Browsing by Author "Saadi Djazia"

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    Picture Fuzzy Orderings and Related Structures
    (University of M'Sila, 2024-07-11) Saadi Djazia
    Abstract: In this thesis, we have discussed and subsequently modified Coung's definitions through the study of the structure of D* (the set of membership degrees), which serves as a prototype of the picture fuzzy set. Through these modified concepts, we introduced some characteristic sets such as support, kernel, α-cuts, strong α-cuts, and the picture fuzzy lines of degree α of a picture fuzzy set, where α is in D*. We demonstrated some of their properties. Also, we presented some decomposition theorems for a picture fuzzy set and extended some of Atanassov's modal operators to the picture fuzzy case. Additionally, we explored some of the fundamental aspects related to picture fuzzy relations, picture fuzzy lattices, and their filters, characterizing them using support, kernel, a-cuts, etc. We also proved some existing results related to picture fuzzy prime filters.