Browsing by Author "Sarra Boudaoud"

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    On the fuzzy pseudo ordered sets
    (Université de M'sila, 2021) Sarra Boudaoud
    In this thesis, we study the notion of fuzzy pseudo ordered sets and some of its interesting properties, and then we introduce the concept of fuzzy trellis as a natural generalization of the trellis introduced by Skala with respect to a fuzzy pseudo order relation. In addition, we introduce the notion of fuzzy ideal (resp. fuzzy filter) as fuzzy sets on a crisp trellis and we present interesting characterizations of these notions. We pay particular attention to the principal fuzzy ideals (resp. filters) on a given trellis, which is more complicated than the same notions on a lattice. At the end, we provide various characterizations of intuitionistic fuzzy ideals (resp. fuzzy filters) on a lattice
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    PRINCIPAL INTUITIONISTIC FUZZY IDEALS AND FILTERS ON A LATTICE
    (Université de M'sila, 2021) Sarra Boudaoud; Lemnaouar Zedam
    In this paper, we generalize the notion of principal ideal (resp. filter) on a lattice to the setting of intuitionistic fuzzy sets and investigate their various characterizations and properties. More specifically, we show that any principal intuitionistic fuzzy ideal (resp. filter) coincides with an intuitionistic fuzzy down-set (resp. up-set) generated by an intuitionistic fuzzy singleton. Afterwards, for a given intuitionistic fuzzy set, we introduce two intuitionistic fuzzy sets: its intuitionistic fuzzy down-set and up-set, and we investigate their interesting properties. Keywords: lattice, intuitionistic fuzzy set, principal intuitionistic fuzzy ideal, principal intuitionistic fuzzy filter. 2010 Mathematics Subject Classification: 03E72, 06B23, 47H10.