A Decision-Making Approach Based on a Multi Q-Hesitant Fuzzy Soft Multi-Granulation Rough Model
Abstract
:1. Introduction
2. Preliminaries
3. Multi Q-Hesitant Fuzzy Soft Sets
- .
- .
- .
- .
- .
- If and , then
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- .
4. Multi Q-Hesitant Fuzzy Soft Rough Set
- By Definition 17, we haveSimilarly, we can obtain that
- If , by Definition 8, for all . Therefore, thus It follows that
- .Hence, .Similarly, we can prove that
- Hence,Similarly, we can prove that .
- If , then, by Definition 8, we have for all , , then
- Similarly, it can be proved.
5. Multi Q-Hesitant Fuzzy Soft Multi-Granulation Rough Set
- By Definition 18, we have,.Similarly, we can obtain that
- If , by Definition 8, for all , therefore, thus it follows that
- Hence, .Similarly, we can prove that
- .Hence, .Similarly, we can prove that
- If , then, by Definition 8, we have for all , , then.
- It can be proved similarly to 1.
6. Photovoltaic Systems Fault Detection Approach
6.1. The Application Model
- If , then the decision maker will choose as the optimal object, where .
- If and , then the decision maker will choose as the optimal object, where .
- If and , then is the determined fault type in level.
Algorithm 1. Photovoltaic systems fault detection |
|
6.2. Example
6.3. Comparative Analysis and Discussion
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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{(0.2)(0.6,0.4)} | {(0.3,0.7)(0.6)} | {(0.5,0.4,0.6)(0.6,0.5)} | {(0.4,0.2)(0.1,0.3)} | |
{(0.8,0.5)(0.2)} | {(0.6,0.9)(0.2,0.9)} | {(0.3)(0.2,0.7)} | {(0.5,0.2,0.1)(0.1,0.5)} | |
{(0.1,0.3)(0.9,0.7,0.2)} | {(0.5,0.1,)(0.6,0.2)} | {(0.4)(0.5)} | {(0.2,0.4)(0.2,0.8)} | |
{(0.5)(0.6)} | {(0.9,0.5)(0.6,0.7,0.4)} | {(0.6)(0.3,0.1)} | {(0.2)(0.6,0.1)} |
{0.1,0.4,0.8} | {0.9,0.3} | {0.5,0.7,0.1} | {0.2,0.6,} | {0.9,0.3} | {0.1,0.2,0.4} | |
{0.5,0.2} | {0.2,0.6} | {0.3,0.1,0.4} | {0.1,0.8} | {0.1,0.3} | {0.4,0.9,0.3} | |
{0.8,0.1} | {0.1,0.8,0.7} | {0.8,0.3} | {0.2,0.6,0.3} | {0.2,0.4,0.9} | {0.6,0.3} | |
{0.3,0.4,0.5} | {0.8,0.3} | {0.5,0.4,0.3} | {0.1,0.6,0.7} | {0.2,0.9} | {0.3,0.1,0.6} | |
{0.2,0.1} | {0.4,0.7,0.8} | {0.6,0.9,0.4} | {0.7,0.1} | {0.8,0.7,0.2} | {(0.4,0.5)} | |
{0.1,0.2,0.4} | {0.7,0.2,0.5} | {0.5,0.6} | {0.1,0.2,0.8} | {0.4,0.2} | {0.7,0.3,0.1} |
{0.6,0.2,0.7} | {0.3} | {0.4,0.8,0.2} | {0.1,0.4} | {0.2,0.7,0.3} | {0.5,0.9} | |
{0.2,0.6} | {0.3,0.4} | {0.2,0.3} | {0.6,0.2} | {0.3,0.9} | {0.1,0.6,0.3} | |
{0.4,0.2,0.6} | {0.1,0.2} | {0.7,0.5,0.7} | {0.8,0.3,0.9} | {0.9,0.8,0.4} | {0.4,0.3} | |
{0.9,0.6} | {0.4,0.8} | {0.3,0.1,0.9} | {0.6,0.5} | {0.7,0.3,0.6} | {0.1,0.7} | |
{0.2,0.1,0.2} | {0.7,0.4} | {0.1,0.5,0.6} | {0.7,0.1,0.3} | {0.2,0.1} | {0.5,0.9,0.6} | |
{0.7,0.8} | {0.3} | {0.4,0.8} | {0.1,0.2,0.4} | {0.2,0.7,0.3} | {0.4,0.5} |
{0.6,0.2,0.1} | {0.2,0.3} | {0.1,0.2,0.9} | {0.2,0.8} | {0.8,0.5,0.6} | {0.7,0.3,0.6} | |
{0.5,0.3} | {0.3,0.1,0.4} | {0.2,0.3} | {0.9,0.1,0.6} | {0.5,0.4} | {0.2,0.7,0.1} | |
{0.4,0.6,0.5} | {0.5,0.1} | {0.2,0.8,0.7} | {0.8,0.7} | {0.5,0.2,0.1} | {0.4,0.3} | |
{0.3,0.4} | {0.8,0.2,0.5} | {0.4,0.9} | {0.1,0.2} | {0.8,0.5,0.3} | {0.5,0.3} | |
{0.4,0.3,0.6} | {0.5,0.4} | {0.4,0.7,0.5} | {0.4,0.6} | {0.7,0.6,0.2} | {0.8,0.9,0.2} | |
{0.8,0.2} | {0.3,0.1,0.3} | {0.9,0.1} | {0.4,0.6,0.7} | {0.3,0.8} | {0.6,0.4,0.7} |
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Alsager, K.M.; Alshehri, N.O.; Akram, M. A Decision-Making Approach Based on a Multi Q-Hesitant Fuzzy Soft Multi-Granulation Rough Model. Symmetry 2018, 10, 711. https://doi.org/10.3390/sym10120711
Alsager KM, Alshehri NO, Akram M. A Decision-Making Approach Based on a Multi Q-Hesitant Fuzzy Soft Multi-Granulation Rough Model. Symmetry. 2018; 10(12):711. https://doi.org/10.3390/sym10120711
Chicago/Turabian StyleAlsager, Kholood Mohammad, Noura Omair Alshehri, and Muhammad Akram. 2018. "A Decision-Making Approach Based on a Multi Q-Hesitant Fuzzy Soft Multi-Granulation Rough Model" Symmetry 10, no. 12: 711. https://doi.org/10.3390/sym10120711