Convexity-Cum-Concavity on Fuzzy Soft Expert Set with Certain Properties

Ihsan, Muhammad Nur; Rahman, Atiqe Ur; Saeed, Muhammad; Khalifa, Hamiden Abd El-Wahed

doi:10.5391/ijfis.2021.21.3.233

Cited by 13 publications

(7 citation statements)

References 17 publications

(19 reference statements)

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“…Convexity has a vital function in optimization, image processing and classification, pattern recognition, and other sub-fields of computational geometry. In order to tackle optimization and other related problems for vague and uncertain data, notions of classical convexity and concavity (Lara et al [28,29]) under s-set environment were characterized initially by Deli [30]; then, this work was further extended by Ihsan et al [31,32], Rahman et al [33], and Salih and Sabir [34] for further investigations on certain variants of convexity. But these notions are not sufficient for handling information with entitlement of multi-argument approximate function (maa-function); therefore, Rahman et al [35] conceptualized the notions of convexity cum concavity under hsset scenarios.…”

Section: Introductionmentioning

confidence: 99%

Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion

Rahman

Saeed

Khan

et al. 2022

Journal of Function Spaces

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Hypersoft set is a novel area of study which is established as an extension of soft set to handle its limitations. It employs a new approximate mapping called multi-argument approximate function which considers the Cartesian product of attribute-valued disjoint sets as its domain and the power set of universe as its co-domain. The domain of this function is broader as compared to the domain of soft approximate function. It is capable of handling the scenario where sub-attribute-valued sets are considered more significant than taking merely single set of attributes. In this study, notions of set inclusion, convex (concave) sets, strongly convex (concave) sets, strictly convex (concave) sets, convex hull, and convex cone are conceptualized for the multi-argument approximate function. Based on these characterized notions, some set-theoretic inequalities are established with generalized properties and results. The set-theoretic version of classical Jensen’s type inequalities is also discussed with the help of proposed notions.

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Section: Introductionmentioning

confidence: 99%

Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion

Rahman

Saeed

Khan

et al. 2022

Journal of Function Spaces

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“…In 2010, a few important entities over SSts appeared as C ¸a gman and Engino glu [12] introduced matrices, Babitha and Sunil [10,11] introduced relations and functions over SSts, followed by anti-symmetric, ordering, transitive closure, and Yang and Guo [35] presented the closure and kernel of soft mappings and soft relations. More contributions towards the operations (extended version) and verification of some properties with respect to these operations were made by different mathematicians [7,15,17,18,25,26,33,34,38]. While set theory was developing by defining algebraic entities as operations, matrices, relations, and functions, as discussed above, on the other side, mathematicians were trying to develop its connection with algebraic structures as well.…”

Section: Introductionmentioning

confidence: 99%

Soft algebraic structures embedded with soft members and soft elements: an abstract approach

Saeed,

Shafique,

Rahman

et al. 2024

J. Math. Computer Sci.

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As a new area of study in pure mathematics, the theory of soft sets is expanding by redefining fundamental ideas as algebraic structures, such as soft groups, soft rings, and soft fields. It also finds applications in other domains, regarding data analysis and decision-making. This study manipulates soft members and soft elements to explore soft structures from a traditional point of view, making it easier to comprehend soft algebraic structures. The soft inverse of a soft member and the soft identity member are generalized for any soft group, and a method to count the number of possible soft subgroups of a soft group is also provided.

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“…Thus, the theories of FS, IFS, pFS, cFS, cIFS and cpFS are extended for soft set to develop novel structures fuzzy soft set (FSS) ( Maji, Biswas & Roy, 2001a ), intuitionistic fuzzy soft set (IFSS) ( Maji, Biswas & Roy, 2001b ), picture fuzzy soft set (pFSS) ( Cuong & Kreinovich, 2014 ), complex fuzzy soft set (cFSS) ( Thirunavukarasu, Suresh & Ashokkumar, 2017 ), complex intuitionistic fuzzy soft set (cIFSS) ( Kumar & Bajaj, 2014 ; Ali et al, 2021 ) and complex picture fuzzy soft set (cpFSS) ( Shanthi, Umamakeswari & Saranya, 2022 ) respectively. Rahman et al (2020) , Ihsan et al (2021) and Ihsan, Saeed & Rahman (2021) made rich contributions refinement in fuzzy set-like structures and convexity in SST-like environments.…”

Section: Introductionmentioning

confidence: 99%

An optimized multi-attribute decision-making approach to construction supply chain management by using complex picture fuzzy soft set

Asghar,

Khan,

Albahar

et al. 2023

PeerJ Computer Science

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Supplier selection is a critical decision-making process for any organization, as it directly impacts the quality, cost, and reliability of its products and services. However, the supplier selection problem can become highly complex due to the uncertainties and vagueness associated with it. To overcome these complexities, multi-criteria decision analysis, and fuzzy logic have been used to incorporate uncertainties and vagueness into the supplier selection process. These techniques can help organizations make informed decisions and mitigate the risks associated with supplier selection. In this article, a complex picture fuzzy soft set (cpFSS), a generalized fuzzy set-like structure, is developed to deal with information-based uncertainties involved in the supplier selection process. It can maintain the expected information-based periodicity by introducing amplitude and phase terms. The amplitude term is meant for fuzzy membership, and the phase term is for managing its periodicity within the complex plane. The cpFSS also facilitates the decision-makers by allowing them the opportunity to provide their neutral grade-based opinions for objects under observation. Firstly, the essential notions and set-theoretic operations of cpFSS are investigated and illustrated with examples. Secondly, a MADM-based algorithm is proposed by describing new matrix-based aggregations of cpFSS like the core matrix, maximum and minimum decision value matrices, and score. Lastly, the proposed algorithm is implemented in real-world applications with the aim of selecting a suitable supplier for the provision of required materials for construction projects. With the sensitivity analysis of score values through Pythagorean means, it can be concluded that the results and rankings of the suppliers are consistent. Moreover, through structural comparison, the proposed structure is proven to be more flexible and reliable as compared to existing fuzzy set-like structures.

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Convexity-Cum-Concavity on Fuzzy Soft Expert Set with Certain Properties

Cited by 13 publications

References 17 publications

Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion

Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion

Soft algebraic structures embedded with soft members and soft elements: an abstract approach

An optimized multi-attribute decision-making approach to construction supply chain management by using complex picture fuzzy soft set

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