure of Single-valued Neutrosophic Set and Applications ». International Journal of Computers Communications & ; Control 14, n^o 1 (14 février 2019) : 78–89. http://dx.doi.org/10.15837/ijccc.2019.1.3430.

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The aim of this paper is to propose a new similarity measure of singlevalued neutrosophic sets (SVNSs). The idea of the construction of the new similarity measure comes from Chi-square distance measure, which is an important measure in the applications of image analysis and statistical inference. Numerical examples are provided to show the superiority of the proposed similarity measure comparing with the existing similarity measures of SVNSs. A weighted similarity is also put forward based on the proposed similarity. Some examples are given to show the effectiveness and practicality of the proposed similarity in pattern recognition, medical diagnosis and multi-attribute decision making problems under single-valued neutrosophic environment.

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Li, Huimin, Yongchao Cao, Limin Su et Qing Xia. « An Interval Pythagorean Fuzzy Multi-criteria Decision Making Method Based on Similarity Measures and Connection Numbers ». Information 10, n^o 2 (25 février 2019) : 80. http://dx.doi.org/10.3390/info10020080.

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Interval Pythagorean fuzzy set (IPFS), which can handle imprecise and ambiguous information, has attracted considerable attention in both theory and practice. However, one of the main difficulties under IPFSs is the comparison between interval numbers. To overcome this shortcoming, connection number theory is first introduced, and interval numbers are transformed into connection numbers in the operating process. Considering that similarity measures play an important role in assessing the degree between ideal and proposal alternatives in the decision making process, this paper aims to develop new similarity measures with IPFSs and apply them to multi-criteria decision making (MCDM) problems. The main contributions of this paper are as follows: (1) introduction of a comparison method through transforming interval numbers into connection numbers; (2) development of three new similarity measures with IPFSs based on the minimum and maximum operators, and investigation of their properties; (3) calculation of the similarity measures considering weights of membership and non-membership degrees; (4) establishment of an interval Pythagorean fuzzy decision making method applying the presented similarity measures. A case study on selecting a project delivery system is made to show the applicability of the proposed approach.

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Tomaževič, Dejan, Boštjan Likar et Franjo Pernuš. « MULTI-FEATURE MUTUAL INFORMATION IMAGE REGISTRATION ». Image Analysis & ; Stereology 31, n^o 1 (15 mars 2012) : 43. http://dx.doi.org/10.5566/ias.v31.p43-53.

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Nowadays, information-theoretic similarity measures, especially the mutual information and its derivatives, are one of the most frequently used measures of global intensity feature correspondence in image registration. Because the traditional mutual information similarity measure ignores the dependency of intensity values of neighboring image elements, registration based on mutual information is not robust in cases of low global intensity correspondence. Robustness can be improved by adding spatial information in the form of local intensity changes to the global intensity correspondence. This paper presents a novel method, by which intensities, together with spatial information, i.e., relations between neighboring image elements in the form of intensity gradients, are included in information-theoretic similarity measures. In contrast to a number of heuristic methods that include additional features into the generic mutual information measure, the proposed method strictly follows information theory under certain assumptions on feature probability distribution. The novel approach solves the problem of efficient estimation of multifeature mutual information from sparse high-dimensional feature space. The proposed measure was tested on magnetic resonance (MR) and computed tomography (CT) images. In addition, the measure was tested on positron emission tomography (PET) and MR images from the widely used Retrospective Image Registration Evaluation project image database. The results indicate that multi-feature mutual information, which combines image intensities and intensity gradients, is more robust than the standard single-feature intensity based mutual information, especially in cases of low global intensity correspondences, such as in PET/MR images or significant intensity inhomogeneity.

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Tiwari, Pratiksha. « Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making ». International Journal of Fuzzy System Applications 10, n^o 1 (janvier 2021) : 64–93. http://dx.doi.org/10.4018/ijfsa.2021010104.

