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

Year 2022, Issue: 40, 60 - 73, 30.09.2022

Davut Kesen , İrfan Deli

https://doi.org/10.53570/jnt.1153262

Cited By: 2

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

• L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338-353.
• R. R. Yager, On the Theory of Bags, International Journal of General Systems 13 (1986) 23-37.
• S. Miyamoto, Fuzzy Multi Sets and Their Generalizations, Workshop on Membrane Computing: Multiset Processing 2235 (2000) 225-235.
• S. Miyamoto, Data Structure and Operations for Fuzzy Multisets, Transactions on Rough Sets II, Lecture Notes in Computer Science 3135 (2004) 189-200.
• S. Sebastian, T. V. Ramakrishnan, Multi-Fuzzy Sets, International Mathematical Forum 5 (50) (2010) 2471-2476.
• S. Sebastian, T. V. Ramakrishnan, Multi-Fuzzy Extensions of Functions, Advances in Adaptive Data Analysis 3 (3) (2011) 339-350.
• 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.
• 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.
• 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.
• 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.
• 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.
• C. Bonferroni, Sulle Medie Multiple di Potenze, Bolletino Matematica Italiana, 5 (1950) 267-270.
• R. R. Yager, On Generalized Bonferroni Mean Operators for Multi-criteria Aggregation, International Journal of Approximate Reasoning 59 (2009) 1279-1286.
• 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.
• Z. Xu, Fuzzy Harmonic Mean Operators, International Journal of Intelligent Systems 24 (2) (2009) 52-172.
• G. W. Wei, FIOWHM Operator and Its Application to Multiple Attribute Group Decision Making, Expert Systems with Applications 38 (4) (2011) 2984-2989.
• 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.
• 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.
• İ. Deli, F. Karaaslan, Generalized Trapezoidal Hesitant Fuzzy Numbers and Their Applications to Multi Criteria Decision-Making Problems, Soft Computing 25 (2021) 1017-1032.
• 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.
• 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.
• 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.
• Z. Xu, Hesitant Fuzzy Sets Theory, Studies in Fuzziness and Soft Computing, Springer, 2014.
• H. J. Zimmermann, Fuzzy Set Theory and Its Applications, Fourth Edition, Kluwer Academic Publishers, Dordrecht, 2001.
• D. Li, Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, Studies in Fuzziness and Soft Computing, 308, Springer, 2014.
• İ. Deli, Bonferroni Mean Operators of Generalized Trapezoidal Hesitant Fuzzy Numbers and Their Application to Decision-making Problems, Soft Computing 25 (2021) 4925-4949.
• 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.