Subsethood measures for interval-valued fuzzy sets based on the aggregation of interval fuzzy implications

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• 作者：Zdenko Taká ; č¹ ; ^{zdenko.takac@stuba.sk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Subsethood measure ; Interval valued fuzzy sets ; Interval aggregation ; Aggregation function ; Fuzzy implication ; Inclusion indicator ; Lipschitz ; Best interval representation
• 刊名：Fuzzy Sets and Systems
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：283
• 期：Complete
• 页码：120-139
• 全文大小：398 K

文摘

The connection between fuzzy subsethood measures and fuzzy implications straightforwardly follows from the definition of inclusion for (crisp) sets. In accordance with this connection we introduce a new constructive method for (weak) fuzzy subsethood measures for interval-valued fuzzy sets based on the aggregation of fuzzy interval implications. For this purpose we generalize aggregation functions and propose a technique for aggregation of intervals. The benefit of our approach lies in the wide range of obtained fuzzy subsethood measures for interval-valued fuzzy sets. Moreover, the method gives the possibility to construct new fuzzy subsethood measures with properties that are appropriate to the situation under investigation. Another advantage of the method is its clear semantic interpretation.