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

İrfan Deli; Davut Kesen

doi:10.54187/jnrs.1369105

EN

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

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.

Details

Primary Language

English

Subjects

Mathematical Logic, Set Theory, Lattices and Universal Algebra

Journal Section

Research Article

Authors

İrfan Deli
0000-0003-1875-1067
Türkiye

Davut Kesen ^*
0000-0002-2096-462X
Türkiye

Publication Date

December 31, 2023

Submission Date

September 30, 2023

Acceptance Date

December 23, 2023

Published in Issue

Year 2023 Volume: 12 Number: 3

DOI

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

IZ

https://izlik.org/JA58ZT86CL

APA

Deli, İ., & Kesen, D. (2023). Bonferroni arithmetic mean operator of trapezoidal fuzzy multi numbers and its decision-making application to crafting the ideal student dormitory. Journal of New Results in Science, 12(3), 166-187. https://doi.org/10.54187/jnrs.1369105

AMA

1.Deli İ, Kesen D. Bonferroni arithmetic mean operator of trapezoidal fuzzy multi numbers and its decision-making application to crafting the ideal student dormitory. JNRS. 2023;12(3):166-187. doi:10.54187/jnrs.1369105

Chicago

Deli, İrfan, and Davut Kesen. 2023. “Bonferroni Arithmetic Mean Operator of Trapezoidal Fuzzy Multi Numbers and Its Decision-Making Application to Crafting the Ideal Student Dormitory”. Journal of New Results in Science 12 (3): 166-87. https://doi.org/10.54187/jnrs.1369105.

EndNote

Deli İ, Kesen D (December 1, 2023) Bonferroni arithmetic mean operator of trapezoidal fuzzy multi numbers and its decision-making application to crafting the ideal student dormitory. Journal of New Results in Science 12 3 166–187.

IEEE

[1]İ. Deli and D. Kesen, “Bonferroni arithmetic mean operator of trapezoidal fuzzy multi numbers and its decision-making application to crafting the ideal student dormitory”, JNRS, vol. 12, no. 3, pp. 166–187, Dec. 2023, doi: 10.54187/jnrs.1369105.

ISNAD

Deli, İrfan - Kesen, Davut. “Bonferroni Arithmetic Mean Operator of Trapezoidal Fuzzy Multi Numbers and Its Decision-Making Application to Crafting the Ideal Student Dormitory”. Journal of New Results in Science 12/3 (December 1, 2023): 166-187. https://doi.org/10.54187/jnrs.1369105.

JAMA

1.Deli İ, Kesen D. Bonferroni arithmetic mean operator of trapezoidal fuzzy multi numbers and its decision-making application to crafting the ideal student dormitory. JNRS. 2023;12:166–187.

MLA

Deli, İrfan, and Davut Kesen. “Bonferroni Arithmetic Mean Operator of Trapezoidal Fuzzy Multi Numbers and Its Decision-Making Application to Crafting the Ideal Student Dormitory”. Journal of New Results in Science, vol. 12, no. 3, Dec. 2023, pp. 166-87, doi:10.54187/jnrs.1369105.

Vancouver

1.İrfan Deli, Davut Kesen. Bonferroni arithmetic mean operator of trapezoidal fuzzy multi numbers and its decision-making application to crafting the ideal student dormitory. JNRS. 2023 Dec. 1;12(3):166-87. doi:10.54187/jnrs.1369105

Cited By

A generalized similarity-based hybrid approach for multi-criteria decision-making with trapezoidal fuzzy multi-numbers and its application

Discover Applied Sciences

https://doi.org/10.1007/s42452-026-08473-9

TR Dizin 31688

EBSCO

Electronic Journals Library	DOAJ	WorldCat
Scilit	SAO/NASA Astrophysics Data System (ADS)	SOBİAD

JNRS is licensed under a Creative Commons Attribution-NonCommercial 4.0 International Licence (CC BY-NC).