Rozprawy doktorskie na temat „Entropic criterion”
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Olson, Christopher. "Entropy as a Criterion for Variable Reduction in Cluster Data". Thesis, North Dakota State University, 2012. https://hdl.handle.net/10365/26760.
Pełny tekst źródłaVuong, Christophe. "Contributions to stochastic analysis for non-diffusive structures". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAT054.
Pełny tekst źródłaThis thesis is concerned with the study of non-diffusive structures. We focus on two classes of such structures.The first subject deals with Malliavin calculus for conditionally independent random variables, which is a special case of discrete Malliavin calculus. It also generalizes the calculus that has been developed for countable products of probability spaces, for independent random variables.In our case, the interest of such a calculus is to complement results in stochastic analysis with proofs of functional inequalities (Poincaré inequality, McDiarmid's inequality) and limit theorems. One of the main applications is the determination of the convergence rate of central limit theorems via the Stein method.By combining Malliavin calculus with the underlying Dirichlet structure of the random variables, we obtain an integration by parts formula which is key to the derivations of so-called Stein bounds of the rates of convergence. We show quantitative limit theorems, including a fourth moment theorem with remainder. In particular, we discuss an application to the asymptotic normality of motif counting in exchangeable random hypergraphs.The second subject studies functionals of a Poisson measure using the notion of invertibility of transformations of that measure on the sample space of random measures. We use the identification of these measures and the associated marked point processes. Invertible transformations are obtained via the Girsanov's theorem, respecting absolute continuity with respect to the reference measure. This results in an entropy criterion for the invertibility of transformations. Finally, we make the connection with stochastic differential equations driven by Poisson measures
Hertz, Anaëlle. "Exploring continuous-variable entropic uncertainty relations and separability criteria in quantum phase space". Doctoral thesis, Universite Libre de Bruxelles, 2018. https://dipot.ulb.ac.be/dspace/bitstream/2013/267632/5/ContratAH.pdf.
Pełny tekst źródłaLe principe d’incertitude se situe au cœur de la physique quantique. Il représente l’une des différences majeures entre des systèmes classiques et quantiques, soit qu’il est impossible de définir un état quantique pour lequel deux observables qui ne commutent pas auraient des valeurs spécifiées simultanément et avec une précision infinie. La formulation originale du principe d’incertitude est due à Heisenberg et est exprimée en termes des variances de deux variables canoniquement conjuguées, telles que la position x et l’impulsion p. Cela fut par la suite généralisé par Schrödinger et Robertson qui ont donné au principe d’incertitude une forme invariante sous transformations symplectiques. Si l’incertitude est mesurée à l’aide de l’entropie différentielle de Shannon plutôt que des variances, il est alors possible de définir d’autres types de relations d’incertitude. Originellement introduites par Białynicki-Birula et Mycielski, elles expriment également l’incompatibilité entre deux variables canoniquement conjuguées. Dans cette thèse, nous proposons différentes améliorations de ces relations d’incertitude entropiques et mettons particulièrement l’accent sur le fait qu’elles s’expriment mieux sous forme de puissances entropiques, une notion empruntée à la théorie de l’information. En premier lieu, nous introduisons une nouvelle relation d’incertitude entropique qui tient compte des corrélations x-p et qui est par conséquent saturée par tous les états purs Gaussiens, ce qui représente une amélioration par rapport à la formulation originale de Białynicki- Birula et Mycielski. En second lieu, nous dérivons une relation d’incertitude entropique valide pour tous les n-uplets de variables non nécessairement canoniquement conjuguées et basée sur la matrice de leurs commutateurs. Nous définissons ensuite une forme plus générale du principe d’incertitude entropique qui combine les deux résultats précédents. Il exprime l’incompatibilité entre deux n-uplets arbitraires de variables et est saturé par tous les états purs Gaussiens. Notons que de ce principe d’incertitude entropique, nous pouvons déduire la forme la plus générale de la relation d’incertitude de Robertson, basée sur la matrice de covariance de n variables. Les résultats précédents soulignent un des points