Implicator and coimplicator integrals
نویسندگان
چکیده
We introduce and study implicator and coimplicator integrals, and investigate their possible application in defining the possibility and necessity of fuzzy sets. First, the definition and properties of implicators and coimplicators on bounded posets are discussed. Then, in analogy with the theory of seminormed and semiconormed fuzzy integrals, implicator and coimplicator integrals are defined. Next, we study the properties of these dual types of integrals. We uncover an interesting relationship between implicator and coimplicator integrals, and seminormed and semiconormed fuzzy integrals, which could also be called conjunctor and disjunctor integrals. Finally, we show that coimplicator and implicator integrals can be used to extend the domain of possibility measures and necessity measures from sets to fuzzy sets.
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