Fuzzy soft set approach to ideal theory of regular AG-groupoids

Feng, Feng; Khan, M. Rashid; Leoreanu-Fotea, V.; Anis, Saima; Ajaib, Nadeem

doi:10.1515/auom-2016-0015

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…Maji et al [22] described the notion of fuzzy SS (FSS) by maxing the notion of FS and SS. Feng et al [23] presented the FSS approach to the ideal theory of regular AG-groupoids. Additionally, Maji et al [24,25] defined the idea of intuitionistic FSS (IFSS) which is the fusion of IFS [9] and SS.…”

Section: Introductionmentioning

confidence: 99%

Complex picture fuzzy N-soft sets and their decision-making algorithm

2021

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We establish in this manuscript a new model complex picture fuzzy N-soft sets (CPFN-SSs) which is the fusion of complex picture fuzzy sets (CPFSs) along with N-soft sets (N-SSs) and a novel definition of CPFSs which is a mixture of complex fuzzy sets (CFSs) and picture fuzzy sets (PFSs). In CPFN-SS notions of N-SSs, fuzzy N-SSs (FN-SSs), intuitionistic FN-SSs (IFN-SSs), picture FN-SSs (PFN-SSs) complex FN-SSs (CFN-SS), complex IFN-SSs (CIFN-SSs) are generalized. We also talk about few basic operations on CPFN-SSs with the assistance of examples. Additionally, we establish two kinds of union (extended and restricted) and intersection (extended and restricted) of CPFN-SSs and illustrate them through examples. We also establish a complement of CPFN-SSs along with an example. Furthermore, we define an algorithm to solve the data in the environment of CPFN-SSs, and then we represent two real-world applications (performance assessment of e-waste recycling program and predication about the champions of FIFA world cup 2022 through audience poll) of our established model in decision-making (DM) to show the advantages and usefulness of the CPFN-SSs. In the end, we represent a comparison of our established model with some existing methods which shows that our established model is more general than existing ones.

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Section: Introductionmentioning

confidence: 99%

Complex picture fuzzy N-soft sets and their decision-making algorithm

2021

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“…They proved that for a locally associative Γ -LA-semigroup S with a left identity, S/ρ is a maximal weakly separative homomorphic image of S, where ρ is a relation on S defined by: aρb if and only if aγ b n = b n+1 and bγ a n = a n+1 for some positive integer n and for all γ ∈ Γ , where a, b ∈ S. In 2014, Abdullah et al [3] introduced the concept of interval-valued (∈, ∈ ∨q)-fuzzy ideals, interval-valued (∈, ∈ ∨q)-fuzzy bi-ideals and interval-valued (∈, ∈ ∨q)-fuzzy quasi-ideals of an LA-semigroup. Nowadays many scholars have studied different aspects of fuzzy subsets on LA-semigroups and Γ -LA-semigroups see [9,11,12,15,20,30,31,36,38,41,45,50]. In 2015, Abbasi and Basar [1] studied quasi-ideals and bi-ideals of locally associative Γ -LA-semigroups, (m, n) simple Γ -LA-semigroups, minimal bi-Γ -ideal, semiprime Γ -ideal and quasi-regular Γ -LA-semigroups.…”

Section: Introductionmentioning

confidence: 99%

On generalizations of quasi-prime ideals of an ordered left almost semigroups

Yiarayong

2021

Afr. Mat.

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The purposes of this paper are to introduce generalizations of quasi-prime ideals to the context of $$\phi $$ ϕ -quasi-prime ideals. Let $$\phi : {\mathcal {I}}(S) \rightarrow {\mathcal {I}}(S) \cup \left\{ \emptyset \right\} $$ ϕ : I ( S ) → I ( S ) ∪ ∅ be a function where $$ {\mathcal {I}}(S)$$ I ( S ) is the set of all left ideals of an ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroup S. A proper left ideal A of an ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroup S is called a $$\phi $$ ϕ -quasi-prime ideal, if for each $$a, b\in S$$ a , b ∈ S with $$ab \in A - \phi (A)$$ a b ∈ A - ϕ ( A ) , then $$a \in A$$ a ∈ A or $$b\in A$$ b ∈ A . Some characterizations of quasi-prime and $$\phi $$ ϕ -quasi-prime ideals are obtained. Moreover, we investigate relationships between weakly quasi-prime, almost quasi-prime, $$\omega $$ ω -quasi-prime, m-quasi-prime and $$\phi $$ ϕ -quasi-prime ideals of ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroups. Finally, we obtain necessary and sufficient conditions of $$\phi $$ ϕ -quasi-prime ideal in order to be a quasi-prime ideal.

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“…Ozturk and Inan (2012) established fuzzy soft subnear rings, (∈, ∈ ∨q) fuzzy subnear rings, and studied some of their basic properties with several examples. Fuzzy soft algebraic structures are also studied various researchers [for Communicated by Ro. examples (Feng 2016;Jun et al 2010;Ma and Zhan 2014;Onar et al 2012;Pazar et al 2012;Patel et al 2015;Reeta and Vimala 2018;Vimala et al 2017;Zhan 2012)].…”

Section: Introductionmentioning

confidence: 99%