essentiels de notre axe de recherche: définir une relation d’incertitude entropique intrinsèquement invariante sous trans- formations symplectiques. Afin d’atteindre cet objectif, notre première tentative est de conjecturer une relation d’incertitude — invariante sous transformations symplectiques — basée sur l’entropie différentielle jointe de la fonction de Wigner. Cette conjecture n’est cependant légitime que pour des états décrits par une fonction de Wigner non-négative. Nous proposons aussi une extension complexe de cette en- tropie dite entropie de Wigner, qui pourrait ouvrir la voie vers une extension (et une preuve) de la conjecture proposée ci-dessus qui serait alors valide pour tous les états quantiques. Comme seconde tentative, en exploitant une connexion avec l’algèbre des moments angulaires, nous introduisons la notion d’observables d’incertitude agissant sur plusieurs copies d’un état. Exprimer la positivité de la variance de notre observable coïncide avec la relation d’incertitude de Schrödinger-Robertson, ce qui suggère que l’entropie discrète de Shannon d’une telle observable fournit une nouvelle mesure de l’incertitude. Cette relation d’incertitude est invariante sous transformations symplectiques.Les critères de séparabilité actuellement disponibles pour les variables continues donnent une condition nécessaire et suffisante afin qu’un état Gaussien bimodal soit séparable, mais laissent de nombreux états intriqués non-Gaussiens non détectés. Dans cette thèse, nous introduisons deux nouveaux critères de séparabilité qui permettent une meilleure détection de l’intrication. La première nouvelle condition est basée sur la connaissance d’un paramètre supplémentaire, à savoir le degré de Gaussianité de l’état, et exploite une connexion avec les relations d’incertitude de Mandilara et Cerf bornées par ce degré de Gaussianité. En particulier, nous donnons l’exemple de familles d’états intriqués non Gaussiens dont l’intrication est détectée par notre critère, mais pas par celui de Duan-Simon. Le second critère de séparabil- ité entropique que nous proposons est basé sur notre nouvelle relation d’incertitude entropique qui tient compte des corrélations x-p. Son principal avantage par rapport au critère de Walborn et al. est de ne nécessiter aucune procédure d’optimisation.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
Sun, Xun. "Ab initio Investigation of Al-doped CrMnFeCoNi High-Entropy Alloys". Licentiate thesis, KTH, Materialvetenskap, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-251330.
Pełny tekst źródłaKoch, David. "Investigation and improvement of criticality calculations in MCNP5 involving Shannon entropy convergence". Thesis, Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/53484.
Pełny tekst źródłaRigau Vilalta, Jaume. "Information theoretic refinement criteria for image synthesis". Phd thesis, Universitat Politècnica de Catalunya, 2006. http://hdl.handle.net/10803/6664.
Pełny tekst źródłaInicialment, el concepte de complexitat d'una escena es analitzat considerant tres perspectives des d'un punt de vista de la visibilitat geomètrica: complexitat en un punt interior, complexitat d'una animació, i complexitat d'una regió. L'enfoc principal d'aquesta tesi és l'exploració i desenvolupament de nous criteris de refinament pel problema de la il·luminació global. Mesures de la teoria de la informació basades en la entropia de Shannon i en la entropia generalitzada de Harvda-Charvát-Tsallis, conjuntament amb les f-divergències, són analitzades com a nuclis del refinement. Mostrem com ens aporten una rica varietat d'eficients i altament discriminatòries mesures que són aplicables al rendering en els seus enfocs de pixel-driven (ray-tracing) i object-space (radiositat jeràrquica).
Primerament, basat en la entropia de Shannon, es defineixen un conjunt de mesures de qualitat i contrast del pixel. S'apliquen al supersampling en ray-tracing com a criteris de refinement, obtenint un algorisme nou de sampleig adaptatiu basat en entropia, amb un alt rati de qualitat versus cost. En segon lloc, basat en la entropia generalitzada de Harvda-Charvát-Tsallis, i en la informació mutua generalitzada, es defineixen tres nous criteris de refinament per la radiositat jeràrquica. En correspondencia amb tres enfocs clàssics, es presenten els oracles basats en la informació transportada, el suavitzat de la informació, i la informació mutua, amb resultats molt significatius per aquest darrer. Finalment, tres membres de la familia de les f-divergències de Csiszár's (divergències de Kullback-Leibler, chi-square, and Hellinger) son analitzats com a criteris de refinament mostrant bons resultats tant pel ray-tracing com per la radiositat jeràrquica.
