In this paper, we introduce a new algebra called ‘EQ-algebra’, which is an alternative algebra of truth values for formal fuzzy logics. It is specified by replacing implication as the main operation with a fuzzy equality. Namely, EQ-algebra is a semilattice endowed with a binary operation of fuzzy equality and a binary operation of multiplication. Implication is derived from the fuzzy equality ...

More general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset is considered, and generalization of fuzzy fated of R0-algebras is discussed. The notion of an (∈,∈∨ qk)-fuzzy fated filter in a R0-algebra is introduced, and several properties are investigated. Characterizations of an (∈,∈∨ qk)-fuzzy fated filter in an R0-algebra are discussed. Using a collection of fate...

In this paper, we introduce the notion of fuzzy associative I-ideals in an IS-algebra with respect to a t-conorm and investigate some of its properties. We discuss the properties of homomorphic image and inverse image of S-fuzzy associative I-ideals in an IS-algebras. Relationship between T -fuzzy associative I-ideals and S-fuzzy fuzzy associative Iideals of an IS-algebra is introduced. Connect...

Abstract An E -fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group. The crisp equality is replaced by a particular fuzzy one denoted by E . Classical group-like properties are formulated as appropriate fuzzy identities special lattice theoretic formulas. We prove basic features of E -fuzzy groups: properties of the unit and inverses, ...

As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They gave a complete characterization of T-measures for a Frank triangular norm T. Here we characterize T-measures with respect to non-Frank strict triangular norms. We show the speciic roles of Frank triangular norms and a newly introduced family, nearly Frank triangular norm...

There is given a construction of the entropy of a dynamical system on arbitrary MV-algebra M. If M is the MV-algebra of characteristic functions of a σ-algebra (isomorphic to the σ-algebra), then the construction leads to the Kolmogorov Sinaj entropy. If M is the MV-algebra (tribe) of fuzzy sets, then the construction coincides with the Maličký modification of the Kolmogorov Sinaj entropy for f...

Recently, the study of fuzzy integral inequalities has gained much attention. The most popular method is using the Sugeno integral 1 . The study of inequalities for Sugeno integral was initiated by Román-Flores et al. 2, 3 and then followed by the others 4–11 . Now, we introduce some basic notation and properties. For details, we refer the reader to 1, 12 . Suppose that Σ is a σ-algebra of subs...