A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making

Zhan, Jianming; Zhu, Kuanyun

doi:10.1007/s00500-016-2119-9

Cited by 108 publications

(24 citation statements)

References 36 publications

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“…The two mathematic models that correspond with these approximation operators have been interconnected by this theorem, which could be regarded as a theoretical proof for the rationality of MSR sets. Benefitting from the notion of MSR set, Zhan et al provided the definition of Z-soft rough fuzzy set in a recent work [17] . Definition 6.…”

Section: The Relationships Between Msr Approximations and Pawlak's Romentioning

confidence: 99%

“…Let ( f , A) be a soft set over U and (U, ϕ) the MSR approximation space. For any fuzzy set µ ∈ F(U), the Z-lower and Z-upper soft rough approximations of µ are denoted by µ ϕ and µ ϕ , respectively, which are fuzzy sets on U given by [17]:…”

Section: The Relationships Between Msr Approximations and Pawlak's Romentioning

confidence: 99%

“…Recently, Shabir et al [16] noticed that Feng et al's soft rough sets [12] suffer from some unexpected properties such as the upper approximation of a non-empty set might be empty and a subset set X might not be contained in its upper approximation. To resolve this problem, Shabir et al [16] modified their soft rough sets and introduced the modified soft rough set (MSR set), which has already been extended to fuzzy soft sets [17], and Z-soft rough fuzzy sets was proposed, and its application in decision-making problems was analyzed.…”

Section: Introductionmentioning

confidence: 99%

“…The utilization of soft rough sets models in decision-making shows a promising prospect. Different decision-making approaches have been put forth based on MSR set [20], Z-soft rough fuzzy sets [17], Z-soft fuzzy rough set [21], and other soft rough sets models [23,24]. If the researchers could have a thorough knowledge of the connections among various soft rough sets, we believe that decision-making approaches under framework of soft rough sets could be applied in a more flexible and reliable way.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Comparative Study of Some Soft Rough Sets

2017

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Through the combination of different types of sets such as fuzzy sets, soft sets and rough sets, abundant hybrid models have been presented in order to take advantage of each other and handle uncertainties. A comparative study of relationships and interconnections of some existing hybrid models has been carried out. Some foundational properties of modified soft rough sets (MSR sets) are analyzed. It is pointed out that MSR approximation operators are some kinds of Pawlak approximation operators, whereas approximation operators of Z-soft rough fuzzy sets are equivalent to approximation operators of rough fuzzy sets. The relationships among F-soft rough fuzzy sets, M-soft rough fuzzy sets and Z-soft rough fuzzy sets are surveyed. A new model called soft rough soft sets has been provided as the generalization of F-soft rough sets, and its application in group decision-making has been studied. Various soft rough sets models show great potential as a tool to solve decision-making problems, and a depth study of the connections among these models contributes to the flexible application of soft rough sets based decision-making approaches.

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Section: The Relationships Between Msr Approximations and Pawlak's Romentioning

confidence: 99%

Section: The Relationships Between Msr Approximations and Pawlak's Romentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Comparative Study of Some Soft Rough Sets

2017

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“…It has been applied in diverse domains such as pattern recognition [31], machine learning [32], knowledge acquisition [33], and decision support systems [34]. Unlike other approaches that deal with vague concepts such as fuzzy set theory, rough set theory provides an objective form of analysis without any preliminary assumptions on membership association, thus, demonstrating power in information granulation [35] and uncertainty analysis [36].…”

Section: Introductionmentioning

confidence: 99%