2024 : 11 : 23
Leila Shahbaz

Leila Shahbaz

Academic rank: Associate Professor
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Education: PhD.
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Research

Title
The Category of 𝑺-Fuzzy Posets
Type
JournalPaper
Keywords
Fuzzy poset, S-fuzzy congruence, Free object, Cofree object, Adjoint pair
Year
2023
Journal Sahand Communications in Mathematical Analysis
DOI
Researchers Leila Shahbaz

Abstract

In this paper, we define and consider, the category FPos-S of all S-fuzzy posets and action-preserving monotone maps between them. S-fuzzy poset congruences which play an important role in studying the categorical properties of S-fuzzy posets are introduced. More precisely, the correspondence between the S-fuzzy poset congruences and the fuzzy action and order preserving maps is discussed. We characterize S-fuzzy poset congruences on the Sfuzzy posets in terms of the fuzzy pseudo orders. Some categorical properties of the category FPos-S of all S-fuzzy posets is considered. In particular, we characterize products, coproducts, equalizers, coequalizers, pullbacks and pushouts in this category. Also, we consider all forgetful functors between the category FPos-S and the categories FPos of fuzzy posets, Pos-S of S-posets, Pos of posets, Act-S of S-acts and Set of sets and study the existence of their left and right adjoints. Finally, epimorphisms, monomorphisms and order embeddings in FPos and FPos-S are studied.