Theory of Bijective Hypersoft Set with Application in Decision Making

Rahman, Atiqe Ur; Saeed, Muhammad; Hafeez, Abida

doi:10.52280/pujm.2021.530705

Cited by 17 publications

(11 citation statements)

References 19 publications

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“…Ihsan et al [ 16 ] discussed the validity of

-sets for the entitlement of multidecisive opinions under expert set environment. Rahman et al [ 17 , 18 , 19 , 20 , 21 , 22 , 23 ] explored the blended operational aspects of

-sets by considering settings such as complex setting, convexity and concavity setting, parameterization setting, rough setting, and bijection setting. They utilized algorithm-based techniques to resolve real-world DM issues.…”

Section: Introductionmentioning

confidence: 99%

A Novel Fuzzy Parameterized Fuzzy Hypersoft Set and Riesz Summability Approach Based Decision Support System for Diagnosis of Heart Diseases

et al. 2022

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Fuzzy parameterized fuzzy hypersoft set (Δ-set) is more flexible and reliable model as it is capable of tackling features such as the assortment of attributes into their relevant subattributes and the determination of vague nature of parameters and their subparametric-valued tuples by employing the concept of fuzzy parameterization and multiargument approximations, respectively. The existing literature on medical diagnosis paid no attention to such features. Riesz Summability (a classical concept of mathematical analysis) is meant to cope with the sequential nature of data. This study aims to integrate these features collectively by using the concepts of fuzzy parameterized fuzzy hypersoft set (Δ-set) and Riesz Summability. After investigating some properties and aggregations of Δ-set, two novel decision-support algorithms are proposed for medical diagnostic decision-making by using the aggregations of Δ-set and Riesz mean technique. These algorithms are then validated using a case study based on real attributes and subattributes of the Cleveland dataset for heart-ailments-based diagnosis. The real values of attributes and subattributes are transformed into fuzzy values by using appropriate transformation criteria. It is proved that both algorithms yield the same and reliable results while considering hypersoft settings. In order to judge flexibility and reliability, the preferential aspects of the proposed study are assessed by its structural comparison with some related pre-developed structures. The proposed approach ensures that reliable results can be obtained by taking a smaller number of evaluating traits and their related subvalues-based tuples for the diagnosis of heart-related ailments.

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“…Ihsan et al [ 16 ] discussed the validity of

-sets for the entitlement of multidecisive opinions under expert set environment. Rahman et al [ 17 , 18 , 19 , 20 , 21 , 22 , 23 ] explored the blended operational aspects of

Section: Introductionmentioning

confidence: 99%

A Novel Fuzzy Parameterized Fuzzy Hypersoft Set and Riesz Summability Approach Based Decision Support System for Diagnosis of Heart Diseases

et al. 2022

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“…They also studied their daily-life applications through DM techniques. Although many researchers studied the extensions of HS-set the contributions of Rahman et al [27,28] and Saeed et al [29,30] are most prominent and relevant to this study.…”

Section: Introductionmentioning

confidence: 99%

Supplier Selection through Multicriteria Decision-Making Algorithmic Approach Based on Rough Approximation of Fuzzy Hypersoft Sets for Construction Project

et al. 2022

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The suppliers play a significant role in supply chain management. In supplier selection, factors like market-based exposure, community-based reputation, trust-based status, etc., must be considered, along with the opinions of hired experts. These factors are usually termed as rough information. Most of the literature has disregarded such factors, which may lead to a biased selection. In this study, linguistic variables in terms of triangular fuzzy numbers (TrFn) are used to manage such kind of rough information, then the rough approximations of the fuzzy hypersoft set (FHS-set) are characterized which are capable of handling such informational uncertainties. The FHS-set is more flexible as well as consistent as it tackles the limitation of fuzzy soft sets regarding categorizing parameters into their related sub-classes having their sub-parametric values. Based on these rough approximations, an algorithm is proposed for the optimal selection of suppliers by managing experts’ opinions and rough information collectively in the form of TrFn-based linguistic variables. To have a discrete decision, a signed distance method is employed to transform the TrFn-based opinions of experts into fuzzy grades. The proposed algorithm is corroborated with the help of a multi-criteria decision-making application to choose the best supplier for real estate builders. The beneficial facets of the put forward study are appraised through its structural comparison with few existing related approaches. The presented approach is consistent as it is capable to manage rough information and expert’s opinions about suppliers collectively by using rough approximations of FHS-set.

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“…Rahman et al 20 gave the idea of convexity on HSS and proved its certain properties. Rahman et al 21 developed the structure of rough HSS and gave an application for the best selection of chemical material in DM. Rahman et al 22 made a novel approach to neutrosophic hypersoft graph and discussed its certain properties.…”

Section: Introductionmentioning

confidence: 99%

“…They also developed the structure of the interval-valued complex FHSS. Rahman et al 24 conceptualized the bijective HSS and discussed its applications in DMPs. Ihsan et al 25 generalized the HSS to hypersoft expert set (HSES) to know the opinions of different experts in different models when attributed sets are further divided into disjoint attribute valued sets.…”

Section: Introductionmentioning

confidence: 99%

An intelligent fuzzy parameterized multi-criteria decision-support system based on intuitionistic fuzzy hypersoft expert set for automobile evaluation

Ihsan

Saeed

Rahman

et al. 2022

Advances in Mechanical Engineering

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In every decision-making scenario, the role of parameters is pertinent but it becomes critical for the situations when parameters are ambiguous to be assessed by the experts so this sort of uncertainty is judged by assigning a fuzzy membership-grade to each parameter. The existing literature on fuzzy parameterization is unable to provide an appropriate model which may cope with hypersoft setting, multi-decisive opinions of experts and intuitionistic setting collectively. This shortcoming leads to the motivation of this study. In this paper, fuzzy parameterized intuitionistic fuzzy hypersoft expert set (FPIFHsES) is characterized which is capable to address the insufficiencies of existing models like fuzzy parameterized intuitionistic fuzzy soft expert set (FPIFSES) for the consideration of multi-argument approximate function. With the entitlement of this function, FPIFHsES tackles the real-life scenario where each attribute is meant to be further classified into its respective sub-attribute valued disjoint set. The FPIFHsES is more flexible and the reliable with the deep analysis of attributes in the decision-support system. The characterization of FPIFHsES is accomplished by employing theoretic, axiomatic, and algorithmic approaches. In order to validate the proposed model, an algorithm is proposed to study its role in decision-making while dealing with a real-world scenario.

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Theory of Bijective Hypersoft Set with Application in Decision Making

Cited by 17 publications

References 19 publications

A Novel Fuzzy Parameterized Fuzzy Hypersoft Set and Riesz Summability Approach Based Decision Support System for Diagnosis of Heart Diseases

A Novel Fuzzy Parameterized Fuzzy Hypersoft Set and Riesz Summability Approach Based Decision Support System for Diagnosis of Heart Diseases

Supplier Selection through Multicriteria Decision-Making Algorithmic Approach Based on Rough Approximation of Fuzzy Hypersoft Sets for Construction Project

An intelligent fuzzy parameterized multi-criteria decision-support system based on intuitionistic fuzzy hypersoft expert set for automobile evaluation

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