This work is framed within the context of computer graphics starting out from the intersection of three fields: rendering, information theory, and complexity.
Initially, the concept of scene complexity is analysed considering three perspectives from a geometric visibility point of view: complexity at an interior point, complexity of an animation, and complexity of a region. The main focus of this dissertation is the exploration and development of new refinement criteria for the global illumination problem. Information-theoretic measures based on Shannon entropy and Harvda-Charvát-Tsallis generalised entropy, together with f-divergences, are analysed as kernels of refinement. We show how they give us a rich variety of efficient and highly discriminative measures which are applicable to rendering in its pixel-driven (ray-tracing) and object-space (hierarchical radiosity) approaches.
Firstly, based on Shannon entropy, a set of pixel quality and pixel contrast measures are defined. They are applied to supersampling in ray-tracing as refinement criteria, obtaining a new entropy-based adaptive sampling algorithm with a high rate quality versus cost. Secondly, based on Harvda-Charvát-Tsallis generalised entropy, and generalised mutual information, three new refinement criteria are defined for hierarchical radiosity. In correspondence with three classic approaches, oracles based on transported information, information smoothness, and mutual information are presented, with very significant results for the latter. And finally, three members of the family of Csiszár's f-divergences (Kullback-Leibler, chi-square, and Hellinger divergences) are analysed as refinement criteria showing good results for both ray-tracing and hierarchical radiosity.
Zhang, Di. "INFORMATION THEORETIC CRITERIA FOR IMAGE QUALITY ASSESSMENT BASED ON NATURAL SCENE STATISTICS". Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2842.
Pełny tekst źródłaThe goal of objective image quality assessment is to introduce a computational quality metric that can predict image or video quality. Many methods have been proposed in the past decades. Traditionally, measurements convert the spatial data into some other feature domains, such as the Fourier domain, and detect the similarity, such as mean square distance or Minkowsky distance, between the test data and the reference or perfect data, however only limited success has been achieved. None of the complicated metrics show any great advantage over other existing metrics.
The common idea shared among many proposed objective quality metrics is that human visual error sensitivities vary in different spatial and temporal frequency and directional channels. In this thesis, image quality assessment is approached by proposing a novel framework to compute the lost information in each channel not the similarities as used in previous methods. Based on natural scene statistics and several image models, an information theoretic framework is designed to compute the perceptual information contained in images and evaluate image quality in the form of entropy.
The thesis is organized as follows. Chapter I give a general introduction about previous work in this research area and a brief description of the human visual system. In Chapter II statistical models for natural scenes are reviewed. Chapter III proposes the core ideas about the computation of the perceptual information contained in the images. In Chapter IV, information theoretic criteria for image quality assessment are defined. Chapter V presents the simulation results in detail. In the last chapter, future direction and improvements of this research are discussed.
David, Afshin. "Modeling and estimation using maximum entropy and minimum mean squared criteria based on partial and noisy observations". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0016/NQ57033.pdf.
Pełny tekst źródłaSuzzi, Nicola. "Valutazione delle prestazioni termo-idrauliche di microcanali a spigoli smussati". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6495/.
Pełny tekst źródłaZander, Claudia. "Classical & quantum dynamics of information and entanglement properties of fermion systems". Thesis, University of Pretoria, 2012. http://hdl.handle.net/2263/28607.
Pełny tekst źródłaThesis (PhD)--University of Pretoria, 2012.
Physics
unrestricted
Kovaříková, Lenka. "Hodnocení investičních možností PRE do malých vodních elektráren". Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-75487.
Pełny tekst źródłaAvila, Manuel. "Optimisation de modèles markoviens pour la reconnaissance de l'écrit". Rouen, 1996. http://www.theses.fr/1996ROUES034.
Pełny tekst źródłaWittner, Otto. "Emergent behavior based implements for distributed network management". Doctoral thesis, Norwegian University of Science and Technology, Department of Telematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-1787.
