Coherence for Fuzzy Measures and Applications to Decision Making

2010 ◽  
pp. 291-304 ◽  
Author(s):  
Antonio Maturo ◽  
Massimo Squillante ◽  
Aldo G. S. Ventre
Keyword(s):  
Decision Making ◽  
Fuzzy Measures

scholarly journals M-CFIS-R: Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 707 ◽  
Author(s):  
Tran Manh Tuan ◽  
Luong Thi Hong Lan ◽  
Shuo-Yan Chou ◽  
Tran Thi Ngan ◽  
Le Hoang Son ◽  
...  
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Inference System ◽  
Granular Computing ◽  
Fuzzy Inference ◽  
Fuzzy Theory ◽  
Rule Base ◽  
Inference System ◽  
Fuzzy Measures ◽  
Fuzzy Similarity

Complex fuzzy theory has strong practical background in many important applications, especially in decision-making support systems. Recently, the Mamdani Complex Fuzzy Inference System (M-CFIS) has been introduced as an effective tool for handling events that are not restricted to only values of a given time point but also include all values within certain time intervals (i.e., the phase term). In such decision-making problems, the complex fuzzy theory allows us to observe both the amplitude and phase values of an event, thus resulting in better performance. However, one of the limitations of the existing M-CFIS is the rule base that may be redundant to a specific dataset. In order to handle the problem, we propose a new Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing called M-CFIS-R. Several fuzzy similarity measures such as Complex Fuzzy Cosine Similarity Measure (CFCSM), Complex Fuzzy Dice Similarity Measure (CFDSM), and Complex Fuzzy Jaccard Similarity Measure (CFJSM) together with their weighted versions are proposed. Those measures are integrated into the M-CFIS-R system by the idea of granular computing such that only important and dominant rules are being kept in the system. The difference and advantage of M-CFIS-R against M-CFIS is the usage of the training process in which the rule base is repeatedly changed toward the original base set until the performance is better. By doing so, the new rule base in M-CFIS-R would improve the performance of the whole system. Experiments on various decision-making datasets demonstrate that the proposed M-CFIS-R performs better than M-CFIS.

scholarly journals Fuzzy Measures in Multi-Criteria Decision Making

2015 ◽  
Vol 62 ◽  
pp. 107-115 ◽  
Author(s):  
Ronald R. Yager ◽  
Naif Alajlan
Keyword(s):  
Decision Making ◽  
Multi Criteria Decision Making ◽  
Fuzzy Measures

scholarly journals Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1081 ◽  
Author(s):  
Peng ◽  
Tian ◽  
Zhang ◽  
Song ◽  
Wang
Keyword(s):  
Decision Making ◽  
Programming Model ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Preference Information ◽  
Fuzzy Measures ◽  
Correlative Relationship

Single-valued neutrosophic sets (SVNSs), which involve in truth-membership, indeterminacy-membership and falsity-membership, play a significant role in describing the decision-makers’ preference information. In this study, a single-valued neutrosophic multi-criteria decision-making (MCDM) approach is developed based on Shapley fuzzy measures and power aggregation operator that takes a correlative relationship among criteria into account and also simultaneously reduces the effects of abnormal preference information. Firstly, two aggregation operators, namely, generalized weighted single-valued neutrosophic power Shapley Choquet average (GWSVNPSCA) operator and generalized weighted single-valued neutrosophic power Shapley Choquet geometric (GWSVNPSCG) operator, are accordingly defined, and the corresponding properties are discussed as well. Secondly, based on the proposed aggregation operators, an integrated MCDM approach is proposed to effectively solve single-valued neutrosophic problems where the weight information is incompletely known. A programming model is constructed to obtain the optimal Shapley fuzzy measure. Next, the proposed operators are utilized to aggregate the decision-makers’ preference information. Finally, a theoretical example with tourism attraction selection is provided to examine the efficacy of the developed approach, in which the results is found reasonable and credible.

