Ranking fuzzy numbers in the setting of possibility theory
TL;DR: A complete set of comparison indices is proposed in the framework of Zadeh's possibility theory and it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers.
About: This article is published in Information Sciences.The article was published on 1983-09-01. It has received 938 citations till now. The article focuses on the topics: Fuzzy number & Fuzzy set operations.
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953 citations
TL;DR: A new method for ranking fuzzy numbers by distance method, based on calculating the centroid point, which can rank more than two fuzzy numbers simultaneously, and the fuzzy numbers need not be normal.
772 citations
TL;DR: A fusion approach of multi-granularity linguistic information for managing information assessed in different linguistic term sets together with its application in a decision making problem with multiple information sources, assuming that the linguistic performance values given to the alternatives by the different sources are represented in linguistic term set with different granularity and/or semantic.
770 citations
Cites background or methods from "Ranking fuzzy numbers in the settin..."
...We apply the degree of possibility of dominance on fuzzy numbers [12] acting on fuzzy sets (ri) in a discrete universe (the BLTS)....
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...We nd that it gives the maximum information for computing a fuzzy preference relation [12]....
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...It is applied in decision-analysis problems where the attractiveness of alternatives must be evaluated and compared [12]....
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TL;DR: This work first makes a survey of the existing main aggregation operators and then proposes some new aggregation operators such as the induced ordered weighted geometric averaging (IOWGA) operator, generalized inducedordered weighted averaging (GIOWA), hybrid weighted averaged (HWA), etc., and briefly classify all of these aggregation operators.
Abstract: In this work, we first make a survey of the existing main aggregation operators and then propose some new aggregation operators such as the induced ordered weighted geometric averaging (IOWGA) operator, generalized induced ordered weighted averaging (GIOWA) operator, hybrid weighted averaging (HWA) operator, etc., and study their desirable properties. Finally, we briefly classify all of these aggregation operators. © 2003 Wiley Periodicals, Inc.
752 citations
TL;DR: Some fuzzy linear programming methods and techniques from a practical point of view are reviewed and some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed.
731 citations
Cites background from "Ranking fuzzy numbers in the settin..."
...He introduced four inequality indices between fuzzy numbers [11] based on the possibility theory [108,14] into mathematical programming problems with fuzzy coe cients....
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References
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Book•
01 Jan 1976
TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
Abstract: Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.
14,565 citations
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
8,918 citations
TL;DR: An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.
2,524 citations
TL;DR: The usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification principle, and the practical use of fuzzified operations is shown to be easy, requiring no more computation than when dealing with error intervals in classic tolerance analysis.
Abstract: A fuzzy number is a fuzzy subset of the real line whose highest membership values are clustered around a given real number called the mean value ; the membership function is monotonia on both sides of this mean value. In this paper, the usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification principle. The practical use of fuzzified operations is shown to be easy, requiring no more computation than when dealing with error intervals in classic tolerance analysis. The field of applications of this approach seems to be large, since it allows many known algorithms to be fitted to fuzzy data.
2,412 citations
Journal Article•
1,405 citations