Fuzzy Decision Support Modeling for Hydrogen Power Plant Selection Based on Single Valued Neutrosophic Sine Trigonometric Aggregation Operators
Abstract
:1. Introduction
2. Preliminaries
- (1)
- if and only ifandfor each
- (2)
- if and only ifand
- (3)
- (4)
- (5)
3. Novel Sine Trigonometric Operational Laws for SVNNs
- (1)
- and
- (2)
- (1)
- (2)
- (3)
- (4)
- (1)
- and
- (2)
- (1)
- Ifthen
- (2)
- Ifthen
- (3)
- Ifthen
- (a)
- then
- (b)
- then
- (c)
- then
- (1)
- (2)
- (1)
- (2)
- (1)
- (2)
- (3)
- (5)
- (5)
4. Novel Sine Trigonometric Aggregation Operators for SFNs
4.1. Sine Trigonometric Weighted Averaging AOs
4.2. Sine Trigonometric Weighted Geometric AOs
4.3. Fundamental Properties of the Proposed AOs
- (1)
- iff
- (2)
- iff
5. Decision-Making Technique
- Step-1
- Summarize the values of each alternative in term of decision matrix with SVNS information.
- Step-2
- Construct the normalized decision matrix from where is calculated as
- Step-3
- Calculate the aggregate information of the decision-makers information either SFWA/SFWG operator.
- Step-4
- If the attribute weights are known as a prior then utilize them. Otherwise, we compute them by utilizing the concept of the entropy measure. For it, the information of criteria based on entropy measure is computed as
- Step-5
- Using proposed sine trigonometric aggregation operators and attributes weight vector, the collective single-valued neutrosophic information of the each alternative are obtained.
- Step-6
- Evaluate the scores values of collective single-valued neutrosophic numbers and rank according the maximum score values. If the score values of two and are same, then find the accuracy degrees and respectively, then we rank the and according the maximum degree.
- Step-7
- Select the optimal alternative according the maximum score value or accuracy degree.
6. Application of Proposed Decision-Making Technique
6.1. Practical Case Study
- Step-1
- Information result of the expert is listed in Table 1;
- Step-2
- Step-3
- In this practical case study, only one expert (decision-maker) is involved, so here we do not need to compute the aggregated decision matrix.
- Step-4
- Known criteria weight vector is:
- Step-5
- Based on the weight vector and utilizing the proposed sine trigonometric AOs, the aggregated single-valued neutrosophic information of each alternatives are obtained in Table 3:
- Step-6
- Compute the score value of the each aggregated single-valued neutrosophic information of each alternative as follows in Table 4.
- Step-7
- Select the optimal alternative according the maximum score value given in Table 5.In our case study, we aim to select the the right location for the hydrogen power plant according to five attributes: Social Aspect, Environment Aspect, Technology Aspect, Economical Aspect, and Site Characteristics. After implementing the designed algorithm steps to the collective data in the form of a single-valued neutrosophic set based on the novel sine trigonometric operational rules. Based on the above computational process, we can conclude that the alternative is the best among the others and therefore it is highly recommended to select for the task/plan that is required.
6.2. Verification and the Comparison Analysis
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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0.45785 | 0.81292 | 0.71225 | 0.71723 | 0.53521 | |
0.45577 | 0.82036 | 0.70536 | 0.70931 | 0.50665 | |
0.39152 | 0.79117 | 0.68839 | 0.64236 | 0.49041 | |
0.39711 | 0.79969 | 0.67968 | 0.63447 | 0.47160 |
Score Ranking | Best Alternative | |
---|---|---|
Existing Operators | Ranking | Best Alternative |
---|---|---|
NWA [57] | ||
SVNWA [64] | ||
SVNOWA [64] | ||
SVNWG [64] | ||
SVNOWG [64] | ||
SVNFWA [65] | ||
SVNHWA [66] | ||
SVNHWA [66] | ||
NWG [45] | ||
SVNFWG [65] | ||
SVNHWG [66] | ||
SVNHWG [66] | ||
SNWEA [54] | ||
L-SVNWA [55] | ||
L-SVNOWA [55] | ||
L-SVNWG [55] | ||
L-SVNOWG [55] |
Proposed Operators | Ranking | Best Alternative |
---|---|---|
L-SVNWA | ||
L-SVNWG | ||
L-SVNOWA | ||
L-SVNOWG |
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Ashraf, S.; Abdullah, S.; Zeng, S.; Jin, H.; Ghani, F. Fuzzy Decision Support Modeling for Hydrogen Power Plant Selection Based on Single Valued Neutrosophic Sine Trigonometric Aggregation Operators. Symmetry 2020, 12, 298. https://doi.org/10.3390/sym12020298
Ashraf S, Abdullah S, Zeng S, Jin H, Ghani F. Fuzzy Decision Support Modeling for Hydrogen Power Plant Selection Based on Single Valued Neutrosophic Sine Trigonometric Aggregation Operators. Symmetry. 2020; 12(2):298. https://doi.org/10.3390/sym12020298
Chicago/Turabian StyleAshraf, Shahzaib, Saleem Abdullah, Shouzhen Zeng, Huanhuan Jin, and Fazal Ghani. 2020. "Fuzzy Decision Support Modeling for Hydrogen Power Plant Selection Based on Single Valued Neutrosophic Sine Trigonometric Aggregation Operators" Symmetry 12, no. 2: 298. https://doi.org/10.3390/sym12020298
APA StyleAshraf, S., Abdullah, S., Zeng, S., Jin, H., & Ghani, F. (2020). Fuzzy Decision Support Modeling for Hydrogen Power Plant Selection Based on Single Valued Neutrosophic Sine Trigonometric Aggregation Operators. Symmetry, 12(2), 298. https://doi.org/10.3390/sym12020298