fuzzy soft incline algebras

In this paper we introduce the notion of soft incline algebras and filter soft incline algebras, and investigate some of their properties. Moreover, we introduce the notions of prime and maximal soft ideal and quotient of soft incline algebras.

Demonstratio Mathematica

The fuzzification of k-ideals (also r-ideals) of inclines is considered, and then we prove the notion of fuzzy ideal and fuzzy k-ideal coincide, and we investigate some properties on fuzzy r-ideals. Using level subsets of an incline with respect to a fuzzy subset A of inclines, we construct the fuzzy r-ideal containing A.

In this paper, first we generalize the existing notion of fuzzy subalgebra of an algebra in such a way that the fuzzy subalgebra of an algebra can be of a subtype of the type of the parent algebra and the underlying set of the fuzzy subalgebra can be a proper subset of the underlying set of the parent algebra via the notions of gf--algebra and gf--subalgebra of a gf--algebra and study some (lattice) algebraic properties of the collection of all gf--subalgebras of a gf-algebra and then using these notions we introduce the notions of pfs--algebra and pfs-subalgebra of a pfs--algebra which generalize the notions of p-soft -algebra, p-soft subalgebra of a p-soft -algebra and the currently existing notions of (normal) fuzzy soft group, fuzzy soft ring, fuzzy soft (left, right) ideal etcetera. Further, we study some (lattice) algebraic properties of pfs--subalgebras of a pfs--algebra.

Malaya Journal of Matematik

In this paper, the idea of intuitionistic fuzzy soft subalgebras, intuitionistic fuzzy soft ideals, and intuitionistic fuzzy soft a-ideals of B-algebra are introduced with many associated properties interrogated. In connection to the intuitionistic fuzzy soft set theory, translations, extensions, and multiplications of intuitionistic fuzzy soft subalgebras, intuitionistic fuzzy ideals, and intuitionistic fuzzy a-ideals are introduced. Interconnected with intuitionistic fuzzy soft translations, intuitionistic fuzzy soft extensions, and intuitionistic fuzzy soft multiplications of intuitionistic fuzzy soft subalgebras, intuitionistic fuzzy soft ideals, and intuitionistic fuzzy soft a-ideals are investigated.

2009

The notion of ∈-soft set and q-soft set based on a fuzzy set is introduced, and characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCIalgebras are provided. Using the notion of (∈,∈∨ q)-fuzzy BCK/BCI subalgebras/ideals, characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCI-algebras are established. AMS subject classifications: 06D72, 06F35, 03G25

2013

In this paper, we have studied the algebraic operations of fuzzy soft sets to establish their basic properties. We have discussed different algebraic structures of fuzzy soft sets under the restricted and extended operations of union and intersection in a comprehensive manner. Logical equivalences have also been made in order to give a complete overview of these structures.

2021

In this paper, the notions of (∈, ∈∨q)-fuzzy soft BCK/BCI-algebras and (∈, ∈∨q)-fuzzy soft sub-BCK/BCI-algebras are introduced, and related properties are investigated. Furthermore, relations between fuzzy soft BCK/BCI-algebras and (∈, ∈∨q)-fuzzy soft BCK/BCI-algebras are displayed. Moreover, conditions for an (∈, ∈∨q)-fuzzy soft BCK/BCI-algebra to be a fuzzy soft BCK/BCI-algebra are provided. Also, the union, the extended intersection, and the "AND"-operation of two (∈, ∈∨q)-fuzzy soft (sub-)BCK/BCI-algebras are discussed, and a characterization of an (∈, ∈∨q)-fuzzy soft BCK/BCI-algebra is established.

Journal of Computer Science and Cybernetics

Following our investigations on some fuzzy algebraic structures started in [6--8], and [9], in the present work, we revisit fuzzy groups and fuzzy ideals and introduce some new examples and then define the notion of fuzzy relation modulo a fuzzy subgroup and modulo a fuzzy ideal. As a consequence, we introduce the right and left cosets modulo a fuzzy relation. This work and the previously cited ones can be considered as a continuation of investigations initiated in [1--5]. Toward our investigation, we have in mind that by introducing these new definitions, the results that we can get should represent generalization of classical and commonly known concepts of algebra.

Arxiv preprint arXiv:1003.4595, 2010

In this paper, we deal with soft MTL-algebras based on fuzzy sets. By means of ∈-soft sets and q-soft sets, some characterizations of (Boolean, G-and MV-) filteristic soft MTL-algebras are investigated. Finally, we prove that a soft set is a Boolean filteristic soft MTL-algebra if and only if it is both a G-filteristic soft MTL-algebra and an MV-filteristic soft MTL-algebra.

In this paper, first we generalize the existing notion of fuzzy subalgebra of an algebra in such a way that the fuzzy subalgebra of an algebra can be of a subtype of the type of the parent algebra and the underlying set of the fuzzy subalgebra can be a proper subset of the underlying set of the parent algebra via the notions of gf--algebra and gf--subalgebra of a gf--algebra and study some (lattice) algebraic properties of the collection of all gf--subalgebras of a gf--algebra and then using these notions we introduce the notions of pfs--algebra and pfs--subalgebra of a pfs--algebra which generalize the notions of p-soft -algebra, p-soft -subalgebra of a p-soft -algebra and the currently existing notions of (normal) fuzzy soft group, fuzzy soft ring, fuzzy soft (left, right) ideal etcetera. Further, we study some (lattice) algebraic properties of pfs--subalgebras of a pfs--algebra.