On Semilattices of Semigroups and Groups

Haq, Shamsul

doi:10.5373/jarpm.426.051210

Cited by 2 publications

(2 citation statements)

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“…An AG-groupoid (Abel-Grassmann's groupoid) was coined by Protic and Stevanovic to describe the same structure [2]. Tis nonassociative (noncommutative) algebraic structure falls between a groupoid and a commutative semigroup [3]. In [1], it was shown that an AG-groupoid S is medial; that is, (ab)(cd) � (ac)(bd) holds for all a, b, c, d ∈ S. A left identity may or may not exist in an AGgroupoid.…”

Section: Introductionmentioning

confidence: 99%

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Applications of AG-Groupoids in Decision-Making via Linear Diophantine Fuzzy Sets

Yousafzai

Zia

Khalaf

et al. 2023

Discrete Dynamics in Nature and Society

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In this paper, we investigated the notion of a linear Diophantine fuzzy set (LDFS) by using the concept of a score function to build the LDF-score left (right) ideals and LDF-score (0,2)-ideals in an AG-groupoid. We used these newly developed LDF-score ideals to characterize an AG-groupoid. We then use the proposed structure in multiattribute decision-making by considering bridge design selection and artificial intelligence-based chatbot selection.

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Section: Introductionmentioning

confidence: 99%

“…Te left identity of an AG-groupoid allows the inverses of elements. If an AG-groupoid has a left identity, then it is unique [3]. An AG-groupoid with a left identity is called an AG-group if it has inverses [4].…”

Section: Introductionmentioning

confidence: 99%

Applications of AG-Groupoids in Decision-Making via Linear Diophantine Fuzzy Sets

Yousafzai

Zia

Khalaf

et al. 2023

Discrete Dynamics in Nature and Society

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Characterizations of Ordered Semigroups in Terms of Anti-fuzzy Ideals

Salam

Ashraf

Mahboob

et al. 2019

Fuzzy Information and Engineering

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Adopting the notion of a (k * , q)-quasi-coincidence of a fuzzy point with a fuzzy set, the idea of an (∈ , ∈ ∨(k * , q k))-antifuzzy left (right) ideal, (∈ , ∈ ∨(k * , q k))-antifuzzy ideal and (∈ , ∈ ∨(k * , q k))-antifuzzy (generalized) bi-ideal in ordered semigroups are proposed, that are the generalization of the idea of an antifuzzy left (right) ideal, antifuzzy ideal and antifuzzy (generalized) bi-ideal in ordered semigroups and a few fascinating characterizations are obtained. In this paper, we tend to focus to suggest a connection between standard generalized bi-ideals and (∈ , ∈ ∨(k * , q k))-antifuzzy generalized biideals. In addition, different classes of regular ordered semigroups are characterized by the attributes of this new idea. Finally, the (k * , k)-lower part of an (∈ , ∈ ∨(k * , q k))-antifuzzy generalized bi-ideal is outlined and a few characterizations are mentioned.

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On Semilattices of Semigroups and Groups

Cited by 2 publications

References 0 publications

Applications of AG-Groupoids in Decision-Making via Linear Diophantine Fuzzy Sets

Applications of AG-Groupoids in Decision-Making via Linear Diophantine Fuzzy Sets

Characterizations of Ordered Semigroups in Terms of Anti-fuzzy Ideals

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