文章基本信息

标题：Aggregation and Related Functions in Fuzzy Set Theory: Dualities and Monotonicity-Based Generalizations
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作者：Radko Mesiar ; Anna Kolesarova
期刊名称：Journal of Automation, Mobile Robotics & Intelligent Systems (JAMRIS)
印刷版ISSN：1897-8649
电子版ISSN：2080-2145
出版年度：2017
卷号：11
期号：3
页码：58
DOI：10.14313/JAMRIS_3-2017/29
出版社：Industrial Research Inst. for Automation and Measurements, Warsaw
摘要：We discuss several extensions of binary Boolean func􀆟-ons ac􀆟ng on the domain [0, 1]. Formally, there are 16disjoint classes of such func􀆟ons, covering a majority ofbinary func􀆟ons considered in fuzzy set theory. We introduceand discuss duali􀆟es in this framework, stressingthe links between different subclasses of consideredfunc􀆟ons, e.g., the link between conjunc􀆟ve and implica􀆟on func􀆟ons. Special classes of considered func􀆟onsare characterized, among others, by par􀆟cular kinds ofmonotonicity. Relaxing these constraints by consideringmonotonicity in one direc􀆟on only, we generalize standardclasses of aggrega􀆟on func􀆟ons, implica􀆟ons, semicopulas,etc., into larger classes called pre-aggrega􀆟ons,pre-implica􀆟ons, pre-semicopulas, etc. Note that the duali􀆟es discussed for the standard classes also relate thenew extended classes of pre-func􀆟ons.
关键词：aggrega􀆟on func􀆟on; conjuctor; direc􀆟onal;monotonicity; disjunctor; duality; implica􀆟on func􀆟on;pre-aggrega􀆟on func􀆟on; pre-implica􀆟on func􀆟on