in this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.we also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

fuzzy order congruences play an important role in studying the categoricalproperties of fuzzy posets. in this paper, the correspondence between the fuzzyorder congruences and the fuzzy order-preserving maps is discussed. we focus onthe characterization of fuzzy order congruences on the fuzzy poset in terms ofthe fuzzy preorders containing the fuzzy partial order. at last, fuzzy completecongruen...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

in this paper we define ( , ) k  q -fuzzy h -sub hemirings, ( , ) k  q -fuzzy h -ideals, ( , ) k  q - fuzzy     h -bi-ideals and ( , ) k  q -fuzzy h -quasi-ideals. we characterize h -hemiregular and h -intrahemiregular hemirings by the properties of their     ( , ) k  q -fuzzy h -ideals, ( , ) k  q -fuzzy h -bi-ideals and     ( , ) k  q -fuzzy h -quasi-...

the starting point of this paper is given by priestley’s papers, where a theory of representation of distributive lattices is presented. the purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. in this way, some results of priestley’s papers are extended. in the main theorem, we show that the category of finite fuzzy priestley space...