“Heart and Mind” Evaluation

2005 ◽  
Vol 9 (5) ◽  
pp. 439-439
Author(s):  
Toshiaki Murofushi ◽  
Keyword(s):  
Decision Making ◽  
Intelligent Systems ◽  
Choquet Integral ◽  
Order Type ◽  
Special Issue ◽  
Möbius Transform ◽  
Fuzzy Measures ◽  
The Third ◽  
Statistical Image Analysis ◽  
Heart And Mind

Special Interest Group in Evaluation (SIG Eval) of Japan Society for Fuzzy Theory and intelligent informatics was founded by Professor Hisao Shiizuka, Kogakuin University, in 1993 to facilitate the exchange of research information within Japan on evaluation problems. Since 1996, SIG Eval has held an annual workshop, the Workshop on Evaluation of Heart and Mind. In addition to the workshop, SIG Eval has edited this special issue on “Heart and Mind” Evaluation. Contributors include those who often speak at the workshop. The first article, “Feasibility Study on Marketing Research Using Eye Movement: An Investigation of Image Presentation using an Eye Camera and Data Processing,” by Shin'ya Nagasawa, Sora Yim, and Hitoshi Hongo, asserts that, in physiological experiments using an eye camera, the user's interest influences purchasing behavior. The second article, “Statistical Image Analysis of Psychological Projective Drawings,” by Kazuhisa Takemura, Iyuki Takasaki, and Yumi Iwamitsu, discusses the use of statistical image analysis to overcome the difficulty in assessing the reliability of projective drawing techniques. The third article, “Fuzzy Least Squares Regression Analysis for Social Judgment Study,” by Kazuhisa Takemura, proposes fuzzy regression analysis in which a dependent variable, independent variables, and regression parameters are represented by triangular fuzzy numbers. The fourth to sixth articles discuss fuzzy measures, or capacities, which are quite popular for their application in subjective evaluation. The fourth article, “Identification of Fuzzy Measures with Distorted Probability Measures,” by Aoi Honda and Yoshiaki Okazaki, classifies fuzzy measures by introducing the concept of order type, and proposes the method of identifying fuzzy measure μ as a distorted probability of the same, or similar, order type as μ The fifth article, “Semiatoms in Choquet Integral Models of Multiattribute Decision Making,” by Toshiaki Murofushi, characterizes the concept of the semiatom in fuzzy measure theory in the multiattribute preference relation represented by a Choquet integral. The last article, “Some Characterizations of k-Monotonicity through the Bipolar Möbius Transform in Bi-Capacities,” by Katsushige Fujimoto and Toshiaki Murofushi, proposes the bipolar Möbius transform as an extension of the conventional Möbius transform of capacities to that of bi-capacities; the concept of bi-capacity was proposed by Grabisch and Labreuche (2002) for modeling decision making on a bipolar scale. We thank the reviewers and contributers for their time and effort in making this special issue possible, and we wish to thank the JACIII editorial board, especially Professors Kaoru Hirota and Toshio Fukuda, the Editors-in-Chief, and Kenta Uchino, Managing Editor, for their support and advice in putting this special issue together. I have assumed the role of General Chair of the Joint Conference of the Third International Conference on Soft Computing and Intelligent Systems and the Seventh International Symposium on Advanced Intelligent Systems (SCIS & ISIS 2006), to be held at Tokyo Institute of Technology, Japan, on September 20--24, 2006. As is customary, selected papers will be published in special issues of this journal. We invite you to submit your research papers and to participate in SCIS & ISIS 2006. For further information, please visit <u>http://scis2006.cs.dm.u-tokai.ac.jp/</u>.

Fuzzy measures of preference and consensus in group decision-making

1977 ◽  
Author(s):  
James Bezdek ◽  
Bonnie Spillman ◽  
Richard Spillman
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Fuzzy Measures

Alternative Representations of Discrete Fuzzy Measures for Decision Making

1997 ◽  
Vol 05 (05) ◽  
pp. 587-607 ◽  
Author(s):  
Michel Grabisch
Keyword(s):  
Decision Making ◽  
Möbius Transformation ◽  
Fuzzy Measures ◽  
Multicriteria Evaluation ◽  
Mobius Transformation ◽  
Additive Measures

This paper introduces three different representations of fuzzy measures, through the Möbius transformation, and the expression of importance and interaction. This leads naturally to the concept of k-order additive measures. It is shown how these concepts can be used in decision making, especially multicriteria evaluation.

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