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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.


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Journal ArticleDOI
Deng-Feng Li1
TL;DR: The concept of a triangular IFN (TIFN) is introduced as a special case of the IFN and a new methodology for ranking TIFNs is developed on the basis of a ratio of the value index to the ambiguity index and applied to multiattribute decision making problems in which the ratings of alternatives on attributes are expressed with TIFN.
Abstract: The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult problem. The aim of this paper is to introduce the concept of a triangular IFN (TIFN) as a special case of the IFN and develop a new methodology for ranking TIFNs. Firstly the concepts of TIFNs and cut sets as well as arithmetical operations are introduced. Then the values and ambiguities of the membership function and the non-membership function for a TIFN are defined. A new ranking method is developed on the basis of the concept of a ratio of the value index to the ambiguity index and applied to multiattribute decision making problems in which the ratings of alternatives on attributes are expressed with TIFNs. The validity and applicability of the proposed method, as well as analysis of the comparison with other methods, are illustrated with a real example.

333 citations

Journal ArticleDOI
TL;DR: It is shown that the method is capable of generating membership functions in accordance with the possibility-probability consistency principle for fuzzy sets whose elements have a defining feature with a known probability density function in the universe of discourse.

333 citations

Reference EntryDOI
15 Oct 2005
TL;DR: In this paper, the grade of membership model is proposed as a straightforward way of performing fuzzy cluster analysis, which has a long history of usage in other contexts and is illustrated by an example involving gene expression data.
Abstract: Usually in cluster analysis, an object is a member of one and only one cluster, a property described as ‘crisp’ membership. Fuzzy cluster analysis allows an object to have partial membership in more than one cluster. Selecting a good membership function is important to the success of the methods. The Grade of Membership model – which has a long history of usage in other contexts – is proposed as a straightforward way of performing fuzzy cluster analysis. The Grade of Membership model is illustrated by an example involving gene expression data. Keywords: Fuzzy cluster; grade of membership; membership function

331 citations

Journal ArticleDOI
TL;DR: This paper provides a general overview of several methods for generating membership functions for fuzzy pattern recognition applications based on heuristics, probability to possibility transformations, histograms, nearest neighbor techniques, feed-forward neural networks, clustering, and mixture decomposition.

331 citations

Journal ArticleDOI
TL;DR: A new method for handling multicriteria fuzzy decision-making problems based on intuitionistic fuzzy sets is presented and can provide a useful way to efficiently help the decision-maker to make his decision.

329 citations


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