| In this thesis,the fuzzy set is combined with semigroup algebra and the famous semigroup — Cliffford Semigroup that is closest to the group is fuzzified from a new Perspective.In other words,the Clifford semigroup is studied from the perspective of fuzzy relation.The concepts of E-fuzzy Clifford semigroup,separable E-fuzzy Clifford semigroup,E-fuzzy Clifford subsemigroup and E-fuzy Clifford subgroups are given,and some related properties are studied.Some differences between a separable E-fuzzy Clifford semigroup and general E-fuzzy Clifford semigroup are discussed.The specific content and related conclusions are as follows:In Chapter three,we blur the Clifford semigroup and define the weak fuzzy equivalence relationship.Then we give the concept of E-fuzzy Clifford semigroup and the theorem of E-fuzzy Clifford semigroup,combined with the weak fuzzy equivalence relation.In terms of separability,some related properties of separable E-fuzzy Clifford semigroups are discussed.Finally,we study the fuzzy quotient of the cut-set decision,and discuss the relationship between the E-fuzzy Clifford semigroup and the fuzzy quotient determined by the ? cut set.In Chapter four,the weak fuzzy equivalence relations defined in the same universe of E-fuzzy Clifford semigroups to give the concept of E-fuzzy Clifford subsemigroups and their decision conditions.Finally,we prove that the intersection of E-fuzzy Clifford subsemigroups also constitutes E.-Fuzzy Clifford subsemigroups.In Chapter five,we study the E-fuzzy groups,E-fuzzy subgroups and related algebraic properties of the non-intersecting subgroups of Clifford semigroups.To illustrate the unique cases of E-fuzzy groups of idempotents elements,and some differences between the general group structure and E-fuzzy group structure.Finally,based on the general algebraic properties,it is proved that the E-fuzzy group has the elimination law and the non-trivial solution to the fuzzy relation equation is solved. |
