Sur les ensembles ordonnés flous intuitionnistes
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Date
2017-12-18
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Université de M'sila
Abstract
In this thesis. First, we investigate the intuitionistic fuzzy ideals and filters on a crisp lattices. Second, we extend the results of fuzzy ideals and filters to intuitionistic fuzzy ideals and filters on intuitionistic fuzzy lattices. For the two approaches, we present interesting characterizations of these notions in terms of lattice operations and in terms of their (α,β)-level sets. Moreover, we extend the notion of prime ideal (resp. prime filter) to prime intuitionistic fuzzy ideal (resp. prime intuitionistic fuzzy filter) with respect to the lattice operations and investigate their various characterizations and properties. For the third point of this work, based on the concept of intuitionistic fuzzy lattice previously proposed by Tripathy et al., we introduce the notion of intuitionistic fuzzy complete lattice and investigate its basic characterizations. In that point, we extend these characterizations by considering others completeness criterions. The characterizations of intuitionistic fuzzy complete lattices expressed in terms of the existence of the supremum or the infimum of their subsets, in terms of intuitionistic fuzzy chains and maximal chains and in terms of intuitionistic fuzzy ascending (resp. descending) chains are given. Furthermore, we will show an intuitionistic fuzzification of Tarski-Davis's fixed point theorem.