We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propo...

A right ternary N -group (RTNG) over a right ternary near-ring N is a generalization of its binary counterpart and fuzzy soft sets are generalization of soft sets which are parameterized family of subsets of a universal set. In this paper fuzzy soft N -subgroups and N -ideals over right ternary N -groups are defined and their basic algebraic properties are studied. Fuzzy soft N -subgroups and N...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function verifies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that t...

Fuzzy relations on the same domain are classified according to the equality of families of cut sets. This equality of fuzzy relations is completely characterized, not only for unit interval valued fuzzy relations, but more generally, for fuzzy relations whose domain is a (complete) lattice. Similar results for fuzzy sets in general are considered in [12]. Applications of the results for fuzzy c...

Our work is a contribution to the model-theoretic study of equality-free fuzzy predicate logics. We present a reduced semantics and we prove a completeness theorem of the logics with respect to this semantics. The main concepts being studied are the Leibniz congruence and the relative relation. On the one hand, the Leibniz congruence of a model identifies the elements that are indistinguishable...

Park et al. (2011) introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, the concept of generalized intuitionistic fuzzy soft equality is introduced and some related properties are derived. It is proved that generalized intuitionistic fuzzy soft equality is congruence relation with res...

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. In this paper, we apply fuzzy soft sets to  hyperrings. The concept of ( , ) q       -fuzzy soft  -hyperideals of  -hyperrings is first introduced. Some new characterizations are investigated. In particular, a ...

The purpose of this note is the study of L-multialgebras and fuzzy congruences of multialgebras. In this regards first the notion of a L-multialgebras are introduced and studied and then the notion of a P -fuzzy relations on multialgebra are given and is applied to introduce the notion of P -fuzzy congruence of multialgebras. Finally, the lattices of P -fuzzy (resp. strong) congruences of multi...