Development and improvement of ranking index in TOPSIS method with pticture fuzzy data

Subject Areas :

Vahide Hojjati NajafAbadi ¹ (Department of Mathematics, Computer Faculty, Najaf Abad Branch, Islamic Azad University, Najaf Abad, Iran)
reza maddahi ² (Department of Mathematics, Computer Faculty, Najaf Abad Branch, Islamic Azad University, Najaf Abad, Iran)

Received: 2023-12-19 Accepted : 2024-08-15

Keywords: Topsis, fuzzy set, intuitive fuzzy set, visual fuzzy set,

Abstract :

Since Professor Lotfi Asgarzadeh introduced the fuzzy set to the world in 1965, many new theories about inaccuracy and uncertainty have emerged. Some of these theories, as a secondary development of fuzzy set theory, proposed a new concept called Picture Fuzzy Set (PFS). On the other hand, one of the methods that is widely used in multi-criteria decision making is called TOPSIS method. In this article, the TOPSIS method is first explained in the presence of fuzzy image data, and then a new ranking index is developed using this method, with the aim of improving its performance. In the following, an example is solved using Excel software to explain the method presented in this article. Also, by solving an example with fuzzy numbers that is presented in the definition of image fuzzy numbers in this research, the necessary changes are made using Excel software and the distance to the ideal and anti-ideal state is calculated. Finally, a new ranking is determined.

References:

A. De Luca, S. T. (1972). A definition of a nonprobabilistic entropy inthe setting of fuzzy sets theory. Inf. Control, 301-312.
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and Systems, 20, 87-96.
Atanassov, K. T. (1986). Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1-18.
C. L. Hwang, K. Y. (1981). Methods for multiple attribute decision making. Mult. attrib. Decis. Mak., 58-191, https://doi.org/10.1007/978-3-642-48318-9_3.
F. E. Boran, S. G. (2009). A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Systems with Applications, 36(8), 11363-11368, https://doi.org/10.1016/j.eswa.2009.03.039.
G. R. Jahanshahloo, F. H. (2006). Extension of the TOPSIS method for decision-making problems with fuzzy data. Applied Mathematics and Computation, 181(2), 1544-1551, https://doi.org/10.1016/j.amc.2006.02.057.
Gandotra, S. N. (2021). Use of (R,S)-Norm concept and TOPSIS approach under picture fuzzy environment for application in multi criteria decision making issues. Materials Today: Proceedings, 307, https://doi.org/10.10.16/j.matpr.2021.03.307.
Hwang, C. a. (1981). Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey. New York: Springer-Verlag, https://doi.org/10.1007/978-3-642-48318-9_3.
Joshi, R. (2020). A nove decision-making method using R-Norm concept and VIKOR approach under picture fuzzy environment. Expert Syst. Appl., 147, https://doi.org/10.1016/j.eswa.2020.113228.
Kreinovich, B. C. (2013). Picture Fuzzy Sets-a new concept for conputational intelligence problems. Departmental Technical Reports, 809, 1-6, https://scholarworks.utep.edu/cs_techrep/809.
LA.Zadeh. (1965). Fuzzy sets. inf. control, 338-353, https://doi.org/10.1016/S0019-9958(65)90241-X.
R. Joshi, S. K. (2016). (R-S)- norm information measure and a relation between coding and questionnaire theory, open Syst. Inf. Dyn., 23, https://doi.org/10.1142/S1230161216500153.
S.A. Sadabadi, A. H.-V. (2022). An Improved Fuzzy TOPSIS Method With a New Ranking Index. World Scientific, 615-641, https://doi.org/10.1142/S0219622021500620.
Son, L. H. (2016). Generalized picture distance measure and applications to picture fuzzy clustering. ELSEVIER, 284-295, https://doi.org/10.1016/j.asoc.2016.05.009.
Tzou, G. H. (1983). Fuzzy Multiple Objective Decision Making: Methods and Applications. Fuzzy Sets and Systems, 11.
V.Kreinovich, B. (2014). Picture fuzzy sets. J. Comput Science and Cybernetics, 409-416, https://doi.org/10.15625/1813-
9663/30/4/5032. Wei, G. (2016). Peacture fuzzy cross-entropy for multiple attribute decision making problems. J. Bus. Econ. Manag, 15, 491-502, https://doi.org/10.3846/16111699.2016.1197147.