Some Research On Structural Theory Of Fuzzy Supersystems

In this paper, we study binary operations on semigroups and hyperopertions on hypersemigroups. Let “о”be a binary operation on a power set(P(S), о). We denote a binary operation on S by “оS”,which is restriction of “о”on S. Then we have the(S, о) is a hypersemigroup if and only if the(P(S), о) is a semigroup. Let(S, о) be a fuzzy hypersemigroup. If we restricted the fuzzy hyperoperation “о” to the set F(S) denoted by “оF”,according to define of fuzzy hypersemigroups(S, о) on [23], then the(F(S), оF) is a semigroup. The fuzzy hyperbi-ideals of fuzzy hypersemigroups has been presented. And the fuzzy hyperinterior ideals has also been presented. Forthermore, regular fuzzy hypersemigroups and intra-regular fuzzy hypersemigroups are characterized. We finished the generalization from semigroups or hypersemigroups to fuzzy hypersemigroups, by the theories of fuzzy hyperstructure. Finally, we introduce the concepts(m, n) quasi–ideals, m-left ideals and n-right ideals of po-Γ-semigroups. The generation theorems of(m, n) quasi–ideals, m-left ideals and nright ideals are obtained by every non-emptyset of po-Γ-semigroups. We prove that any(m, n)quasi–ideal of po-Γ-semigroups can be expressed as the intersection of a m-left ideal and a nright ideal of po-Γ-semigroups, Moreover any minimal(m, n) quasi–ideal of po-Γ-semigroups can be expressed as the intersection of a minimal m-left ideal and a minimal n-right ideal of po-Γ-semigroups. Finally characterizations of(m, n) quasi simple po-Γ-semigroups are given by(m, n) quasi–ideals. As an application of results of this paper, some results of quasi-ideals,left ideals and right ideals of po-Γ-semigroups are obtained.In Chapter One, we introduce some background informations and concepts of this paper.In Chapter two, we obtain relationships between binary operations on semigroups and binary hyperoperations on hypersemigroups. We also obtain relationships between binary operations on semigroups and fuzzy hyperoperations on fuzzy hypersemigroups.In Chapter three, the fuzzy hyperbi-ideals of fuzzy hypersemigroups has been presented.And the fuzzy hyperinterior ideals has also been presented. Forthermore, regular fuzzy hypersemigroups and intra-regular fuzzy hypersemigroups are characterized.In Chapter four, we obtain the the concepts(m, n) quasi –ideals, m-left ideals and n-right ideals of po-Γ-semigroups. And characterizations of(m, n) quasi simple po-Γ-semigroups are given by(m, n) quasi–ideals. Some results of quasi-ideals, left ideals and right ideals of po-Γ-semigroups are obtained.