Inclusion and subsethood measure for interval-valued fuzzy sets and for continuous type-2 fuzzy sets

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• 作者：Zdenko Taká ; ?^a ; ^b ; ^takac@ku.sk ; ^{zdenko.takac@stuba.sk}
• 关键词：Type-2 fuzzy sets ; Interval-valued fuzzy sets ; Inclusion ; Inclusion indicator ; Subsethood ; Subsethood measure ; Alpha plane representation
• 刊名：Fuzzy Sets and Systems
• 出版年：2013
• 出版时间：1 August, 2013
• 年：2013
• 卷：224
• 期：Complete
• 页码：106-120
• 全文大小：371 K

文摘

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 -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 -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.