An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method
Abstract
:1. Introduction
2. Preliminaries
3. Improved Projection Measures of SVNSs
3.1. The Improved Single-Valued Neutrosophic Projection Measure
3.2. The Single-Valued Neutrosophic Bidirectional Projection Measure
3.3. The Single-Valued Neutrosophic Bidirectional Projection Difference Measure
4. The Single-Valued Neutrosophic Projection-Based QUALIFLEX Method
5. An Illustrative Example
5.1. An Illustration of the Proposed Method
5.2. Comparison Analysis
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Criteria | Suppliers | ||
---|---|---|---|
(0.5,0.6,0.7) | (0.6,0.5,0.5) | (0.5,0.6,0.6) | |
(0.5,0.3,0.4) | (0.6,0.5,0.2) | (0.6,0.3,0.2) | |
(0.5,0.4,0.4) | (0.7,0.3,0.3) | (0.5,0.4,0.3) | |
(0.7,0.3,0.2) | (0.5,0.2,0.4) | (0.6,0.1,0.3) | |
(0.6,0.2,0.3) | (0.5,0.4,0.2) | (0.7,0.2,0.5) | |
(0.7,0.3,0.2) | (0.6,0.4,0.3) | (0.6,0.2,0.6) | |
(0.8,0.6,0.4) | (0.7,0.4,0.6) | (0.6,0.2,0.4) | |
(0.7,0.3,0.5) | (0.8,0.2,0.4) | (0.7,0.2,0.3) | |
(0.7,0.3,0.4) | (0.8,0.2,0.4) | (0.7,0.3,0.4) |
Criteria | Suppliers | ||
---|---|---|---|
(0.7,0.4,0.5) | (0.5,0.5,0.6) | (0.6,0.4,0.5) | |
(0.5,0.3,0.4) | (0.6,0.5,0.2) | (0.6,0.3,0.2) | |
(0.5,0.4,0.4) | (0.7,0.3,0.3) | (0.5,0.4,0.3) | |
(0.7,0.3,0.2) | (0.5,0.2,0.4) | (0.6,0.1,0.3) | |
(0.6,0.2,0.3) | (0.5,0.4,0.2) | (0.7,0.2,0.5) | |
(0.7,0.3,0.2) | (0.6,0.4,0.3) | (0.6,0.2,0.6) | |
(0.8,0.6,0.4) | (0.7,0.4,0.6) | (0.6,0.2,0.4) | |
(0.7,0.3,0.5) | (0.8,0.2,0.4) | (0.7,0.2,0.3) | |
(0.7,0.3,0.4) | (0.8,0.2,0.4) | (0.7,0.3,0.4) |
−0.0505 | −0.0476 | 0.0029 | −0.0476 | −0.0505 | −0.0029 | ||
−0.0658 | −0.0698 | −0.0040 | −0.0698 | −0.0658 | 0.0039 | ||
−0.0078 | −0.0427 | −0.0349 | −0.0427 | −0.0078 | 0.0349 | ||
0.0774 | 0.0596 | −0.0178 | 0.0596 | 0.0774 | 0.0178 | ||
−0.0786 | 0.0900 | 0.1686 | 0.0900 | −0.0786 | −0.1686 | ||
0.0265 | 0.1290 | 0.1025 | 0.1290 | 0.0265 | −0.1025 | ||
0.0243 | −0.0843 | −0.1086 | −0.0843 | 0.0243 | 0.1086 | ||
−0.0045 | −0.0461 | −0.0416 | −0.0461 | −0.0045 | 0.0416 | ||
0.0188 | 0 | −0.0188 | 0 | 0.0188 | 0.0188 | ||
0.0505 | 0.0029 | −0.0476 | 0.0029 | 0.0505 | 0.0476 | ||
0.0658 | −0.0040 | −0.0698 | −0.0040 | 0.0658 | 0.0698 | ||
0.0078 | −0.0349 | −0.0427 | −0.0349 | 0.0078 | 0.0427 | ||
−0.0774 | −0.0178 | 0.0596 | −0.0178 | −0.0774 | −0.0596 | ||
0.0786 | 0.1686 | 0.0900 | 0.1686 | 0.0786 | −0.0900 | ||
−0.0265 | 0.1025 | 0.1290 | 0.1025 | −0.0265 | −0.1290 | ||
−0.0243 | −0.1086 | −0.0843 | −0.1086 | −0.0243 | 0.0843 | ||
0.0045 | −0.0416 | −0.0461 | −0.0416 | 0.0045 | 0.0461 | ||
−0.0188 | −0.0188 | 0 | −0.0188 | −0.0188 | 0 | ||
0.0476 | −0.0029 | −0.0505 | −0.0029 | 0.0476 | 0.0505 | ||
0.0698 | 0.0040 | −0.0658 | 0.0040 | 0.0698 | 0.0658 | ||
0.0427 | 0.0349 | −0.0078 | 0.0349 | 0.0427 | 0.0078 | ||
−0.0596 | 0.0178 | 0.0774 | 0.0178 | −0.0596 | −0.0774 | ||
−0.0900 | −0.1686 | −0.0786 | −0.1686 | −0.0900 | 0.0786 | ||
−0.1290 | −0.1025 | −0.0265 | −0.1025 | −0.1290 | −0.0265 | ||
0.0843 | 0.1086 | 0.0243 | 0.1086 | 0.0843 | −0.0243 | ||
0.0461 | 0.0416 | −0.0045 | 0.0416 | 0.0461 | 0.0045 | ||
0 | 0.0188 | 0.0188 | 0.0188 | 0 | −0.0188 |
−0.0053 | 0.0068 | 0.0121 | 0.0068 | −0.0053 | −0.0121 | ||
0.0053 | 0.0121 | 0.0068 | 0.0121 | 0.0053 | −0.0069 | ||
−0.0069 | −0.0121 | −0.0053 | −0.0121 | −0.0069 | 0.0053 |
0.0137 | −0.0106 | 0.0243 | 0.0106 | −0.0243 | −0.0137 |
References | Aggregation Operator | Rankings |
Ye [31] | Algebraic norm | |
Garg [32] | Frank norm () | |
Liu et al. [50] | Hamacher operator () | or |
Peng et al. [51] | Einstein norm | |
References | Measure | Rankings |
Ye [34] | Cosine similarity | |
Ye [36] | Cross entropy | |
Ye [37] | Bidirectional projection Projection | |
References | Outranking | Rankings |
Peng et al. [29] | ELECTRE III | |
The proposed method | Projection |
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Tian, C.; Zhang, W.Y.; Zhang, S.; Peng, J.J. An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method. Mathematics 2019, 7, 39. https://doi.org/10.3390/math7010039
Tian C, Zhang WY, Zhang S, Peng JJ. An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method. Mathematics. 2019; 7(1):39. https://doi.org/10.3390/math7010039
Chicago/Turabian StyleTian, Chao, Wen Yu Zhang, Shuai Zhang, and Juan Juan Peng. 2019. "An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method" Mathematics 7, no. 1: 39. https://doi.org/10.3390/math7010039
APA StyleTian, C., Zhang, W. Y., Zhang, S., & Peng, J. J. (2019). An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method. Mathematics, 7(1), 39. https://doi.org/10.3390/math7010039