Topic
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: This paper applies a fuzzy membership to each input point and reformulate the SVMs such that different input points can make different contributions to the learning of decision surface.
Abstract: A support vector machine (SVM) learns the decision surface from two distinct classes of the input points. In many applications, each input point may not be fully assigned to one of these two classes. In this paper, we apply a fuzzy membership to each input point and reformulate the SVMs such that different input points can make different contributions to the learning of decision surface. We call the proposed method fuzzy SVMs (FSVMs).
1,374 citations
24 Jun 2013
TL;DR: A new class of non-standard fuzzy subset called Pythagorean fuzzy subsets is introduced and the related idea of Pythgorean membership grades is introduced, with a focus on the negation operation and its relationship to the Pythagorian theorem.
Abstract: We introduce a new class of non-standard fuzzy subsets called Pythagorean fuzzy subsets and the related idea of Pythagorean membership grades. We focus on the negation operation and its relationship to the Pythagorean theorem. We compare Pythagorean fuzzy subsets with intuitionistic fuzzy subsets. We look at the basic set operations for the Pythagorean fuzzy subsets.
1,369 citations
TL;DR: The relationship between intutionistic fuzzy set and hesitant fuzzy set is discussed, based on which some operations and aggregation operators for hesitant fuzzy elements are developed and their application in solving decision making problems is given.
1,352 citations
TL;DR: A function to help in the ordering of fuzzy subsets of the unit interval is introduced, which is the integral of the mean of the level sets associated with the fuzzy subset.
1,302 citations
TL;DR: This paper presents a fuzzy c-means (FCM) algorithm that incorporates spatial information into the membership function for clustering and yields regions more homogeneous than those of other methods.
1,296 citations