BL-algebras have been invented by P. Hájek [3] in order to provide an algebraic proof of the completeness theorem of “Basic Logic” (BL, for short) arising from the continuous triangular norms, familiar in the fuzzy logic framework. The above notion is generalized to an algebraic system in which the required conditions are fulfilled (Definition 2.1). Filters in BL-algebras are also defined. A fi...

Revealed preference theory was initiated by Samuelson [8] as a way of defining the rational behaviour of a consumer in terms of a preference relation associated with a demand function. This topic has been axiomatically treated by Arrow (1959), Richter (1966), Sen (1971) and many others. Papers Banerjee (1995), Georgescu (2004; 2005) attempt at developing a theory of revealed preference for fuzz...

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...

Fuzzy control has achieved numerous successful industrial applications. However, stability analysis for fuzzy control systems remains a difficult problem, and most of the critical comments on fuzzy control are due to the lack of a general method for its stability analysis. Although significant research efforts have been made in the literature, appropriate tools for this issue have yet to be fou...

In this article, the problem of exponential mean-square stability analysis is discussed for uncertain networked control systems expressed by a stochastic T-S fuzzy model. general, characteristics random occurrence multipath packet dropouts often exist in signal transmission network. For dealing with difficult point, dynamic output feedback strategy combining Bernoulli theory employed. Then, del...

A b s t r a c t. We investigate some properties of two varieties of algebras arising from quantum computation quasi-MV algebras and √ ′ quasi-MV algebras first introduced in [13], [12] and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of √ ′ quasiMV algebras...

Algebraic properties and structures of intuitionistic $$L-$$ fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly, we put forward the notion compatible relation, monoid associated with relation can be effectively constructed, construct two monoids different congruence relations given ILFMA, then prove that they isomorphic. Furthermore, u...

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...