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Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

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Li, Jun Feng, Wen Zhan Dai et Hui Jiao Wang. « Multi-Objective Evolutionary Algorithm Based on the Fuzzy Similarity Measure ». Key Engineering Materials 439-440 (juin 2010) : 225–30. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.225.

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Evolutionary algorithm has gained a worldwide popularity among multi-objective optimization. This paper proposes a novel multi-objective evolutionary algorithm based on the fuzzy similarity measure. First, the best solution of every objective among the multi-objectives is obtained and they are regarded on as the referenced vector. Second, the fuzzy similarity measure between every individual and the referenced vector is solved and the fuzzy similarity measure is acted as fitness of the individual. Moreover, the pareto optimal sets are solved by means of adaptive genetic algorithm. The variety of population is kept by means of adaptive probability of crossover and mutation. At last, the algorithm is used to optimize the design parameters of cylinder helical compression spring. Simulation examples show the effectiveness of the approach proposed.

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Sinha, Hari Om Sharan. « Enhancement of “Technique for Order Preference by Similarity to Ideal Solution” Approach for Evaluating the Web Sources to Select as External Source for Web Warehousing ». International Journal of Natural Computing Research 6, n^o 1 (janvier 2017) : 1–16. http://dx.doi.org/10.4018/ijncr.2017010101.

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The main concern of this paper is to evaluate the web sources, which are to be selected as external data sources for web warehousing. In order to identify the web sources, they are evaluated on the ground of their multiple features. For it, Multi Criteria Decision Making (MCDM) approach has been used. Here, among all the MCDM approach, the focus is on “Technique for Order Preference by Similarity to Ideal Solution” (TOPSIS) approach and proposing an enhancement in this method. The conventional TOPSIS approach uses Euclidean Distance to measure the similarity. Here, Jeffrey Divergence has been proposed to measure the similarity instead of Euclidean Distance which includes all the symmetric distances during computation. The Euclidean Distance only measures unidirectional distance whereas the Jeffrey Divergence includes multidirectional distances. Unidirectional distance includes only distance in one dimension but multidirectional distances includes differences, so more relevant in web sources evaluation. Experimental analysis for both the variations of TOPSIS approach have been conducted and the result shows the enhancement in the selection of web sources.

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Yang, Fengqin, Yuanyuan Xing, Hongguang Sun, Tieli Sun et Siya Chen. « An Ontology-Based Semantic Similarity Measure Considering Multi-Inheritance in Biomedicine ». Mathematical Problems in Engineering 2015 (2015) : 1–9. http://dx.doi.org/10.1155/2015/305369.

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Computation of semantic similarity between words for text understanding is a vital issue in many applications such as word sense disambiguation, document categorization, and information retrieval. In recent years, different paradigms have been proposed to compute semantic similarity based on different ontologies and knowledge resources. In this paper, we propose a new similarity measure combining both superconcepts of the evaluated concepts and their common specificity feature. The common specificity feature considers the depth of the Least Common Subsumer (LCS) of two concepts and the depth of the ontology to obtain more semantic evidence. The multiple inheritance phenomenon in a large and complex taxonomy is taken into account by all superconcepts of the evaluated concepts. We evaluate and compare the correlation obtained by our measure with human scores against other existing measures exploiting SNOMED CT as the input ontology. The experimental evaluations show the applicability of the measure on different datasets and confirm the efficiency and simplicity of our proposed measure.

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Bui, Quang-Thinh, My-Phuong Ngo, Vaclav Snasel, Witold Pedrycz et Bay Vo. « Information measures based on similarity under neutrosophic fuzzy environment and multi-criteria decision problems ». Engineering Applications of Artificial Intelligence 122 (juin 2023) : 106026. http://dx.doi.org/10.1016/j.engappai.2023.106026.

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Yang, Jie, Wei Zhou et Shuai Li. « Similarity measure for multi-granularity rough approximations of vague sets ». Journal of Intelligent & ; Fuzzy Systems 40, n^o 1 (4 janvier 2021) : 1609–21. http://dx.doi.org/10.3233/jifs-200611.

