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 X is a BCI-algebra and n is an element of N. Let D be a set, let f be a function from N into D, and let n be a natural number. Then f(n) is an element of D. Let G be a non empty BCI structure with 0. The functor BCI-powerG yielding a function from (the carrier of G) × N into the carrier of G is defined as follows: (Def. 1) For every element x of G holds (BCI-powerG)(x, 0) = 0G and...

the aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in bcialgebras and to investigate some of their properties. several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of bci-algebras i...

In the present paper, we introduce the notion of generalized left derivation of a BCI-algebra X , construct several examples, and investigate related properties. Also establish some results on regular generalized left derivation. Furthermore, for a generalized left derivation H, the concept of a H-invariant generalized left derivation is introduced, and examples are discussed. Using this concep...

The conception of the bipolar complex fuzzy set (BCFS) is one fundamental and significant modifications (FS) to tackle tricky awkward information. BCFS has a rich wider structure been utilized in various fields. In this article, we introduce concept (BCF) subalgebras (BCFSAs), BCF ideals (BCFIs) BCK/BCI-algebra along with certain properties. Further, investigate relations between BCFSA BCFI nec...

The concepts of (internal, external) cubic soft sets, P-cubic (resp. R-cubic) soft subsets, R-union (resp. R-intersection, P-union, Pintersection) of cubic soft sets, and the complement of a cubic soft set are introduced, and several related properties are investigated. We apply the notion of cubic soft sets to BCK/BCI-algebras, and introduce the notion of cubic soft BCK/BCI-algebras. A charact...

In this paper we consider pseudo-BCK/BCI-algebras. In particular, we consider properties of minimal elements (x ≤ a implies x = a) in terms of the binary relation ≤ which is reflexive and antisymmetric along with several more complicated conditions. Some of the properties of minimal elements obtained bear resemblance to properties of B-algebras in case the algebraic operations ∗ and ◦ are ident...

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 ...