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Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.


Papers
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Journal ArticleDOI
Yiyu Yao1
TL;DR: Based on rough membership functions and rough inclusion functions, the Bayesian decision-theoretic analysis is adopted to provide a systematic method for determining the precision parameters by using more familiar notions of costs and risks.

537 citations

Book
03 Dec 2007
TL;DR: The new concepts were introduced by Mendel and Liang allowing the characterization of a type-2 fuzzy set with a superior membership function and an inferior membership function; these two functions can be represented each one by atype-1 fuzzy set membership function.
Abstract: Type-2 fuzzy sets are used for modeling uncertainty and imprecision in a better way. These type-2 fuzzy sets were originally presented by Zadeh in 1975 and are essentially "fuzzy fuzzy" sets where the fuzzy degree of membership is a type-1 fuzzy set. The new concepts were introduced by Mendel and Liang allowing the characterization of a type-2 fuzzy set with a superior membership function and an inferior membership function; these two functions can be represented each one by a type-1 fuzzy set membership function. The interval between these two functions represents the footprint of uncertainty (FOU), which is used to characterize a type-2 fuzzy set.

534 citations

Journal ArticleDOI
TL;DR: The results indicate the proposed fuzzy BWM can not only obtain reasonable preference ranking for alternatives but also has higher comparison consistency than the BWM.
Abstract: Fuzzy best-worst method is proposed to solve the issues under fuzzy environment.A consistency ratio for fuzzy best-worst method is proposed for verification.The results indicate the fuzzy best-worst method outperforms best-worst method.The fuzzy best-worst method has a higher comparison consistency. Considering the vagueness frequently representing in decision data due to the lack of complete information and the ambiguity arising from the qualitative judgment of decision-makers, the crisp values of criteria may be inadequate to model the real-life multi-criteria decision-making (MCDM) issues. In this paper, the latest MCDM method, namely best-worst method (BWM) was extended to the fuzzy environment. The reference comparisons for the best criterion and for the worst criterion were described by linguistic terms of decision-makers, which can be expressed in triangular fuzzy numbers. Then, the graded mean integration representation (GMIR) method was employed to calculate the weights of criteria and alternatives with respect to different criteria under fuzzy environment. According to the concept of BWM, the nonlinearly constrained optimization problem was built for determining the fuzzy weights of criteria and alternatives with respect to different criteria. The fuzzy ranking scores of alternatives can be derived from the fuzzy weights of alternatives with respect to different criteria multiplied by fuzzy weights of the corresponding criteria, and then the crisp ranking score of alternatives can be calculated by employing GMIR method for optimal alternative selection. Meanwhile, the consistency ratio was proposed for fuzzy BWM to check the reliability of fuzzy preference comparisons. Three case studies were performed to illustrate the effectiveness and feasibility of the proposed fuzzy BWM. The results indicate the proposed fuzzy BWM can not only obtain reasonable preference ranking for alternatives but also has higher comparison consistency than the BWM.

534 citations

Journal ArticleDOI
TL;DR: It is found that measures that account for ordering on the base variable proved to be more highly correlated with subjects' actual similarity judgments, and, surprisingly, the best measures were ones that focus on only one “slice” of the membership function.

533 citations

Journal ArticleDOI
TL;DR: The concept of picture fuzzy sets (PFS), which are direct extensions of the fuzzy sets and the intuitonistic fuzzy sets, are introduced and the basic preliminaries of PFS theory are presented.
Abstract: In this paper, we introduce the concept of picture fuzzy sets (PFS), which are direct extensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS with some properties are considered. The following sections are devoted to the Zadeh Extension Principle, picture fuzzy relations and picture fuzzy soft sets. Here, the basic preliminaries of PFS theory are presented.

528 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202353
2022123
2021340
2020354
2019385
2018433