Pseudoeffect algebras are non-commutative generalizations of effect algebras, which can serve as models of both quantum structures and non-commutative logics. The main contribution of this study is twofold. Firstly, we initiate an order-theoretic extension of pseudoeffect algebras, called partially ordered pseudoeffect algebras (abbreviated po-PEAs). Secondly, we investigate the fuzzy ideal the...

The notions of intuitionistic fuzzy T-ideals in BCI-algebras are introduced.Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy T-idealare provided. Using a collection of T-ideals, intuitionistic fuzzy T-ideals areestablished.

We consider the fuzzification of the notion of fuzzy multiply positive implicative hyper BCK-ideals of BCK-algebras and then some related results are obtained. Using the concept of level subsets, we give a characterization of a fuzzy multiply positive implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzymultiply positive implicative hyper BCK-ideal. Moreov...

Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S....

In this paper we introduce the notion of interval-valued (i.v.) fuzzy prime and semiprime ideals of a hypersemiring and study different properties of these two ideals. Finally, we examine the strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a hypersemiring and characterize the equivalence of primeness, strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a fu...