Affiliations: [a] School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China
| [b] Department of Mathematical Engineering, Polytechnic University of Tirana, Albania
Correspondence:
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Corresponding author. Waqar Khan, School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China. E-mail: [email protected].
Abstract: We introduce the notion of fuzzy Abel-Grassmann’s hypergroupoid, hypercongruence, fuzzy hypercongruence, fuzzy strong hypercongruence, compatible relations in an Abel-Grassmann’s hypergroupoid. This paper is aimed to study fuzzy hyperideals, smallest fuzzy hyperideals, fuzzy equivalence relations, fuzzy compatible fuzzy strong compatible, fuzzy hypercongruences, fuzzy strong hypercongruences, fuzzy regular, fuzzy strong regular relations and fuzzy hypercongruences in Abel-Grassmann’s hypergroupoids. Characterizations of hypercongruences, their corresponding quotient structure, homomorphisms and an important theorem on embedding Abel-Grassmann’s hypergroupoids by means of fuzzy sets. We show that each hypergroupoid is embedded into a poe-hypergroupoid of all fuzzy subsets of an Abel-Grassmann’s hypergroupoid.
