Bonferroni arithmetic mean operator of trapezoidal fuzzy multi numbers and its decision-making application to crafting the ideal student dormitory

Year 2023, Volume: 12 Issue: 3, 166 - 187, 31.12.2023

İrfan Deli , Davut Kesen

https://doi.org/10.54187/jnrs.1369105

https://izlik.org/JA58ZT86CL

Abstract

Trapezoidal fuzzy multi-numbers (TFM-numbers) are widely used in the decision-making process when choosing among various potential values for alternatives. In this context, we present a methodology for multiple attribute decision-making problems in terms of TFM-numbers. This is why we have developed an aggregation technique known as the TFM-Bonferroni arithmetic mean operator. This operator is utilized to aggregate information represented by TFM-numbers. We then gave an examination of its properties and discussed its special cases. Furthermore, we introduce an approach designed to tackle multiple attribute decision-making as part of TFM environments. We subsequently apply this approach to solve multi-attribute decision-making problems. To illustrate its practicality, we provide an example in daily life. Finally, we offer an analysis table that facilitates a comparative evaluation of our proposed approach against existing methods.

Keywords

Fuzzy multi set , Trapezoidal fuzzy number , Trapezoidal fuzzy multi numbers , Bonferroni arithmetic mean , Multiple attribute decision making

