Fuzzy covering-based rough set on two different universes and its application

Bin, Yang

doi:10.1007/s10462-021-10115-y

Cited by 16 publications

(4 citation statements)

References 85 publications

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“…Zhu [59] investigated topological approaches to CRSs. Yang [47] pioneered fuzzy CRSs on two different universes with application in DM. Zhang and Dai [54] redefined FRS models in fuzzy β-covering approximation spaces.…”

Section: B An Overview On the Development Of Covering-based Rssmentioning

confidence: 99%

A Novel Approach for Fuzzification of Rough Sets Based on Fuzzy Preference Relation: Properties and Application to Medicine Selection Problem

Gul,

Ayub,

Shabir

et al. 2024

IEEE Access

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Preference analysis is a significant component in decision-making (DM) when selecting an optimal alternative. By comparing any two alternatives pairwise, preference relations (PRs) effectively depict the preference degrees of decision-makers (DMrs). The rough set theory (RST) has been effectively applied to cope with preference analysis by swapping the equivalence relation (Er) with the dominance relation (DR). In this study, we propose new transfer functions to construct alternatives' upward/downward fuzzy preference degree (FPD) for evaluating upward and downward fuzzy PRs (FPRs). Based on these newly proposed transfer functions, we present a novel method for fuzzifying RSs called the upward αfuzzified preference rough sets (α ↑ -FPRSs). The basic properties of the proposed α ↑ -FPRSs are thoroughly studied. Moreover, several uncertainty measures related to α ↑ -FPRSs are presented. Meanwhile, we offered the notion of upward fuzzy β-covering (UFβC) and upward fuzzy β-neighborhood (UFβ-nghd), upward β-neighborhood (Uβ-nghd), and several related properties are explored. Based on UFβ-nghd and Uβ-nghd, we construct two new models of UFβC rough sets (UFβ-CRSs) along with their properties. We formulate a novel technique of multi-attribute DM (MADM). To legitimise the practicality of our proposed model, we provide a real-life example of selecting an appropriate medication to treat a specific disease. Finally, we look into the efficacy of the launched scheme through a comparison study.INDEX TERMS Rough set, Preference analysis, Upward fuzzy β-covering, MADM.

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Section: B An Overview On the Development Of Covering-based Rssmentioning

confidence: 99%

A Novel Approach for Fuzzification of Rough Sets Based on Fuzzy Preference Relation: Properties and Application to Medicine Selection Problem

Gul,

Ayub,

Shabir

et al. 2024

IEEE Access

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“…As it is well-known that the interior and closure topological operators behave similarly to the lower and upper approximations; so, in forthcoming works, we plan to study the counterparts of these models via topological structures. In addition, we will benefit from the hybridization of rough set theory with some approaches such as soft sets and fuzzy sets [30], [34] to introduce these approximation spaces via these hybridized frames and show their role in efficiently dealing with uncertain knowledge.…”

Section: Rank1mentioning

confidence: 99%

Improvement of Approximation Spaces Using Maximal Left Neighborhoods and Ideals

Al-shami

Hosny

2022

IEEE Access

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Rough set theory was introduced by Pawlak, in 1982, as a methodology to discover structural relationships within imprecise and uncertain data. This theory has been generalized using the idea of neighborhood systems to be more efficient to get rid of uncertainty and deal with a wide scope of practical applications. Motivated by this idea, in this work, we initiate novel generalized rough set models using the concepts of "maximal left neighborhoods and ideals". Their basic features are studied and the relationships between them are revealed. The main merits of these models, as we prove, are first to preserve almost all major properties of approximation operators with respect to the Pawlak model. Second, they keep the monotonic property, which leads to an efficient evaluation of the uncertainty in the data, and third, these models enlarge the knowledge gotten from the information systems because they minimize the vagueness regions more than some previous models. We complete this manuscript by applying the proposed approach to analyze educational data and illustrate its role to improve the obtained classifications of objects and show the great performance of the present approach against other ones. Elucidative examples that support the obtained results are provided.

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“…Zhang and Zhan (2019) contributed fuzzy soft 𝛽-coverings and defined four different fuzzy soft 𝛽covering based fuzzy rough sets (FS𝛽CFRS). Yang (2022) proposed fuzzy covering based rough set over dual universe as an extension of single universe concept.…”

Section: Introductionmentioning

confidence: 99%

Generalized Z-fuzzy soft β-covering based rough matrices and its application to MAGDM problem based on AHP method

Sivaprakasam

Angamuthu

2023

Decis. Mak. Appl. Manag. Eng.

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Fuzzy, rough, and soft sets are different mathematical tools mainly developed to deal with uncertainty. Combining these theories has a wide range of applications in decision analysis. In this paper, we defined a generalized Z-fuzzy soft -covering-based rough matrices. Some algebraic properties are explored for this newly constructed matrix. The main aim of this paper is to propose a novel MAGDM model using generalized Z-fuzzy soft -covering-based rough matrices. A MAGDM algorithm based on the AHP method is created to recruit the best candidate for an assistant professor job in an institute, and a numerical example is presented to demonstrate the created method.

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Fuzzy covering-based rough set on two different universes and its application

Cited by 16 publications

References 85 publications

A Novel Approach for Fuzzification of Rough Sets Based on Fuzzy Preference Relation: Properties and Application to Medicine Selection Problem

A Novel Approach for Fuzzification of Rough Sets Based on Fuzzy Preference Relation: Properties and Application to Medicine Selection Problem

Improvement of Approximation Spaces Using Maximal Left Neighborhoods and Ideals

Generalized Z-fuzzy soft β-covering based rough matrices and its application to MAGDM problem based on AHP method

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