Trapezoidal Spherical Fuzzy Numbers and its Application to Fuzzy Risk Analysis
DOI:
https://doi.org/10.12723/mjs.65.8Keywords:
Trapezoidal Fuzzy Number, Spherical Fuzzy Set, Fuzzy Risk Analysis, Ranking FunctionAbstract
Spherical fuzzy sets are a broader type of fuzzy sets that have the ability to handle various scenarios using their membership, non-membership, and neutral membership grades. These sets require that the total of the squares of these grades be no greater than one. This condition extends the possible values for the three grades and enables decision makers to have a wider range of options when assessing a situation. In solving real life problems, it is necessary to describe a real number as a spherical fuzzy set to incorporate the fuzziness, thus, the need to use trapezoidal spherical fuzzy numbers (TSFN). In this paper, the membership functions of the TSFN, their arithmetic operations and their properties are discussed. Also, a ranking function is proposed to order the TSFNs. All these are used to solve a fuzzy risk analysis problem whose parameters are presented as TSFNs.
References
Shahzaib Ashraf, Saleem Abdullah, Tahir Mahmood, Fazal Ghani, and Tariq Mahmood. Spherical fuzzy sets and their applications in multi-attribute decision making problems. Journal of Intelligent & Fuzzy Systems, 36(3):2829–2844, 2019.
K.T. Atanassov. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20:87–96, 1986.
T.M. Athira, S.J. John, and H. Garg. Entropy and distance measures of pythagorean fuzzy soft sets and their applications. Journal of Intelligent and Fuzzy Systems, pages 1–14, 2019.
Abit Balin. A novel fuzzy multi-criteria decision-making methodology based upon the spherical fuzzy sets with a real case study. Iranian Journal of Fuzzy Systems, 17(4):167–177, 2020.
B.C. Cuong and V. Kreinovich. Picture fuzzy sets-a new concept for computational intelligence problems. Proceedings of 2013 ThirdWorld Congress on Information and Communication Technologies (WICT 2013), IEEE, pages 1–6, 2013.
Irfan Deli and Naim C¸ a˘gman. Spherical fuzzy numbers and multi-criteria decision-making. Springer, 2021
H. Garg. Some picture fuzzy aggregation operators and their applications to multicriteria decision-making.Arabian Journal for Science and Engineering, 42(12):5275–5290, 2017.
Fatma Kutlu G¨undo˘gdu and Cengiz Kahraman. Spherical fuzzy analytic hierarchy process (ahp) and its application to industrial robot selection. In International Conference on Intelligent and Fuzzy Systems, pages 988–996. Springer, 2019.
F. Kutlu G¨undo˘gdu and Kahraman C. A novel fuzzy topsis method using emerging interval-valued sphericalfuzzy sets. Eng Appl Artif Intell, 85:307–323, 2019.
Cengiz Kahraman, Fatma Kutlu G¨undogdu, Sezi C¸ evik Onar, and Basar Oztaysi. Hospital location selection using spherical fuzzy topsis. In EUSFLAT Conf., 2019.
Cengiz Kahraman and Fatma Kutlu G¨undo˘gdu. Decision Making with Spherical Fuzzy Sets: Theory and Applications - Studies in Fuzziness and Soft Computing, volume 392.
K.T.Atanassov and G.Gargov. Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31:343–349, 1989.
Fatma Kutlu G¨undo˘gdu and Cengiz Kahraman. A novel vikor method using spherical fuzzy sets and its application to warehouse site selection. Journal of Intelligent & Fuzzy Systems, 37(1):1197–1211, 2019.
Peide Liu, Baoying Zhu, and Peng Wang. A multi-attribute decision-making approach based on spherical fuzzy sets for yunnan baiyao’s r&d project selection problem. International Journal of Fuzzy Systems,21(7):2168–2191, 2019.
Tahir Mahmood, Muhammad Ilyas, Zeeshan Ali, and Abdu Gumaei. Spherical fuzzy sets-based cosine similarity and information measures for pattern recognition and medical diagnosis. IEEE Access, 9:25835– 25842, 2021.
Tahir Mahmood, Kifayat Ullah, Qaisar Khan, and Naeem Jan. An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Computing and Applications, 31(11):7041–7053, 2019.
Manoj Mathew, Ripon K Chakrabortty, and Michael J Ryan. A novel approach integrating ahp and topsis under spherical fuzzy sets for advanced manufacturing system selection. Engineering Applications of Artificial Intelligence, 96:103988, 2020.
S¸erif Ozl¨u and Faruk Karaaslan. Correlation coefficient of t-spherical type-2 hesitant fuzzy sets and their ¨applications in clustering analysis. Journal of Ambient Intelligence and Humanized Computing, pages 1–29, 2021.
V. Mohedano P. Burillo, H.Bustince. Some definition of intuitionistic fuzzy number. Fuzzy based expert systems, fuzzy Bulgarian enthusiasts, pages 28–30, 1994.
R.R.Yager. Pythagorean fuzzy subsets. IFSA World Congress and NAFIPS Annual Meeting, IEEE, pages 57–61, 2013.
Kifayat Ullah, Harish Garg, Tahir Mahmood, Naeem Jan, and Zeeshan Ali. Correlation coefficients for t-spherical fuzzy sets and their applications in clustering and multi-attribute decision making. Soft Computing, 24(3):1647–1659, 2020.
Kifayat Ullah, Tahir Mahmood, and Naeem Jan. Similarity measures for t-spherical fuzzy sets with applications in pattern recognition. Symmetry, 10(6):193, 2018.
Mei-Qin Wu, Ting-You Chen, and Jian-Ping Fan. Divergence measure of t-spherical fuzzy sets and its applications in pattern recognition. IEEE Access, 8:10208–10221, 2019.
Mei-Qin Wu, Ting-You Chen, and Jian-Ping Fan. Similarity measures of t-spherical fuzzy sets based on the cosine function and their applications in pattern recognition. IEEE Access, 8:98181–98192, 2020.
L.A. Zadeh. Fuzzy sets. Information and Control, 8:338–353, 1965.
Shouzhen Zeng, Harish Garg, Muhammad Munir, Tahir Mahmood, and Azmat Hussain. A multi-attribute decision making process with immediate probabilistic interactive averaging aggregation operators of tspherical fuzzy sets and its application in the selection of solar cells. Energies, 12(23):4436, 2019.
Additional Files
Published
Issue
Section
License
Copyright (c) 2023 V. Dhanalakshmi
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
