Inclusion and subsethood measure for interval-valued fuzzy sets and for continuous type-2 fuzzy sets
Fuzzy Sets and SystemsPublished 16 January 2013
Zdenko Takáč
Citations43
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TL;DR
A special subsethood measure for ordinary fuzzy sets is focused on, based on @a-cut representation, and it is shown, how to compute subsethood measures for continuous type-2 fuzzy sets with no need for discretizing of universe.
Abstract
The main aim of this paper is to propose new subsethood measures for continuous, general type-2 fuzzy sets. For this purpose, we introduce inclusions and subsethood measures for interval-valued fuzzy sets first. Then, using an α-plane representation for type-2 fuzzy sets, we extend these inclusions and subsethood measures to general type-2 fuzzy sets. Subsethood measures for interval-valued fuzzy sets (hence, also for type-2 fuzzy sets) rely on already known subsethood measures for ordinary fuzzy sets. We focus on a special subsethood measure for ordinary fuzzy sets, based on α-cut representation, and show, how to compute subsethood measures for continuous type-2 fuzzy sets with no need for discretizing of universe. This is a very interesting and useful property of proposed subsethood measures, which is one of the reason, why our approach has less computational demand than the others.
Keywords
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