An Extended Method Using Topsis and Vikor for Multiple Attribute Decision Making With Multiple Decision Makers and Single Valued Neutrosophic Numbers

Pouresmaeil, Hassan; Shivanian, Elyas; Khorram, Esmaile; Fathabadi, H. Salehi

doi:10.17654/as050040261

Cited by 29 publications

(17 citation statements)

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“…As simplified forms of neutrosophic sets, Smarandache [10], Wang et al [11,12] and Ye [13] introduced single-valued neutrosophic sets (SVNSs) and interval neutrosophic sets (INSs), and simplified neutrosophic sets (SNSs) as subclasses of neutrosophic sets for easy engineering applications. Since then, SVNSs, INSs, and SNSs have been widely applied to various areas, such as image processing [14][15][16], decision-making [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], clustering analyses [33,34], medical diagnoses [35,36], and fault diagnoses [37]. Recently, Ali et al [38] and Jun et al [39] have extended cubic sets to the neutrosophic sets and proposed the concepts of neutrosophic cubic sets (NCSs), including internal NCSs and external NCSs, subsequently introducing some logic operations of NCSs, such as the P-union, P-intersection, R-union, and R-intersection of NCSs.…”

Section: Introductionmentioning

confidence: 99%

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

2017

Symmetry

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Abstract:The neutrosophic cubic set can contain much more information to express its interval neutrosophic numbers and single-valued neutrosophic numbers simultaneously in indeterminate environments. Hence, it is a usual tool for expressing much more information in complex decision-making problems. Unfortunately, there has been no research on similarity measures of neutrosophic cubic sets so far. Since the similarity measure is an important mathematical tool in decision-making problems, this paper proposes three cosine measures between neutrosophic cubic sets based on the included angle cosine of two vectors, distance, and cosine functions, and investigates their properties. Then, we develop a cosine measures-based multiple attribute decision-making method under a neutrosophic cubic environment in which, from the cosine measure between each alternative (each evaluated neutrosophic cubic set) and the ideal alternative (the ideal neutrosophic cubic set), the ranking order of alternatives and the best option can be obtained, corresponding to the cosine measure values in the decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to illustrate the application and feasibility of the developed decision-making method.

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Section: Introductionmentioning

confidence: 99%

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

2017

Symmetry

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“…Furthermore, we compared the proposed methods with related methods and discovered that the selection result using the proposed methods was the same as the majority of existing methods. In the future, we will make further research bipolar neutrosophic sets, using, e.g., the technique for order preference by similarity to an ideal solution (TOPSIS) and VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje, that means: multicriteria optimization and compromise solution, with pronunciation: vikor) methods with BNS [23], the weighted aggregated sum product assessment (WASPAS) method with BNS [24], the Multi-Attribute Market Value Assessment ( MAMVA) method with BNS [25], and so on [26][27][28].…”

Section: Discussionmentioning

confidence: 99%

Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment

Fan

Feng

et al. 2019

Mathematics

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In real applications, most decisions are fuzzy decisions, and the decision results mainly depend on the choice of aggregation operators. In order to aggregate information more scientifically and reasonably, the Heronian mean operator was studied in this paper. Considering the advantages and limitations of the Heronian mean (HM) operator, four Heronian mean operators for bipolar neutrosophic number (BNN) are proposed: the BNN generalized weighted HM (BNNGWHM) operator, the BNN improved generalized weighted HM (BNNIGWHM) operator, the BNN generalized weighted geometry HM (BNNGWGHM) operator, and the BNN improved generalized weighted geometry HM (BNNIGWGHM) operator. Then, their propositions were examined. Furthermore, two multi-criteria decision methods based on the proposed BNNIGWHM and BNNIGWGHM operator are introduced under a BNN environment. Lastly, the effectiveness of the new methods was verified with an example.Mathematics 2019, 7, 97 2 of 16 and put forward the bipolar fuzzy set (BFS). The founder of the fuzzy set theory, Zadeh, also affirmed that the bipolar fuzzy set theory was a breakthrough in traditional fuzzy set theory [10]. Then, Zemankova et al. [11] discussed a more generalized multipolar fuzzy problem, and pointed out that the multipolar fuzzy problem can be divided into multiple bipolar fuzzy problems. Chen et al. [12] studied m-polar fuzzy sets. Bosc and Pivert [13] introduced a study on fuzzy bipolar relational algebra. Manemaran and Chellappa [14] gave some applications of bipolar fuzzy groups. Zhou and Li [15] introduced some applications of bipolar fuzzy sets in semiring. Deli et al. [16] put forward a bipolar neutrosophic set (BNS), which can describe bipolar information. Later, some studies about BNS were put forward [17][18][19][20]. In this paper, we propose four Heronian mean operators for bipolar neutrosophic number (BNN). Compared with the literature [17][18][19], the HM operator can embody the interaction between attributes to avoid unreasonable situations in information aggregation. Compared with the literature [20], the Bonferroni mean (BM) aggregation operator not only neglects the relationship between each attribute and itself, but also considers the relationship between each attribute and other attributes repeatedly. However, the BM aggregation operator has large computational complexity, but the Heronian mean (HM) can overcome these two shortcomings.The remaining sections are organized as follows: some related concepts are reviewed in Section 2. The four operators are defined and their properties are investigated in Section 3; these four operators are BNN generalized weighted HM (BNNGWHM), BNN improved generalized weighted HM (BNNIGWHM), BNN generalized weighted geometry HM (BNNGWGHM), and BNN improved generalized weighted geometry HM (BNNIGWGHM). Multi-criteria decision-making (MCDM) methods based on the BNNIGWHM and BNNIGWGHM operators are established in Section 4. A numerical example is provided and the effects of parameters p and q are analyzed in Section 5. The conclusion...

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“…Ye [33] proposed two similarity measures between INNs. The SVNS and INS have received more and more attention since their appearance [34][35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

VIKOR Method for Interval Neutrosophic Multiple Attribute Group Decision-Making

Huang

Wei

2017

Information

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Abstract:In this paper, we will extend the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method to multiple attribute group decision-making (MAGDM) with interval neutrosophic numbers (INNs). Firstly, the basic concepts of INNs are briefly presented. The method first aggregates all individual decision-makers' assessment information based on an interval neutrosophic weighted averaging (INWA) operator, and then employs the extended classical VIKOR method to solve MAGDM problems with INNs. The validity and stability of this method are verified by example analysis and sensitivity analysis, and its superiority is illustrated by a comparison with the existing methods.

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An Extended Method Using Topsis and Vikor for Multiple Attribute Decision Making With Multiple Decision Makers and Single Valued Neutrosophic Numbers

Cited by 29 publications

References 0 publications

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment

VIKOR Method for Interval Neutrosophic Multiple Attribute Group Decision-Making

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