REVISITING SOME FUZZY ALGEBRAIC STRUCTURES
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https://doi.org/10.15625/1813-9663/38/3/17039Keywords:
Fuzzy relation, Fuzzy equivalence relation, Fuzzy cosetAbstract
Following our investigations on some fuzzy algebraic structures started in [6--8], and [9], in the present work, we revisit fuzzy groups and fuzzy ideals and introduce some new examples and then define the notion of fuzzy relation modulo a fuzzy subgroup and modulo a fuzzy ideal. As a consequence, we introduce the right and left cosets modulo a fuzzy relation. This work and the previously cited ones can be considered as a continuation of investigations initiated in [1--5]. Toward our investigation, we have in mind that by introducing these new definitions, the results that we can get should represent generalization of classical and commonly known concepts of algebra.
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