Book ChapterDOI
Fuzzy measures and fuzzy integrals—a survey
Michio Sugeno
- pp 251-257
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TLDR
The concept of fuzzy sets (precisely speaking, fuzzy subsets of an ordinary set) is nothing but an extended concept of ordinary sets, and the concept of probabilities is absolutely different from that of sets.Abstract:
As is well-known in recent years, there are two kinds of uncertainities, randomness and fuzziness, which can be both dealt with from a mathematical point of view. We know the concept of probabilities with respect to randomness and also that of fuzzy sets with respect to fuzziness. This fact tempts us to discuss fuzzy sets in comparison with probabilities. However, such a direct comparison must fail. The concept of fuzzy sets (precisely speaking, fuzzy subsets of an ordinary set) is nothing but an extended concept of ordinary sets. We have to notice that the concept of probabilities is absolutely different from that of sets. To discuss our problem in detail, let us consider probabilities for the time being. There are a number of interpretations for probabilities: classical probabilities (originated by Laplace); measure theoretical probabilities (by Kolmogorov); subjective probabilities in Bayesian statistics; probabilities as logics and so on.read more
Citations
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Journal ArticleDOI
Pythagorean membership grades in multicriteria decision making
TL;DR: The issue of having to choose a best alternative in multicriteria decision making leads the problem of comparing Pythagorean membership grades to be considered, and a variety of aggregation operations are introduced for these Pythagorian fuzzy subsets.
Journal ArticleDOI
Evaluating intertwined effects in e-learning programs: A novel hybrid MCDM model based on factor analysis and DEMATEL
TL;DR: Empirical experimental results show the proposed new novel hybrid MCDM model is capable of producing effective evaluation of e-learning programs with adequate criteria that fit with respondent's perception patterns, especially when the evaluation criteria are numerous and intertwined.
Journal ArticleDOI
Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets
Xiaolu Zhang,Zeshui Xu +1 more
TL;DR: Some novel operational laws of PFSs are defined and an extended technique for order preference by similarity to ideal solution method is proposed to deal effectively with them for the multicriteria decision‐making problems with PFS.
Journal ArticleDOI
Generalized Orthopair Fuzzy Sets
TL;DR: It is noted that as q increases the space of acceptable orthopairs increases and thus gives the user more freedom in expressing their belief about membership grade, and introduces a general class of sets called q-rung orthopair fuzzy sets in which the sum of the ${\rm{q}}$th power of the support against is bonded by one.
References
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Journal ArticleDOI
Probability measures of Fuzzy events
TL;DR: In probability theory, an event, A, is a member of a a-field, CY, of subsets of a sample space ~2, where CY is any collection of disjoint events.
Journal ArticleDOI
A model of learning based on fuzzy information
M. Sugeno,T. Terano +1 more
TL;DR: Using fuzzy measures and fuzzy integrals, a mathematical model of learning is presented which is able to learn through fuzzy information and is compared with an ordinary Bayesian learning model.
Book ChapterDOI
Conditional fuzzy measures and their applications
T. Terano,M. Sugeno +1 more
TL;DR: This chapter introduces a set function, that is, conditional fuzzy measure and a relation between a priori and a posteriori fuzzy measures, very useful for describing any kind of transition of fuzzy phenomena such as communication of rumors, the reprint of color photograph, and the development of human abilities by education.