Pełny tekst źródłaNetwork and system management has always been of concern for telecommunication and computer system operators. The need for standardization was recognised already 20 years ago, hence several standards for network management exist today. However, the ever-increasing number of units connected to networks and the ever-increasing number of services being provided results in significant increased complexity of average network environments. This challenges current management systems. In addition to the general increase in complexity the trend among network owners and operators of merging several single service networks into larger, heterogeneous and complex full service networks challenges current management systems even further. The full service networks will require management systems more powerful than what is possible to realize basing systems purely on todays management standards. This thesis presents a distributed stochastic optimization algorithm which enables implementations of highly robust and efficient management tools. These tools may be integrated into management systems and potentially make the systems more powerful and better prepared for management of full service networks.
Emergent behavior is common in nature and easily observable in colonies of social insects and animals. Even an old oak tree can be viewed as an emergent system with its collection of interacting cells. Characteristic for any emergent system is how the overall behavior of the system emerge from many relatively simple, restricted behaviors interacting, e.g. a thousand ants building a trail, a flock of birds flying south or millions of cells making a tree grow. No centralized control exist, i.e. no single unit is in charge making global decisions. Despite distributed control, high work redundancy and stochastic behavior components, emergent systems tend to be very efficient problem solvers. In fact emergent systems tend to be both efficient, adaptive and robust which are three properties indeed desirable for a network management system. The algorithm presented in this thesis relates to a class of emergent behavior based systems known as swarm intelligence systems, i.e. the algorithm is potentially efficient, adaptive and robust.
On the contrary to other related swarm intelligence algorithms, the algorithm presented has a thorough formal foundation. This enables a better understanding of the algorithm’s potentials and limitations, and hence enables better adaptation of the algorithm to new problem areas without loss of efficiency, adaptability or robustness. The formal foundations are based on work by Reuven Rubinstein on cross entropy driven optimization. The transition from Ruinstein’s centralized and synchronous algorithm to a distributed and asynchronous algorithm is described, and the distributed algorithm’s ability to solve complex problems (NP-complete) efficiently is demonstrated.
Four examples of how the distributed algorithm may be applied in a network management context are presented. A system for finding near optimal patterns of primary/backup paths together with a system for finding cyclic protection paths in mesh networks demonstrate the algorithm’s ability to act as a tool helping management system to ensure quality of service. The algorithm’s potential as a management policy implementation mechanism is also demonstrated. The algorithm’s adaptability is shown to enable resolution of policy conflicts in a soft manner causing as little loss as possible. Finally, the algorithm’s ability to find near optimal paths (i.e. sequences) of resources in networks of large scale is demonstrated.
Mrabet, Elyes. "Optimisation de la fiabilité des structures contrôlées". Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEC011/document.
Pełny tekst źródłaThe present work deals with the parameters optimization of tuned mass dampers (TMD) used in the control of vibrating linear structures under stochastic loadings. The performance of the TMD device is deeply affected by its parameters that should be carefully chosen. In this context, several optimization strategies can be found in the literature and among them the stochastic structural optimization (SSO) and the reliability based optimization (RBO) are particularly addressed in this dissertation.The first part of this work in dedicated to the calculation of the optimal bounds solutions of the TMD parameters in presence of uncertain but bounded (UBB) structural parameters. The bounds of the optimal TMD parameters are obtained using an approximation technique based on Taylor expansion followed by interval extension. The numerical investigations applied with one degree of freedom (1DOF) and with multi-degree of freedom (multi-DOF) systems showed that the studied technique is suitable for the SSO strategy and that it’s less appropriate for the RBO strategy.As immediate consequence of the obtained results in the first part of this work, in the second part a method, called the continuous-optimization nested loop method (CONLM), providing the exact range of the optimal TMD parameters is presented and validated. The numerical studies demonstrated that the CONLM is time consuming and to overcome this disadvantage, a second method is also presented. The second method is called the monotonicity based extension method (MBEM) with box splitting. Both methods have been applied in the context of the RBO strategy with 1DOF and multi-DOF systems. The issue of effectiveness and robustness of the presented optimum bounds of the TMD parameters is also addressed and it has been demonstrated that the optimum solution corresponding to the deterministic context (deterministic structural parameters) provide good effectiveness and robustness.Another aspect of RBO approach is dealt in the third part of the present work. Indeed, a new RBO strategy of TMD parameters based on energetic criterion is presented and validated. The new RBO approach is linked to a new failure mode characterized by the exceedance of the power dissipated into the controlled structure over a certain threshold during some interval time. Based on the outcrossing approach and the Rice’s formula, the new strategy is firstly applied to 1DOF system and exact expression of the failure probability is calculated. After that, a multi-DOF system is considered and the minimum cross entropy method has been used providing an approximation to the failure probability and then the optimization is carried out. The numerical investigations showed the superiority of the presented strategy when compared with other from the literature
Santos, Jorge Manuel Fernandes dos. "Data classification with neural networks and entropic criteria". Doctoral thesis, 2007. http://hdl.handle.net/10216/12749.