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Vague sets are a further extension of fuzzy sets. In rough set theory, target concept can be characterized by different rough approximation spaces when it is a vague concept. The uncertainty measure of vague sets in rough approximation spaces is an important issue. If the uncertainty measure is not accurate enough, different rough approximation spaces of a vague concept may possess the same result, which makes it impossible to distinguish these approximation spaces for charactering a vague concept strictly. In this paper, this problem will be solved from the perspective of similarity. Firstly, based on the similarity between vague information granules(VIGs), we proposed an uncertainty measure with strong distinguishing ability called rough vague similarity (RVS). Furthermore, by studying the multi-granularity rough approximations of a vague concept, we reveal the change rules of RVS with the changing granularities and conclude that the RVS between any two rough approximation spaces can degenerate to granularity measure and information measure. Finally, a case study and related experiments are listed to verify that RVS possesses a better performance for reflecting differences among rough approximation spaces for describing a vague concept.

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Sinha, Hariom Sharan. « Enhancement of TOPSIS for Evaluating the Web-Sources to Select as External Source for Web-Warehousing ». International Journal of Rough Sets and Data Analysis 5, n^o 1 (janvier 2018) : 117–30. http://dx.doi.org/10.4018/ijrsda.2018010108.

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In this paper, the main concern is to evaluate the web-sources, which are to be selected as an external source for web-warehousing. In order to identify the web sources, they are evaluated on the basis of their multiple features. For it, Multi-Criteria Decision Making (MCDM) approach is used. In this paper, among all the MCDM approach, the focus is on “Technique for Order Preference by Similarity to Ideal Solution” (TOPSIS) approach and proposing an enhancement in this method. The traditional TOPSIS approach uses Euclidean Distance to measure the similarity. Here, Jeffrey Divergence has been proposed instead of Euclidean Distance to compute the similarity measure which includes asymmetric and symmetric distances during computation. Experimental analysis of both the variations of TOPSIS approach have been conducted and the result shows the enhancement in the selection of web sources.

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Idarrou, Ali. « A New Structural Similarity Measure : Clustering of Multi-Structured Documents ». International Journal of Advanced engineering, Management and Science 3, n^o 6 (2017) : 681–89. http://dx.doi.org/10.24001/ijaems.3.6.11.

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Al-Qudah, Yousef, et Nasruddin Hassan. « Complex Multi-Fuzzy Soft Set : Its Entropy and Similarity Measure ». IEEE Access 6 (2018) : 65002–17. http://dx.doi.org/10.1109/access.2018.2877921.

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Xu, Jian, Jiapeng Mu et Gaorong Chen. « A multi-view similarity measure framework for trouble ticket mining ». Data & ; Knowledge Engineering 127 (mai 2020) : 101800. http://dx.doi.org/10.1016/j.datak.2020.101800.

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Liu, Donghai, Yan Luo et Zaiming Liu. « The Linguistic Picture Fuzzy Set and Its Application in Multi-Criteria Decision-Making : An Illustration to the TOPSIS and TODIM Methods Based on Entropy Weight ». Symmetry 12, n^o 7 (14 juillet 2020) : 1170. http://dx.doi.org/10.3390/sym12071170.

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The paper considers the multi-criteria decision-making problem based on linguistic picture fuzzy information. Firstly, we propose the concept of linguistic picture fuzzy set(LPFS), where the positive-membership, the neutral-membership and the negative-membership are represented by linguistic variables, and its operation rules are also discussed. The linguistic picture fuzzy weighted averaging (LPFWA) operator and linguistic picture fuzzy weighted geometric (LPFWG) operator are developed based on the proposed operation rules. Secondly, we propose the generalized weighted distance measure, the generalized weighted Hausdorff distance measure, and the generalized hybrid weighted distance measure between LPFSs and discuss their properties. Thirdly, we extend the technique for order of preference by similarity to the ideal solution (TOPSIS) method and the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method to the proposed distance measure, and the linguistic picture fuzzy entropy method is proposed to calculate the weights of the criteria. Finally, an illustrative example is given to verify the feasibility and effectiveness of the proposed methods, the comparative analysis with other existing methods and sensitivity analysis of the proposed methods are also discussed.

