Hesitant Anti-Fuzzy Soft Set in BCK-Algebras

Soft Computing, 2018

Molodtsov (Comput Math Appl 37:19-31, 1999) introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced by Babitha and John (J New Results Sci 3:98-107, 2013). The aim of this paper is to apply notion of hesitant fuzzy soft set for dealing with several kinds of theories in BCK-algebras. The notions of hesitant fuzzy soft implicative ideal, hesitant fuzzy soft positive implicative ideal and hesitant fuzzy soft commutative ideal in BCK-algebras are introduced and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra (ideal) and hesitant fuzzy soft (implicative, positive implicative and commutative) ideals are discussed. Conditions for a hesitant fuzzy soft ideal to be a hesitant fuzzy soft implicative ideal (positive implicative and commutative) are given and provided. Application of hesitant fuzzy soft sets in decision making is investigated. Keywords Hesitant fuzzy (implicative-positive implicative and commutative) ideals in BCK-algebras • Hesitant fuzzy soft (implicative-positive implicative and commutative) ideals in BCK-algebras Communicated by A. Di Nola.

The Scientific World Journal, 2014

As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories inBCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (closed) hesitant fuzzy soft ideals are introduced, and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra and a (closed) hesitant fuzzy soft ideal are discussed. Conditions for a hesitant fuzzy soft set to be a hesitant fuzzy soft subalgebra are given, and conditions for a hesitant fuzzy soft subalgebra to be a hesitant fuzzy soft ideal are provided. Characterizations of a (closed) hesitant fuzzy soft ideal are considered.

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

2020

This paper aims to extend the concept of anti-type of hesitant fuzzy sets on UP-algebras to anti-type of hesitant fuzzy soft sets over UP-algebras by merging the concept of anti-type of hesitant fuzzy sets and soft sets. Further, we discuss the concepts of anti-hesitant fuzzy soft strongly UP-ideals, anti-hesitant fuzzy soft UPideals, anti-hesitant fuzzy soft UP-filters, and anti-hesitant fuzzy soft UP-subalgebras of UP-algebras and provide some properties.

Communications of the Korean Mathematical Society, 2011

Molodtsov [5] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to an implicative ideal of BCK-algebras. The notion of implicative soft ideals in BCKalgebras and implicative idealistic soft BCK-algebras is introduced, and related properties are investigated. Relations between implicative soft ideals and commutative (resp. positive implicative) soft ideals are discussed. Also, relations between implicative idealistic soft BCK-algebras and commutative (resp. positive implicative) idealistic soft BCK-algebras are provided.

Journal of Applied Mathematics, 2013

The concepts of a positive implicative (∈, ∈)-intuitionistic fuzzy ideal and a positive implicative falling intuitionistic fuzzy ideal are introduced, and several properties are investigated. Characterizations of a positive implicative (∈, ∈)-intuitionistic fuzzy ideal are obtained, and relations between a positive implicative (∈, ∈)-intuitionistic fuzzy ideal and an intuitionistic fuzzy ideal are discussed. Conditions for an intuitionistic fuzzy ideal to be a positive implicative (∈, ∈)-intuitionistic fuzzy ideal are provided, and relations between a positive implicative (∈, ∈)-intuitionistic fuzzy ideal, a falling intuitionistic fuzzy ideal and a positive implicative falling intuitionistic fuzzy ideal are considered. Conditions for a falling intuitionistic fuzzy ideal to be positive implicative are given.

Journal of Intelligent & Fuzzy Systems, 2019

Fuzzy soft set theory is applied to hyper BCK-algebras. The notion of fuzzy soft positive implicative hyper BCK-ideals is introduced, and several properties are investigated. The relation between fuzzy soft positive implicative hyper BCK-ideal and fuzzy soft hyper BCK-ideal is considered. Characterizations of fuzzy soft positive implicative hyper BCKideal are provided. Using the notion of positive implicative hyper BCK-ideal, a fuzzy soft weak (strong) hyper BCK-ideal is established.

2020

Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established.

Article Reviea, 2021

In this paper, the author contributed the concepts of fuzzy soft positive implicative hyper BCK-ideal of types (, ⊆, ⊆), (, , ⊆) and (⊆, , ⊆) are introduced some related properties are considered. Relations between double-framed soft hyper BCK-ideal and double-framed soft strong hyper BCK-ideal are discussed. Additionally, the author demonstrate that the level set of fuzzy soft positive implicative hyper BCK-ideal of types (, ⊆, ⊆), (, , ⊆) and (⊆, , ⊆) are positive implicative hyper BCK ideal of types (, ⊆, ⊆), (, , ⊆) and (⊆, , ⊆), respectively. The conditions for a fuzzy soft set to be a fuzzy soft positive implicative hyper BCK-ideal of types (, ⊆, ⊆), (, , ⊆) and (⊆, , ⊆), are initiated respectively, and the circumstances for a fuzzy soft set to be a fuzzy soft weak hyper BCK-ideal are also considered.

Applications and Applied Mathematics: An International Journal (AAM), 2020

Several generalizations and extensions of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets and fuzzy multisets, etc. Using the Torra's hesitant fuzzy sets, the notions of Sup-hesitant fuzzy ideals in BCK/BCI-algebras are introduced, and its properties are investigated. Relations between Sup-hesitant fuzzy subalgebras and Sup-hesitant fuzzy ideals are displayed, and characterizations of Sup-hesitant fuzzy ideals are discussed.