Pełny tekst źródłaSantos, Jorge Manuel Fernandes dos. "Data classification with neural networks and entropic criteria". Tese, 2007. http://hdl.handle.net/10216/12749.
Pełny tekst źródłaSilva, Igor Vladimiro Agostinho Proença da. "Missing signal restoration by means of an entropy criterion". Master's thesis, 2009. http://hdl.handle.net/10216/59880.
Pełny tekst źródłaSilva, Igor Vladimiro Agostinho Proença da. "Missing signal restoration by means of an entropy criterion". Dissertação, 2009. http://hdl.handle.net/10216/59880.
Pełny tekst źródłaBai, Je-Ruei, i 白哲睿. "Polarimetric Radar and Entropy Applied to Target Identification and Criterion for Radar Antenna Design". Thesis, 2018. http://ndltd.ncl.edu.tw/handle/9qr9st.
Pełny tekst źródła國立臺灣大學
電信工程學研究所
106
Target identification has drawn lots of attentions in remote sensing and radar applications. Among various algorithms, the polarimetric entropy is a powerful means to discriminate between different targets. This thesis begins with a brief review of the statistical entropy, the polarimetric radar and scattering matrix, and the formulation of polarimetric entropy and its physical interpretation. Then, the formulas are discussed qualitatively, and based on the discussion, a criterion for radar antenna design is proposed to enhance the target-identifying efficacy. Next, an exemplary scenario is considered, in which the radar antenna is designed following the proposed criterion. After performing full-wave scattering simulations on the scenario, the polarimetric entropies can readily be calculated, and the results outperform those in the conventional paradigm. Additionally, an experiment in anechoic chamber is designed and performed to demonstrate the feasibility and performance of this algorithm in realistic environment. Besides, some invariance properties of polarimetric radar are also introduced to be used in conjunction with polarimetric entropy to enlighten prospective works in the field of radar target identification. To this end, the support vector machine (SVM), well known in machine learning, is adopted. Preliminary simulations are conducted to demonstrate the effectiveness of the concept. Finally, a brief conclusion of this work and some potential future works are given at the end of this thesis. We hope that they can inspire those who are interested in radar target identification.
"Contrast properties of entropic criteria for blind source separation : a unifying framework based on information-theoretic inequalities". Université catholique de Louvain, 2007. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-02162007-112342/.
Pełny tekst źródłaChiu, Min-han, i 邱珉漢. "New Selection Criteria for Tone Reservation Technique Based on Cross-Entropy Algorithm in OFDM Systems". Thesis, 2011. http://ndltd.ncl.edu.tw/handle/86565425631479788766.
