Molodtsov's soft set theory provides a general mathematical framework for dealing with uncertainty. The concepts of (M, N)-SI implicative (Boolean) filters of BL-algebras are introduced. Some good examples are explored. The relationships between (M, N)-SI filters and (M, N)-SI implicative filters are discussed. Some properties of (M, N)-SI implicative (Boolean) filters are investigated. In part...

The study of BCK-algebras was initiated by K. Iséki in 1966 as a generalization of the concept of set-theoretic difference and propositional calculus. The hyperstructure theory (called also multialgebras) is introduced in 1934 by Marty [6] at the 8th congress of Scandinavian Mathematicians. Around the 40’s, several authors worked on hypergroups, especially in France and in the United States, bu...

In this paper, the notation of interior KU-algebra and some related definitions are introduced. Various characterisations for have been proved. The concept positive implicative prove results regarding also presented. addition, KU-ideals several properties these ideals

the notion of vague ideals in pseudo mv-algebras is introduced,and several properties are investigated. conditions for a vague set to be avague ideal are provided. conditions for a vague ideal to be implicative aregiven. characterizations of (implicative, prime) vague ideals are discussed.the smallest vague ideal containing a given vague set is established. primeand implicative extension proper...

‎in this paper‎, ‎the notion of the radical of a filter in‎ ‎residuated lattices is defined and several characterizations of‎ ‎the radical of a filter are given‎. ‎we show that if f is a‎ ‎positive implicative filter (or obstinate filter)‎, ‎then‎ ‎rad(f)=f‎. ‎we proved the extension theorem for radical of filters in residuated lattices‎. ‎also‎, ‎we study the radical‎ ‎of filters in linearly o...

This paper is devoted to the foldness theory of implicative ideals in BCK-algebras. We use the fuzzy point concept to give some characterizations of fuzzy n-fold implicative ideals and establish some relationships with various n-fold ideals. We also construct some algorithms for studying the foldness of implicative ideals in BCK-algebras. AMS Mathematics Subject Classification: 06F35, 13A15, 8A...

At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...

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...