A Cubic Set Theoretical Approach to Linear Space

Vijayabalaji, S.; Sivaramakrishnan, S.

doi:10.1155/2015/523129

Cited by 11 publications

(5 citation statements)

References 12 publications

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“…The findings of this work can be applied to a variety of algebraic structures-for instance, semigroups, Γ-semigroups, fields, normed rings, and hemirings (see, [36][37][38][39][40][41]). Furthermore, the conception of a C k P structure used in this article can be analyzed according to the ideas in [42][43][44][45], which will pave the way for a lot of future research.…”

Section: Discussionmentioning

confidence: 99%

Algebraic Perspective of Cubic Multi-Polar Structures on BCK/BCI-Algebras

Al-Masarwah

Alshehri

2022

Mathematics

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Cubic multipolar structure with finite degree (briefly, cubic k-polar (CkP) structure) is a new hybrid extension of both k-polar fuzzy (kPF) structure and cubic structure in which CkP structure consists of two parts; the first one is an interval-valued k-polar fuzzy (IVkPF) structure acting as a membership grade extended from the interval P[0,1] to P[0,1]k (i.e., from interval-valued of real numbers to the k-tuple interval-valued of real numbers), and the second one is a kPF structure acting as a nonmembership grade extended from the interval [0,1] to [0,1]k (i.e., from real numbers to the k-tuple of real numbers). This approach is based on generalized cubic algebraic structures using polarity concepts and therefore the novelty of a CkP algebraic structure lies in its large range comparative to both kPF algebraic structure and cubic algebraic structure. The aim of this manuscript is to apply the theory of CkP structure on BCK/BCI-algebras. We originate the concepts of CkP subalgebras and (closed) CkP ideals. Moreover, some illustrative examples and dominant properties of these concepts are studied in detail. Characterizations of a CkP subalgebra/ideal are given, and the correspondence between CkP subalgebras and (closed) CkP ideals are discussed. In this regard, we provide a condition for a CkP subalgebra to be a CkP ideal in a BCK-algebra. In a BCI-algebra, we provide conditions for a CkP subalgebra to be a CkP ideal, and conditions for a CkP subalgebra to be a closed CkP ideal. We prove that, in weakly BCK-algebra, every CkP ideal is a closed CkP ideal. Finally, we establish the CkP extension property for a CkP ideal.

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Section: Discussionmentioning

confidence: 99%

Algebraic Perspective of Cubic Multi-Polar Structures on BCK/BCI-Algebras

Al-Masarwah

Alshehri

2022

Mathematics

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“…Later on, Jun et al [35] suggested the concept of the cubic set (CS), which is considered a useful tool for dealing with any disagreements between agreed interval values and vice versa. Based on CS, Vijayabalaji and Sivaramakrishnan [36] defined certain conceptions of cubic linear spaces such as "P-union, P-intersection, R-union, and Rintersection" as well as their related internal and external cubic linear spaces. Mahmood et al [37] developed the cubic hesitant fuzzy set by combining hesitant data with the CS.…”

Section: Introductionmentioning

confidence: 99%

A novel decision-making approach based on sine trigonometric cubic Pythagorean fuzzy aggregation operators

Rahim

Amin

Ali

2023

Preprint

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The objective of this study is to imitate several efficient sine-trigonometric operational laws to handle the decision-making process under the cubic Pythagorean fuzzy set environment. The sine-trigonometric function provides the periodicity and symmetry of the origin in nature and satisfies the potentials of decision-makers over the considerations of the decision-making process. keeping the advantages of the sine function and the significance of the cubic Pythagorean fuzzy set, we demonstrate the novel sine trigonometric operational laws under the cubic Pythagorean fuzzy environment. Based on these operational laws, novel sine trigonometric cubic Pythagorean fuzzy aggregation operators are developed. This study mainly focuses on a decision-making approach for multi-criteria decision-making problems that is based on proposed aggregation operators with given weight information of the criterion. Lastly, to demonstrate the efficiency, an illustration is presented. Sensitivity and comparison analyses are used to evaluate the method’s permanency and rationality.

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“…Later Gu Wexiang and Lu [18] redefined the concept of fuzzy field and fuzzy linear space and gave some fundamental properties. Vijaybalaji et al further advanced the theory to cubic linear space combining interval-valued fuzzy linear space and fuzzy linear space and their properties are presented in [17].…”

Section: Introductionmentioning

confidence: 99%

N-Cubic Sets Applied to Linear Spaces

Kavyasree¹,

Reddy²

2022

KgJMat

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The concept of N-fuzzy sets is a good mathematical tool to deal with uncertainties that use the co-domain [−1, 0] for the membership function. The notion of N-cubic sets is defined by combining interval-valued N-fuzzy sets and N-fuzzy sets. Using this N-cubic sets, we initiate a new theory called N-cubic linear spaces. Motivated by the notion of cubic linear spaces we define P-union (resp. R-union), P-intersection (resp. R-intersection) of N-cubic linear spaces. The notion of internal and external N-cubic linear spaces and their properties are investigated.

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A Cubic Set Theoretical Approach to Linear Space

Cited by 11 publications

References 12 publications

Algebraic Perspective of Cubic Multi-Polar Structures on BCK/BCI-Algebras

Algebraic Perspective of Cubic Multi-Polar Structures on BCK/BCI-Algebras

A novel decision-making approach based on sine trigonometric cubic Pythagorean fuzzy aggregation operators

N-Cubic Sets Applied to Linear Spaces

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