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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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TL;DR: Application of generalised fuzzy soft sets in decision making problem and medical diagnosis problem has been shown and some of their properties are studied.
Abstract: In this paper, we define generalised fuzzy soft sets and study some of their properties. Application of generalised fuzzy soft sets in decision making problem and medical diagnosis problem has been shown.
380 citations
TL;DR: The similarity measures are developed and the notions of positive ideal intuitionistic fuzzy set and negative ideal intuitionist fuzzy set are defined and applied to multiple attribute decision making under intuitionists fuzzy environment.
Abstract: Atanassov (1986) defined the notion of intuitionistic fuzzy set, which is a generalization of the notion of Zadeh' fuzzy set. In this paper, we first develop some similarity measures of intuitionistic fuzzy sets. Then, we define the notions of positive ideal intuitionistic fuzzy set and negative ideal intuitionistic fuzzy set. Finally, we apply the similarity measures to multiple attribute decision making under intuitionistic fuzzy environment.
379 citations
01 Dec 2013
TL;DR: A new notion of picture fuzzy sets is introduced, which are directly extensions of fuzzy sets and of intuitonistic fuzzy sets (Atanassov).
Abstract: Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory, other try to handle imprecision and uncertainty in different way. In this paper, we introduce a new notion of picture fuzzy sets (PFS), which are directly extensions of fuzzy sets and of intuitonistic fuzzy sets (Atanassov). Then some operations on picture fuzzy sets are defined and some properties of these operations are considered. Here the basic preliminaries of PFS theory are presented.
378 citations
04 Nov 2002
TL;DR: It is shown that the k-harmonic means method is superior on simple low-dimensional synthetic datasets and image segmentation tasks, and that having a soft membership function is essential for finding high-quality clusterings, but having a non-constant data weight function is useful also.
Abstract: We investigate here the behavior of the standard k-means clustering algorithm and several alternatives to it: the k-harmonic means algorithm due to Zhang and colleagues, fuzzy k-means, Gaussian expectation-maximization, and two new variants of k-harmonic means. Our aim is to find which aspects of these algorithms contribute to finding good clusterings, as opposed to converging to a low-quality local optimum. We describe each algorithm in a unified framework that introduces separate cluster membership and data weight functions. We then show that the algorithms do behave very differently from each other on simple low-dimensional synthetic datasets and image segmentation tasks, and that the k-harmonic means method is superior. Having a soft membership function is essential for finding high-quality clusterings, but having a non-constant data weight function is useful also.
371 citations
TL;DR: The concepts of correlation and correlation coefficient of interval-valued intuitionistic fuzzy sets are introduced and their first properties are studied and two decomposition theorems of the correlation are introduced.
371 citations