A Novel Operator to Solve Decision-Making Problems Under Trapezoidal Fuzzy Multi Numbers and Its Application

Abstract

This article investigates solutions to multiple attribute decision-making (MADM) problems in which the attribute values take the form of trapezoidal fuzzy multi-numbers. To do this, this paper proposes a kind of mean aggregation operator called the Bonferroni harmonic mean operator for aggregating trapezoidal fuzzy information. Then, an approach that is a solution algorithm has been developed to find a solution to multi-attribute decision-making problems. Afterwards, an illustrative example has been given to verify the developed approach and to show its usefulness and efficiency. Finally, a comparison table has been presented to compare the proposed method with some existing methods.

Keywords

• Fuzzy multi sets
• trapezoidal fuzzy multi numbers
• Bonferroni harmonic mean
• multiple attribute decision making

References

1. L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338-353.
2. R. R. Yager, On the Theory of Bags, International Journal of General Systems 13 (1986) 23-37.
3. S. Miyamoto, Fuzzy Multi Sets and Their Generalizations, Workshop on Membrane Computing: Multiset Processing 2235 (2000) 225-235.
4. S. Miyamoto, Data Structure and Operations for Fuzzy Multisets, Transactions on Rough Sets II, Lecture Notes in Computer Science 3135 (2004) 189-200.
5. S. Sebastian, T. V. Ramakrishnan, Multi-Fuzzy Sets, International Mathematical Forum 5 (50) (2010) 2471-2476.
6. S. Sebastian, T. V. Ramakrishnan, Multi-Fuzzy Extensions of Functions, Advances in Adaptive Data Analysis 3 (3) (2011) 339-350.
7. V. Uluçay, İ. Deli, M. Şahin, Trapezoidal Fuzzy Multi-Number and Its Application to Multi-Criteria Decision-Making Problems, Neural Computing and Applications 30 (5) (2018) 1469-1478.
8. İ. Deli, M. A. Kele\c{s}, Distance Measures on Trapezoidal Fuzzy Multi-Numbers and Application to Multi-Criteria Decision-Making Problems, Soft Computing 25 (2021) 5979-5992.

9. M. Şahin, V. Uluçay, F. S. Yılmaz, Dice Vector Similarity Measure Based on Multi-Criteria Decision Making with Trapezoidal Fuzzy Multi-Numbers, Neutrosophic Triplet Structures Volume I, Chapter 13 (2017) Pons Editions, Brussels, Belgium.
10. M. Şahin, V. Uluçay, F. S. Yılmaz, Improved Hybrid Vector Similarity Measures and Their Applications on Trapezoidal Fuzzy Multi Numbers, Neutrosophic Triplet Structures Volume I, Chapter 12 (2019) Pons Editions, Brussels, Belgium.
11. V. Uluçay, A New Similarity Function of Trapezoidal Fuzzy Multi-Numbers Based on Multi-Criteria Decision Making, Journal of the Institute of Science and Technology 10 (2) (2020) 1233-1246.
12. C. Bonferroni, Sulle Medie Multiple di Potenze, Bolletino Matematica Italiana, 5 (1950) 267-270.
13. R. R. Yager, On Generalized Bonferroni Mean Operators for Multi-criteria Aggregation, International Journal of Approximate Reasoning 59 (2009) 1279-1286.
14. G. Beliakov, S. James, J. Mordelová, T. Rückschlossová, R. R. Yager, Generalized Bonferroni Mean Operators in Multi-criteria Aggregation, Fuzzy Sets and Systems 161 (2010) 2227-2242.
15. Z. Xu, Fuzzy Harmonic Mean Operators, International Journal of Intelligent Systems 24 (2) (2009) 52-172.
16. G. W. Wei, FIOWHM Operator and Its Application to Multiple Attribute Group Decision Making, Expert Systems with Applications 38 (4) (2011) 2984-2989.
17. H. Sun, M. Sun, Generalized Bonferroni Harmonic Mean Operators and Their Application to Multiple Attribute Decision Making, Journal of Computer Information Systems 8 (14) (2012) 5717-5724.
18. İ. Deli, A TOPSIS Method by Using Generalized Trapezoidal Hesitant Fuzzy Numbers and Application to a Robot Selection Problem, Journal of Intelligent and Fuzzy Systems 38 (1) (2020) 779-793.
19. İ. Deli, F. Karaaslan, Generalized Trapezoidal Hesitant Fuzzy Numbers and Their Applications to Multi Criteria Decision-Making Problems, Soft Computing 25 (2021) 1017-1032.
20. H. Wang, X. Wang, L. Wang, Multi-Criteria Decision Making Based on Archimedean Bonferroni Mean Operators of Hesitant Fermatean 2-Tuple Linguistic Terms, Complexity 4 (2019) 1-19.
21. V. Torra, Y. Narukawa, On Hesitant Fuzzy Sets and Decision, in: H. T. Jeon, K. C. Min, K. W. Oh (Eds.), IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, pp. 1378-1382.
22. M. Xia, Z. Xu, Generalized Intuitionistic Fuzzy Aggregation Based on Hamacher t-conorm and t-norm, International Journal of Intelligent Systems 27 (2011) 23-47.
23. Z. Xu, Hesitant Fuzzy Sets Theory, Studies in Fuzziness and Soft Computing, Springer, 2014.
24. H. J. Zimmermann, Fuzzy Set Theory and Its Applications, Fourth Edition, Kluwer Academic Publishers, Dordrecht, 2001.
25. D. Li, Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, Studies in Fuzziness and Soft Computing, 308, Springer, 2014.
26. İ. Deli, Bonferroni Mean Operators of Generalized Trapezoidal Hesitant Fuzzy Numbers and Their Application to Decision-making Problems, Soft Computing 25 (2021) 4925-4949.
27. W. Su, J. Zhou, S. Zeng, C. Zhang, K. Yu, A Novel Method for Intuitionistic Fuzzy MAGDM with Bonferroni Weighted Harmonic Means, Recent Patents on Computer Science 10 (2017) 178-189.