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Chen, Liuxin, Nanfang Luo et Xiaoling Gou. « A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy ». Journal of Intelligent & ; Fuzzy Systems 40, n^o 1 (4 janvier 2021) : 235–50. http://dx.doi.org/10.3233/jifs-191374.

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In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

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Kądziołka, Kinga. « The Promethee II Method in Multi-Criteria Evaluation of Cryptocurrency Exchanges ». Economic and Regional Studies / Studia Ekonomiczne i Regionalne 14, n^o 2 (1 juin 2021) : 131–45. http://dx.doi.org/10.2478/ers-2021-0010.

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Abstract Subject and purpose of work: The aim of this work is to present the application possibilities of ECONOMIC AND REGIONAL STUDIES STUDIA EKONOMICZNE I REGIONALNE ISSN 2083-3725 Volume 14, No. 2, 2021 ECREG STUDIES Vol. 14, No. 2, 2021 the weights of criteria is proposed, which maximizes the similarity of the final ranking to the other ones. Materials and methods: PROMETHEE II method and taxonomic measure were used to create rankings of exchanges. Hierarchical clustering combined with the k-means algorithm www.ers.edu.pl PDF OPEN ACCESS eISSN 2451-182X available data published on the Internet were analysed. Results: There was a high consistency in the ordering of exchanges when a multi-criteria and a multi-dimensional approach were used. Four groups of exchanges with a similar level of the values of net flows were identified. Exchanges in group one were characterized by the highest average net flows. Conclusions: The multi-criteria approach can be used as an alternative to the multi-dimensional assessment of cryptocurrency exchanges. The proposed simulation method for determining the weights of criteria can be helpful in case the researcher has no information about the importance of the criteria.

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Akdağ, Murat, et Mehmet Serhat Can. « Tuning of controller parameters using Pythagorean fuzzy similarity measure based on multicriteria decision making for stable and time delayed unstable plants ». PeerJ Computer Science 9 (10 août 2023) : e1504. http://dx.doi.org/10.7717/peerj-cs.1504.

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This paper proposes a tuning method based on the Pythagorean fuzzy similarity measure and multi-criteria decision-making to determine the most suitable controller parameters for Fractional-order Proportional Integral Derivative (FOPID) and Integer-order Proportional Integral-Proportional Derivative (PI-PD) controllers. Due to the power of the Pythagorean fuzzy approach to evaluate a phenomenon with two memberships known as membership and non-membership, a multi-objective cost function based on the Pythagorean similarity measure is defined. The transient and steady-state properties of the system output were used for the multi-objective cost function. Thus, the determination of the controller parameters was considered a multi-criteria decision-making problem. Ant colony optimization for continuous domains (ACOR) and artificial bee colony (ABC) optimization are utilized to minimize multi-objective cost functions. The proposed method in the study was applied to three different systems: a second-order non-minimum phase stable system, a first-order unstable system with time delay, and a fractional-order unstable system with time delay, to validate its effectiveness. The cost function utilized in the proposed method is compared with the performance measures widely used in the literature based on the integral of the error, such as IAE (Integral Absolute Error), ITAE (Integral Time Absolute Error), ISE (Integral Square Error), and ITSE (Integral Time Square Error). The proposed method provides a more effective control performance by improving the system response characteristics compared to other cost functions. With the proposed method, the undershoot rate could be significantly reduced in the non-minimum phase system. In the other two systems, significant improvements were achieved compared to other methods by reducing the overshoot rate and oscillation. The proposed method does not require knowing the mathematical model of the system and offers a solution that does not require complex calculations. The proposed method can be used alone. Or it can be used as a second and fine-tuning method after a tuning process.

