New Soft Rough Set Approximations

Alkhazaleh, Shawkat; Marei, Emad

doi:10.5391/ijfis.2021.21.2.123

Cited by 6 publications

(27 citation statements)

References 38 publications

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“…A similar relationship between SS and RS was established by Feng et al [8]. Alkhazaleh and Marei [9] put forward new SRS approximations. Feng et al [10] proposed generalized uni-int DM schemes based on choice value SSs.…”

Section: Introductionsupporting

confidence: 60%

A Study on Soft Multi-Granulation Rough Sets and Their Applications

et al. 2022

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Rough set (RS) and soft set (SS) theories are two successful mathematical approaches to dealing with uncertainty in data analysis. The classical soft rough set (SRS) theory proposed by Feng et al. [8] offers a formal theoretical framework for solving the uncertainty under a single granulation environment. However, it is essential to note that the SRS theory cannot be applied in the context of multi-granulation in the real world. To address this issue, in this paper, we introduce the idea of soft multi-granulation RS (SMGRS) model based on two soft binary relations (S-BRs). Axiomatic operations, lower soft rough approximation space (lower SRA-space) and upper soft rough approximation space (upper SRA-space), are defined through after sets of soft relations. After that, the concept of SMGRSs is applied to a significant part of commutative algebra, group theory. In this respect, the primitive notions of SRAspaces are defined with the help of two normal soft groups (NSGs). In groups, several important structural properties related to SMGRS are investigated in detail with illustrative examples. It is shown that SMGRS in groups may be influential in decision-making (DM) by some numerical examples. To demonstrate the flexibility, superiority, and effectiveness of the suggested technique, some comparative examples are given with some existing methods.

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Section: Introductionsupporting

confidence: 60%

A Study on Soft Multi-Granulation Rough Sets and Their Applications

et al. 2022

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“…The following two examples demonstrate the validity of properties (2) and (3) in Proposition 4.2. Example 5.5 Example 3.7 in [3] shows that even if N = (L, T ) is a full soft increasing set, it may not be a full soft set.…”

Section: Isr Incmentioning

confidence: 99%

“…The increasing (decreasing) soft rough approach builds on the foundations of these previous models and offers a more specific and broader method for solving real-life problems. It is a modified version of the approach proposed by Shawkat et al [3] and addresses some of the limitations of their method, such as the modified soft lower approximation of the universe set not being equal to the universe and the modified soft upper approximation of the empty set not being empty.…”

Section: Introductionmentioning

confidence: 99%

“…

The paper presents a novel method for generating increasing and decreasing soft rough set approximations that addresses limitations of a previous approach by Shawkat et al [3], which suffered from issues such as the modified soft lower approximation not being equal to the universe set and the modified soft upper approximation being empty. The proposed method is described through propositions and examples and can be applied to both qualitative and quantitative real-world problems.

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confidence: 99%

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Increasing and Decreasing Soft RoughSet Approximations

El-Sheikh

Kandil

Hussien

2023

Preprint

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The paper presents a novel method for generating increasing and decreasing soft rough set approximations that addresses limitations of a previous approach by Shawkat et al. [3], which su ered from issues such as the modi ed soft lower approximation not being equal to the universe set and the modi ed soft upper approximation being empty. The proposed method is described through propositions and examples and can be applied to both qualitative and quantitative real-world problems. It is compared to the classical soft rough set model and aims to improve accuracy by converting partial ordered relations to linear ordered relations, such as directed or total directed relations, where every subset becomes crisp. The concepts and results are illustrated through examples. Overall, the new method o ers a generic solution that addresses the shortcomings of the previous approach and can improve the accuracy of soft rough set approximations in various domains. Mathematics Subject Classi cation (2020): 03C55, 03E04, 54G20 and 92C50.

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“…The generalizations of fuzzy rough sets constructed using fuzzy covering were studied in [6,7]. New types of generalized rough sets based on neighborhoods with medical applications were studied in [8][9][10][11][12][13][14][15][16][17]. The second research strategy is changing the type of relations from equivalence to tolerance relations to generalize rough sets in [18] and using similarity relations in [19].…”

Section: Introductionmentioning

confidence: 99%