Pełny tekst źródła國立中山大學
通訊工程研究所
99
This thesis considers the use of the tone reservation (TR) technique in orthogonal frequency division multiplexing (OFDM) systems. The nonlinear distortion is usually introduces by the high power amplifiers (HPA) used in wireless communications systems. It orders to reduce the inter-modulation distortion (IMD) in OFDM systems. In addition to the original peak-to-average power ratio (PAPR)-reduction criterion, we propose signal-to-distortion plus noise power ratio (SDNR) criterion and distortion power plus inverse of signal power (DIS) criterion. Based on these criteria, the cross-entropy (CE) algorithm is introduced to determine desired values of the peak reduction carriers (PRCs) to improve the bit error rate (BER) of nonlinearly distorted. Computational complexity is always the major concern of PAPR technique. Therefore, the real-valued PRCs and the modified transform decomposition (MTD) method are introduced here to dramatically decrease complexity of inverse fast Fourier transform (IFFT) operation with slightly performance loss. The simulation results show that the proposed criteria provide a better BER performance and a lower computational complexity.
FERRARESE, MORENO. "L’analisi della domanda per la realizzazione di parcheggi urbani: un’entropia logit-multidimensionale come criterio d’equilibrio, nella ricerca del miglior modello di fattibilita’ economico-finanziaria per il project financing". Doctoral thesis, 2012. http://hdl.handle.net/11562/463737.
Pełny tekst źródłaThe objective of this study, is to develop an approach of integrating, for the design context on the use of urban areas to be reserved or already used for parking, the countless opportunities in the field of planning, with the use of scientific practices from the point of view of transport and mobility economists. The expected result of the analysis, is to develop a new econometric model, as a useful support for the decision maker of the projects, taking into account and analyze what determines the demand for transportation in a context of sustainability and esteem of the parameters relating to the quality attributes of service (for example: the value of time, the theory of needs, goals, strategies, actions) with respect to the use of land for different types of users of urban parks. A detailed analysis of the question becomes, therefore, the instrument for careful planning and economic planning of any new public "entrepreneurial" initiative. In this sense, any economic plan, which addresses the demand analysis, can be defined as the link between the "strategy" and "operating" or, in other words, the instrument, or in a sense very more restrictive the study, which allows reliable and ensure formalization of strategic economic activity and address, for verification of results from operations, through the control of management.
Zhou, Y., Qichun Zhang, H. Wang, P. Zhou i T. Chai. "EKF-Based Enhanced Performance Controller Design for Nonlinear Stochastic Systems". 2017. http://hdl.handle.net/10454/17347.
Pełny tekst źródłaIn this paper, a novel control algorithm is presented to enhance the performance of the tracking property for a class of nonlinear and dynamic stochastic systems subjected to non-Gaussian noises. Although the existing standard PI controller can be used to obtain the basic tracking of the systems, the desired tracking performance of the stochastic systems is difficult to achieve due to the random noises. To improve the tracking performance, an enhanced performance loop is constructed using the EKF-based state estimates without changing the existing closed loop with a PI controller. Meanwhile, the gain of the enhanced performance loop can be obtained based upon the entropy optimization of the tracking error. In addition, the stability of the closed loop system is analyzed in the mean-square sense. The simulation results are given to illustrate the effectiveness of the proposed control algorithm.
This work was supported in part by the PNNL Control of Complex Systems Initiative and in part by the National Natural Science Foundation of China under Grants 61621004,61573022 and 61333007.
Chiu, Jiun-Yao, i 邱俊耀. "A Recommender System Based on Entropy of Multiple Criteria Decision Making and Domain Ontology-An Example of Anti-diabetic Medicines". Thesis, 2011. http://ndltd.ncl.edu.tw/handle/17780956370371645054.
Pełny tekst źródła朝陽科技大學
資訊管理系碩士班
99
Generally speaking, we have to consider the effect of many factors when making a decision. The recommended system can help user to analyze needs and give suggestions with complex information. Our research focuses on the assistance of medical suggestion for doctors. According to the statistics of Department of Health, diabetes was one of the top ten causes of death in Taiwan in 2009. Therefore, developing an effective treatment for diabetes is very important. The fact is that the amount of diabetes specialists is not enough and not all diabetic patients can be treated by specialists. We present this recommender system to help treatment. The purpose is to develop a recommender system to assist the general practitioner (GP) to make more appropriate decision in selecting anti-diabetic medicines. First, we built up the ontology of diabetic knowledge, and then multiples criteria decision making method (MCDM) was applied to compute for medication. Entropy was used to compute data of patients’ profile. With medicine knowledge ontology, the results of calculation will list appropriate medications. Finally, the system will show the preference of medications to doctors.
