Processing of the certain information, especially inferences based on certain information. Is based on classical two-valued logic. Due to strict and complete logical foundation (classical logic), making inference levels. Thus, it is natural and necessary to attempt to establish some rational logic system as the logical foundation for uncertain information processing. It is evident that this kin...

In this paper, we have studied the notion of nearness $d$-algebras which is a generalization BCK-algebras (or NBCK-algebra for short). Therefore, it defined that notions d$-subalgebra, d-ideal in $d$-algebras. Afterward, investigated relations among them and gave some examples.

BCK-modules were introduced as an action of a BCK-algebra over Abelian group. Homomorphisms form exact sequence which is called BCK-sequence. In this paper, we study homomorphisms BCK-modules. We show that have module structure. Moreover, sequences Hom functors are BCK-sequences.

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras corresponde to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. The aim of this paper i...

We study the soft sets applied on the structure of filters of BCK-algebras. A connection between soft BCK-algebras and filteristic soft BCK-algebras is given also. Finally, important operations such as intersection, union, “AND”, “OR”, and subset operations of soft filters and filteristic soft BCK-algebras are investigated.

We present Kripke semantics for some substructural logics with weakening, known as logics with BCK implication. This work is a continuation of the work of Allwein and Dunn on Kripke semantics for Linear Logic, which in turn rested on Dunn’s Gaggle Theory and on Urquhart’s Representation Theory for nondistributive lattices. The basic idea in the representation theory is to use maximally disjoint...

In this note, by using the concept of Bipolar-valued fuzzy set, the notion of bipolar-valued fuzzy BCK/BCI-algebra is introduced. Moreover, the notions of (strong) negative s-cut (strong) positive t-cut are introduced and the relationship between these notions and crisp subalgebras are studied.

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

We study the properties and relations of fuzzy pseudo-filters of pseudo-BCK algebras. After we discuss the equivalent conditions of fuzzy normal pseudo-filter of pseudo-BCK algebra (pP), we propose fuzzy implicative pseudo-filter and its relation with fuzzy Boolean filter of (bounded) pseudo-BCK algebras (pP). Then two open problems: “In pseudo-BCK algebra or bounded pseudo-BCK algebra, Is the ...