A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making

Zhan, Jianming; Liu, Qi; Herawan, Tutut

doi:10.1016/j.asoc.2016.09.012

Cited by 168 publications

(40 citation statements)

References 50 publications

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“…After Shabir's SR-set, some better different conclusions were obtained than the Feng's SR-set. It is pointed out that Zhan in [25] made use of Shabir's SR-sets to study SR-hemirings and discussed the properties of SR-hemirings. At the same time, Zhan et al also put up a corresponding multicriteria group decision making.…”

Section: Resultsmentioning

confidence: 99%

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A study on soft rough semigroups and corresponding decision making applications

2017

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Abstract:In this paper, we study a kind of soft rough semigroups according to Shabir's idea. We define the upper and lower approximations of a subset of a semigroup. According to Zhan's idea over hemirings, we also define a kind of new C -soft sets and C C -soft sets over semigroups. In view of this theory, we investigate the soft rough ideals (prime ideals, bi-ideals, interior ideals, quasi-ideals, regular semigroups). Finally, we give two decision making methods: one is for looking a best a parameter which is to the nearest semigroup, the other is to choose a parameter which keeps the maximum regularity of regular semigroups.

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Section: Resultsmentioning

confidence: 99%

“…More recently, Zhang in [24] gave a way of multi-attribute decision making based on SR-sets. According to this kind of SR-set, Zhan et al [25] discussed SR-hemirings under C -soft sets and C C -soft sets and obtained some different conclusions. At the same time, Zhan et al made corresponding multicriteria for group decision making.…”

Section: Introductionmentioning

confidence: 99%

A study on soft rough semigroups and corresponding decision making applications

2017

Self Cite

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“…The exploitation of soft sets and hybrid soft sets models in decision-making shows a great development in the recent years [18][19][20][21][22]. The utilization of soft rough sets models in decision-making shows a promising prospect.…”

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%

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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“…Most of them are vague than precise, and uncertainty is a common research topic of many branches of science (economics, engineering, environment, management science, medical science, and so on). However, uncertainty is an unintelligible expression without a straightforward description, and many theories were established, such as probability theory, fuzzy set theory [1][2][3], intuitionistic fuzzy set theory [4], hesitant fuzzy set theory [5][6][7][8], soft set theory [9][10][11][12], rough set theory [13][14][15][16][17], granular computing [18][19][20][21][22][23][24][25][26][27], et al…”

Section: Introductionmentioning

confidence: 99%

New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

Zhang

2017

Symmetry

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Abstract:In this paper, some new operations and basic properties of picture fuzzy relations are intensively studied. First, a new inclusion relation (called type-2 inclusion relation) of picture fuzzy relations is introduced, as well as the corresponding type-2 union, type-2 intersection and type-2 complement operations. Second, the notions of anti-reflexive kernel, symmetric kernel, reflexive closure and symmetric closure of a picture fuzzy relation are introduced and their properties are explored. Moreover, a new method to solve picture fuzzy comprehensive evaluation problems is proposed by defining the new composition operation of picture fuzzy relations, and the picture fuzzy comprehensive evaluation model is built. Finally, an application example (about investment risk) of picture fuzzy comprehensive evaluation is given, and the effective experiment results are obtained.

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A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making

Cited by 168 publications

References 50 publications

A study on soft rough semigroups and corresponding decision making applications

A study on soft rough semigroups and corresponding decision making applications

A Comparative Study of Some Soft Rough Sets

New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

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