Hussain, Zahid, i 胡杉奕. "Distance, similarity and entropy for hesitant fuzzy sets based on Hausdorff metric with applications to multi-criteria decision making and clustering". Thesis, 2018. http://ndltd.ncl.edu.tw/handle/2ac4kx.
Pełny tekst źródła中原大學
應用數學研究所
107
Distance, similarity and entropy play an indispensable role in almost every field of our daily life settings. Distance and similarity measures are widely used to differentiate between two sets or objects. While entropy measures the fuzziness in a fuzzy set. Different distance and similarity measures have been proposed for hesitant fuzzy sets (HFSs) in the literature, but either they are in sufficient or not reflect desirable results. In this manuscript, the construction of new distance and similarity measures between HFSs based on Hausdorff metric is proposed. We first present a novel and simple method for calculating a distance between HFSs based on Hasudorff metric in a suitable and intuitive way. Two main features of the proposed approach are: (1) not necessary to add a minimum value, a maximum value or any value to the shorter one of hesitant fuzzy elements (HFEs) for extending it to the larger one of HFEs; and (2) no need to arrange HFEs either in ascending or descending order. This is because adding such values and arrangements of elements will not put any impact on final results. We then extend distance to similarity measure between HFSs. Next, measuring uncertainty for an HFS is computed by an amount of distinction between an HFS and its complement. Hausdorff metric is used to calculate a distance between an HFS and its complement which assists us to construct novel entropy of HFSs. An axiomatic definition of entropy measure for HFSs is also given in this dissertation. The proposed entropy is proved to satisfy all axioms. Furthermore, more generalizations of the proposed entropy allow us to onstruct different entropy measures of HFSs which reflect that the closer of an HFS to its complement shows less distinction between them and produces the larger entropy measure of the HFS, and also the more distinction between them gives smaller amount of uncertainty. Furthermore, we claim some properties and also several examples are presented to compare our proposed distance, similarity and entropy measures with existing methods. We apply the proposed distance of HFSs to multi-criteria decision making and the similarity measure of HFSs to clustering. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is used to construct hesitant fuzzy (TOPSIS) based on the proposed entropy measure to solve multicriteria decision making problems. Finally, expository examples are utilized to manifest simplicity, practicability and effectiveness of our proposed distance, similarity and entropies as compared to existing methods. The comparison results demonstrate that the proposed distance, similarity and entropy measures are much simpler, intuitive and better than most existing methods.
Wabnitz, Paul. "Sarnak’s Conjecture about Möbius Function Randomness in Deterministic Dynamical Systems". 2016. https://ul.qucosa.de/id/qucosa%3A16796.
Pełny tekst źródłaThe thesis in hand deals with a conjecture of Sarnak from 2010 about the orthogonality of sequences induced by deterministic dynamical systems to the Möbius μ-function. Its main results are the ergodic theorem with Möbius weights, which is a measure theoretic (weaker) version of Sarnak’s conjecture, and the already assured validity of Sarnak’s conjecture in special cases, where we have exemplarily chosen the Thue–Morse shift and skew product extensions of rational rotations on the significance of the Möbius function for number theory. Since it is essential for the understanding of Sarnak’s conjecture we give an introduction to the theory of entropy of dynamical systems based on the definitions of Adler–Konheim–McAndrew, Bowen–Dinaburg and Kolmogorov–Sinai. Furthermore, we calculate the topological entropy of the Thue–Morse shift and of skew product extensions of rotations on the circle. We study the ergodic decomposition for T-invariant measures on compact metric spaces with continuous transformations T, which we will need for the proof of the ergodic theorem with Möbius weights. Thereafter, we prove the namely weighted ergodic theorem. We give a sufficient condition for Sarnak’s conjecture to hold for a given dynamical system, which we make use of in the following chapter. Thereupon, it is varified that Sarnak’s conjecture holds for the Thue–Morse shift and for skew product extensions of rational rotations on the circle. Lastly, it is shown that Sarnak’s conjecture from one of Chowla.