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Saidin, Mohamad Shahiir, Lai Soon Lee, Hsin-Vonn Seow et Stefan Pickl. « Fuzzy Divergence Measure Based on Technique for Order of Preference by Similarity to Ideal Solution Method for Staff Performance Appraisal ». Mathematics 12, n^o 5 (28 février 2024) : 714. http://dx.doi.org/10.3390/math12050714.

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Fuzzy set theory has extensively employed various divergence measure methods to quantify distinctions between two elements. The primary objective of this study is to introduce a generalized divergence measure integrated into the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach. Given the inherent uncertainty and ambiguity in multi-criteria decision-making (MCDM) scenarios, the concept of the fuzzy α-cut is leveraged. This allows experts to establish a broader spectrum of rankings, accommodating fluctuations in their confidence levels. To produce consistent criteria weights with the existence of outliers, the fuzzy Method based on the Removal Effects of Criteria (MEREC) is employed. To showcase the viability and effectiveness of the proposed approach, a quantitative illustration is provided through a staff performance review. In this context, the findings are compared with other MCDM methodologies, considering correlation coefficients and CPU time. The results demonstrate that the proposed technique aligns with current distance measure approaches, with all correlation coefficient values exceeding 0.9. Notably, the proposed method also boasts the shortest CPU time when compared to alternative divergence measure methodologies. As a result, it becomes evident that the proposed technique yields more sensible and practical results compared to its counterparts in this category.

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García, Vicente, J. Salvador Sánchez et Ana I. Marqués. « Synergetic Application of Multi-Criteria Decision-Making Models to Credit Granting Decision Problems ». Applied Sciences 9, n^o 23 (22 novembre 2019) : 5052. http://dx.doi.org/10.3390/app9235052.

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Although various algorithms have widely been studied for bankruptcy and credit risk prediction, conclusions regarding the best performing method are divergent when using different performance assessment metrics. As a solution to this problem, the present paper suggests the employment of two well-known multiple-criteria decision-making (MCDM) techniques by integrating their preference scores, which can constitute a valuable tool for decision-makers and analysts to choose the prediction model(s) more properly. Thus, selection of the most suitable algorithm will be designed as an MCDM problem that consists of a finite number of performance metrics (criteria) and a finite number of classifiers (alternatives). An experimental study will be performed to provide a more comprehensive assessment regarding the behavior of ten classifiers over credit data evaluated with seven different measures, whereas the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Preference Ranking Organization METHod for Enrichment of Evaluations (PROMETHEE) techniques will be applied to rank the classifiers. The results demonstrate that evaluating the performance with a unique measure may lead to wrong conclusions, while the MCDM methods may give rise to a more consistent analysis. Furthermore, the use of MCDM methods allows the analysts to weight the significance of each performance metric based on the intrinsic characteristics of a given credit granting decision problem.

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Hajduk, Sławomira. « Multi-Criteria Analysis of Smart Cities on the Example of the Polish Cities ». Resources 10, n^o 5 (8 mai 2021) : 44. http://dx.doi.org/10.3390/resources10050044.

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This paper presents the application of a Multi-Criteria Decision Making (MCDM) method for the ranking of smart cities. During the construction of the MCDM techniques, the importance of the decision-making approach for the linear ordering of 66 Polish cities with powiat status was presented. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) was used for evaluation. The method has been verified by applying it to measure urban smartness. The TOPSIS method allowed compilation for a final ranking, taking into account publicly available indicators of the smart cities concept. The work uses data from the Local Data Bank Polish Central Statistical Office (LDB). The author conducted a literature review of research papers related to smart cities and MCDM methods dated from 2010 to 2020. Based on calculations using the TOPSIS method, the results obtained that the city of Krakow has the highest value to become a smart city.

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