Distinct so far existing arithmetics of fuzzy numbers, usually stemming from the Zadeh’s extensional principle, do not preserve some of the important properties of the standard arithmetics of real numbers. Although one cannot expect that a generalization of the standard arithmetic will preserve precisely all its properties, the most important properties should be preserved at least in a weakene...

We present a family of algebraic structures, called rectangular bilattices, which serve as a natural accommodation and powerful generalization to both intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs). These structures are useful on one hand to clarify the exact nature of the relationship between the above two common extensions of fuzzy sets, and on the other hand provide ...

we present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. first, we introduce a hyper bck-algebra induced by a max-min general fuzzy automaton. then, we study the properties of this hyper bck-algebra. particularly, some theorems and results for hyper bck-algebra are proved. for example, it is shown that this structure consists of different ty...

$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...

Many problems arise in practical applications when data is extracted from a group of experts, all of whom do not collectively agree. The theory of Type 2 Fuzzy Multisets is capable of modelling these types of uncertainties in decision making. The purpose of this paper is to introduce the study of various algebraic structures of Type 2 Fuzzy Multisets. As a beginning of this study, the concept o...

in this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.

In this work we present novel methods of generating fuzzy implications from the given ones. We show that these methods lead to various and much richer algebraic structures on the set of all fuzzy implications than obtained in the literature so far.

Fuzzy subgroups and T -vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T -vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T -indistinguishability operators (fuzzy equivalence relations). In this pa...

our aim in this paper is to introduce the notion of fuzzy soft near-subtraction semigroupsand fuzzy soft ideals of near-subtraction semigroups. we discuss some important properties of these new fuzzy algebraic structure and investigate some examples and counter examples.

In this paper we shall describe a very natural extension of MV-algebras, the divisible MV-algebras (DMV). Such algebraic structures will be used to give a formal description of rules of fuzzy control.