References

• L. A. Zadeh, Fuzzy sets, Information and Control 8 (3) (1965) 338-353.
• A. Sarkar, G. Sahoo, U. C. Sahoo, Application of fuzzy logic in transportation planning, International Journal on Soft Computing 3 (2) (2012) 1-21.
• S. Şahin, B. Bozkurt, A. Kargın, Comparing the social justice leadership behaviors of school administrators according to teacher perceptions using classical and fuzzy logic, in: F. Smarandache M. Şahin, D. Bakbak, V. Uluçay, A. Kargın (Eds.), NeutroAlgebra Theory, Vol. I, The Educational Publisher Inc., United States, 2021, Ch. 9, pp. 145-160.
• S. Şahin, M. Kısaoğlu, A. Kargın, In determining the level of teachers' commitment to the teaching profession using classical and fuzzy logic, in: F. Smarandache M. Şahin, D. Bakbak, V. Uluçay, A. Kargın (Eds.), Neutrosophic Algebraic Structures and Their Applications, Vol. 1, NSIA Publishing House, Gallup, 2022, Ch. 12, pp. 183-200.
• J. G. Dijkman, H. V. Haeringen, S. J. De Lange, Fuzzy numbers, Journal of Mathematical Analysis and Applications 92 (2) (1983) 301-341.
• R. Srinivasan, N. Karthikeyan, A. Jayaraja, A proposed technique to resolve transportation problem by trapezoidal fuzzy numbers, Indian Journal of Science and Technology 14 (20) (2021) 1642-1646.
• D. Dubois, L. Foulloy, G. Mauris, H. Prade, Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities, Reliable Computing 10 (4) (2004) 273-297.
• S. S. Roseline, E. C. H. Amirtharaj, Generalized fuzzy Hungarian method for generalized trapezoidal fuzzy transportation problem with ranking of generalized fuzzy numbers, International Journal of Applied Mathematics Statistical Sciences 3 (1) (2014) 5-12.
• M. Antonio, On some structures of fuzzy numbers, Iranian Journal of Fuzzy Systems 6 (4) (2009) 49-59.
• D. Chakraborty, D. Guha, Addition two generalized fuzzy numbers, International Journal of Industrial Mathematics 2 (1) (2010) 9-20.
• 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, Bonferroni mean operators of generalized trapezoidal hesitant fuzzy numbers and their application to decision-making problems, Soft Computing 25 (6) (2021) 4925-4949.
• İ. Deli, M. A. Keleş, Distance measures on trapezoidal fuzzy multi-numbers and application to multi-criteria decision-making problems, Soft Computing 25 (8) (2021) 5979-5992.
• M. Riaz, M. R. Hashmi, Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems, Journal of Intelligent and Fuzzy Systems 37 (4) (2019) 5417-5439.
• A. Aydoğdu, Novel linear Diophantine fuzzy information measures based decision making approach using extended VIKOR method, IEEE Access 11 (2023) 95526-95544.
• P. Panpho, P. Yiarayong, $(p,q)$-Rung linear Diophantine fuzzy sets and their application in decision-making, Computational and Applied Mathematics 42 (8) (2023) Article Number 324 35 pages.
• R. R. Yager, On the theory of bags, International Journal of General Systems 13 (1) (1986) 23-37.
• T. V. Ramakrishnan, S. Sebastian, A study on multi-fuzzy sets, International Journal of Applied Mathematics 23 (4) (2010) 713-721.
• S. Sebastian, R. John, Multi-fuzzy sets and their correspondence to other sets, Annals of Fuzzy Mathematics and Informatics 11 (02) (2015) 341-348.
• M. Sadaaki, Fuzzy multisets and their generalizations, in: C. S. Calude, G. P\u{a}un, G. Rozenberg, A. Salomaa (Eds.), Multiset Processing, Vol. 2235 of Lecture Notes in Computer Science, Springer, Cham, 2001, pp. 225-235.
• S. Sebastian, T. V. Ramakrishnan, Multi-fuzzy extensions of functions, Advances in Adaptive Data Analysis 3 (3) (2011) 339-350.
• S. Sebastian, T. V. Ramakrishnan, Multi-fuzzy topology, International Journal of Applied Mathematics 24 (1) (2011) 117-129.
• S. Sebastian, T. V. Ramakrishnan, Multi-fuzzy sets: An extension of fuzzy sets, Fuzzy Information and Engineering 3 (1) (2011) 35-43.
• A. S. Thomas, S. J. John,Multi-fuzzy rough sets and relations, Annals of Fuzzy Mathematics and Informatics 7 (5) (2014) 807-815.
• 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.
• M. A. Keleş, $N$-valued fuzzy numbers and application to multiple criteria decision making problems, Master's Thesis Kilis 7 Aralık University (2019) Kilis.
• M. Şahin, V. Uluçay, F. S. Yılmaz, Dice vector similarity measure of trapezoidal fuzzy multi-numbers based on multi-criteria decision making, in: F. Smarandache, M. Şahin (Eds.), Neutrosophic Triplet Structures, Vol. 1, Pons Publishing House, Brussels, 2019, Ch. 13, pp. 185-197.
• D. Kesen, Arithmetic-geometric operators on trapezoidal fuzzy multi numbers and their application to decision making problems, Master's Thesis Kilis 7 Aralık University (2021) Kilis.
• D. Kesen, İ. Deli, Trapezoidal fuzzy multi aggregation operator based on Archimedean norms and their application to multi attribute decision-making problems, in: S. Broumi, P. K. Nagajaran, M. G. Voskoglou, S. A. Edalatpanah (Eds.), Data-Driven Modelling with Fuzzy Sets: Embracing Uncertainty, CRC Press/Taylor & Francis Group, Florida, 2023, (In Press).
• M. Şahin, İ. Deli, D. Kesen, A Decision-making method under trapezoidal fuzzy multi-numbers based on centroid point and circumcenter of centroids, in: F. Smarandache, M. Şahin, D. Bakbak, V. Uluçay, A. Kargın (Eds.), Neutrosophic SuperHyperAlgebra and New Types of Topologies, Vol. 1, Global Knowledge Publishing House, Florida, 2023, Ch. 8, pp. 148-171.
• C. Bonferroni, Sulle medie multiple di potenze, Bolletino Matematica Italiana 5 (3-4) (1950) 267-270.
• R. R. Yager, On generalized Bonferroni mean operators in multi-criteria aggregation, International Journal of Approximate Reasoning 50 (8) (2009) 1279-1286.
• B. Zhu, Z. S. Xu, M. M. Xia, Hesitant fuzzy geometric Bonferroni means, Information Sciences 205 (1) (2012) 72-85.
• Z. Xu, Hesitant fuzzy sets theory, 1th Edition, Springer, Switzerland, 2014.
• S. Wan, Y. Zhu, Triangular intuitionistic fuzzy triple Bonferroni harmonic mean operators and application to multi-attribute group decision making, Iranian Journal of Fuzzy Systems 13 (5) (2016) 117-145.
• H. Wang, X. Wang, L. Wang, Multi-criteria decision making based on Archimedean Bonferroni mean operators of hesitant Fermatean 2-Tuple linguistic terms, Complexity 2019 (2019) Article ID 5705907 19 pages.
• L. A. Perez-Arellano, F. Blanco-Mesa, E. Leon-Castro, V. Alfaro-Garcia, Bonferroni prioritized aggregation operators applied to government Trans-parency, Mathematics 9 (1) (2021) 1-19.
• H. Garg, Y. Deng, Z. Ali, T. Mahmood, Decision-making strategy based on Archimedean Bonferroni mean operators under complex Pythagorean fuzzy information, Computational and Applied Mathematics 41 (4) (2022) Article Number 152 40 pages.
• M. Yahya, S. Abdullah, M. Qiyas, Analysis of medical diagnosis based on fuzzy credibility dombi Bonferroni mean operator, Journal of Ambient Intelligence and Humanized Computing 14 (9) (2023) 12709-12724.
• D. Kesen, İ. Deli, A novel operator to solve decision-making problems under trapezoidal fuzzy multi numbers and its application, Journal of New Theory (40) (2022) 60-73.
• S. R. Hait, R. Mesiar, P. Gupta, D. Guha, D. Chakraborty, The Bonferroni mean-type pre-aggregation operators construction and generalization: Application to edge detection, Information Fusion 80 (2022) 226-240.
• S. Radenovic, W. Ali, T. Shaheen, U. H. Iftikhar, F. Akram, H. Toor, Multiple attribute decision-making based on Bonferroni mean operators under square root fuzzy set environment, Journal of Computational and Cognitive Engineering 2 (3) (2022) 1-5.
• A. Kaufmann, M. M. Gupta, Fuzzy mathematical models in engineering and management science, Elsevier Science Publishers, Amsterdam, 1988.
• İ. Deli, D. Kesen, Bonferroni geometric mean operator of trapezoidal fuzzy multi numbers and its application to multiple attribute decision making problems, in: F. Smarandache, M. Şahin, D. Bakbak, V. Uluçay, A. Kargın (Eds.), Neutrosophic SuperHyperAlgebra and New Types of Topologies, Vol. 1, Global Knowledge Publishing House, Florida, 2023, Ch. 13, pp. 237-252.
• D. Diakoulaki, G. Mavrotas, L. Papayannakis, Determining objective weights in multiple criteria problems: The critic method, Computers & Operations Research 22 (7) (1995) 763-770.
• S. M. Yu, H. Zhou, X. H. Chen, J. Q. Wang, A multi-criteria decision-making method based on Heronian mean operators under linguistic hesitant fuzzy environment, Asia-Pacific Journal of Operational Research 32 (5) (2015) 1-35.
• 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.