Abstract Fuzzy set (FS) theory and rough sets (RSs) are constructed to accommodate the data uncertainty. In contrast, bipolar FS (BFS) can tackle uncertainty bipolarity of in different circumstances. This article aims introduce idea fuzzy ideals semigroup (SG), which is a generalization concept BFSs (RBFSs) an SG. We also investigate roughness subsemigroup (BF-SSG) with help congruence relation...

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...

The bipolar fuzzy (BF) set is an extension of the used to solve uncertainty having two poles, positive and negative. rough a useful mathematical technique handle vagueness impreciseness. major objective this paper analyze notion approximation BF ideals semirings by combining theories sets. Then, idea subsemirings (ideals, bi-ideals interior ideals) developed. In addition, are characterized uppe...

In this paper, we study fuzzy congruence relations and kernel ideals of an Ockham algebra A , f , whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions derived for ideal...

The definition of open bisimilarity on the χ-processes does not give rise to a sensible relation on the χ-processes with the mismatch operator. The paper proposes ground open congruence as a principal open congruence on the χ-processes with the mismatch operator. The algebraic properties of the ground congruence is studied. The paper also takes a close look at barbed congruence. This relation i...

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...