The logic MTL, Monoidal t-norm based logic was presented by F. Estva and L. Godo and discuss several properties of MTL-algebra in [6] The Boolean logic (BL) was introduced by P. Hajek and discuss the properties in [1].The fuzzy reasoning and implication operators was discussed by Ying in ([2],[3]). A proper logical system for fuzzy propositional calculus and a innovative arithmetical configurat...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

EQ-algebras were introduced by Nov?ak in [16] as an algebraic structure of truth values for fuzzy type theory (FTT). Nov?k and De Baets [18] various kinds such good, residuated, lattice ordered EQ-algebras. In any logical structures, using filters, one can construct other structures. With this inspirations, means fantastic filters we MV-algebras. Also, study prelinear introduce a new kind filte...

Soft set theory is a mathematical approach that provides solution for dealing with uncertain data. As a standard soft set, it can be represented as a Boolean-valued information system, and hence it has been used in hundreds of useful applications. Meanwhile, these applications become worthless if the Boolean information system contains missing data due to error, security or mishandling. Few res...

Applying the idea of soft set theory to lattice implication algebras, the novel concept of (implicative) filteristic soft lattice implication algebras which related to (implicative) filter(for short, (IF -)F -soft lattice implication algebras) are introduced. Basic properties of (IF -)F -soft lattice implication algebras are derived. Two kinds of fuzzy filters (i.e.(∈,∈ ∨qk)((∈,∈ ∨ qk))-fuzzy (...

I. A Boolean function of n variables, considered as a subset of t he discl'cLe uni t n-cube Bn> is called cellular if each of its connected components is a face of Bn. Hammin g'~ determination of optimal binary single-error-detectin g codes is generalized to a characteri zation of all propel' cellular functions with the greatest possible number of clements . II. An analysis is made of a class o...

In order to research the logical system whose propositional value is given in a lattice from the semantic viewpoint, Xu [7] proposed the concept of lattice implication algebras, and discussed some of their properties. Xu and Qin [8] introduced the notion of implicative filters in a lattice implication algebra, and investigated some of their properties. Turunen [5] introduced the notion of Boole...

This paper presents a characteristic set method for solving Boolean equations, which is more efficient and has better properties than the general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors al...

We present a characteristic set method for solving Boolean equations, which is more efficient and has better properties than the general characteristic set method. In particular, we give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. We also prove that a characteris...