APPLICATION OF TOPSIS FUZZY METHOD FOR DECISION MAKING USING SYNTACTICALLY INDEPENDENT LINGUISTIC VARIABLES
Abstract
Uncertain and imprecise data are typical for multicriteria problems, making fuzzy set theory an adequate tool for their solution. The objective of this paper is to apply the TOPSIS method in a fuzzy environment using syntactically independent linguistic variables. Due to the frequent occurrence of fuzzy concepts in decision-making data, crisp values are insufficient for modelling real-world situations. In the proposed approach, the evaluation of each alternative and the weight of each criterion are expressed by syntactically independent linguistic variables, whose arbitrary values are determined through the semantics of the base terms. An approach to calculating arbitrary (non-base) values of linguistic variables used by an expert is considered. The base values of the syntactically independent linguistic variables used are specified by triangular fuzzy numbers. The proposed approach is well suited for solving group decision-making problems in a fuzzy environment, where an expert or group of experts is not constrained by a limited number of fuzzy assessments. Here, fuzzy variables representing the values of the syntactically independent linguistic variables "criterion importance" and "criterion score" are considered as weighting coefficients for criterion importance and evaluation of qualitative criteria. The paper proposes using the centre of gravity method to calculate the distance between two triangular fuzzy numbers. In accordance with the fuzzy TOPSIS concept, a proximity coefficient is defined to determine the ranking order of all alternatives by calculating the distances to the fuzzy positive ideal solution (PIS) and the fuzzy negative ideal solution (NIS). An example is provided to illustrate the proposed approach
References
1. Dyer J.S., Fishburn P.C., Steuer R.E., Zionts S., Deb K. Multiple Criteria Decision Making, Multiattrib-ute Utility Theory: Recent Accomplishments and What Lies Ahead, Management Science, 2008, Vol. 54, No. 7, pp. 1336-1349. DOI: 10.1287/mnsc.1070.0838.
2. Hwang C.L., Yoon K. Multiple Attributes Decision Making Methods and Applications. Springer, Berlin Heidelberg, 1981. DOI: 10.1007/978-3-642-48318-9.
3. Teghem J., Delhaye C., Kunsch P.L. An interactive decision support system (IDSS) for multicriteria decision aid, Mathematical and Computer Modeling, 1989, Vol. 12, No. 10-11, pp. 1311-1320. DOI: 10.1016/0895-7177(89)90370-1.
4. Bellman R.E., Zadeh L.A. Decision-making in a fuzzy environment, Management Science, 1970, Vol. 17, No. 4, pp. 141-164. DOI: 10.1287/mnsc.17.4.B141.
5. Borisov A.N., Alekseev A.V., Krumberg O.A., Merkuryeva G.V., Popov V.A. Modeli prinyatiya resheniy na osnove lingvisticheskoy peremennoy [Models of decision-making based on a linguistic variable]. Ri-ga: Zinatne, 1982, 256 p.
6. Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning–I, Infor-mation Sciences, 1970, Vol. 8, No. 3, pp. 199-249. DOI: 10.1016/0020-0255(75)90036-5.
7. Herrera F., Herrera-Viedma E., Verdegay J.L. A model of consensus in group decision making under linguistic assessments, Fuzzy Sets and Systems, 1996, Vol. 78, pp. 73-87. DOI: 10.1016/0165-0114(95)00107-7.
8. Nădăban S., Dzitac S., Dzitac I. Fuzzy TOPSIS: A General View, Procedia Computer Science, 2016, Vol. 91, pp. 823-831. DOI: 10.1016/j.procs.2016.07.088.
9. Yang T., Hung C.C. Multiple-attribute decision making methods for plant layout design problem, Robot-ics and Computer-Integrated Manufacturing, 2007, Vol. 23, No. 1, pp. 126-137. DOI: 10.1016/j.rcim.2005.12.002.
10. Chen C.T. Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets and Systems, 2000, Vol. 114, No. 1, pp. 1-9. DOI: 10.1016/S0165-0114(97)00377-1.
11. Kaufmann A., Gupta M.M. Introduction to Fuzzy Arithmetic: Theory and Applications. New York: Van Nostrand Reinhold, 1985.
12. Kaufmann A. Introduction to the theory of fuzzy subsets. New York: Academic Press, 1975.
13. Zimmermann H.J. Fuzzy Set Theory and its Applications. Kluwer Academic Publishers, Boston Dor-drecht London, 1991. DOI: 10.1007/978-94-015-7949-0.
14. Buckley J.J. Fuzzy hierarchical analysis, Fuzzy Sets and Systems, 1985, Vol. 17, No. 3, pp. 233-247. DOI: 10.1016/0165-0114(85)90090-9.
15. Malyshev N.G., Bershtein L.S., Bozhenyuk A.V. Nechetkie modeli dlya expertnykh system v SAPR [Fuzzy models for expert systems in CAD]. Moscow, Energoatomizdat, 1991, 136 p.
16. Zwick R., Carlstein E., Budescu D.V. Measures of similarity among fuzzy concepts: A comparative anal-ysis, International Journal of Approximate Reasoning, 1987, Vol. 1, No. 2, pp. 221-242. DOI: 10.1016/0888-613X(87)90015-6.
17. Ebadi M.J., AhmadianHosseini A., Salahshour S., Suleiman M., Ismail F., Shahryari B. A New Dis-tance Measure for Trapezoidal Fuzzy Numbers, Mathematical Problems in Engineering, 2013. DOI: 10.1155/2013/424186.
18. Liu G., Wang X. A Trapezoidal Fuzzy Number-Based VIKOR Method with Completely Unknown Weight Information, Symmetry, 2023, Vol. 15, No. 2, 559. DOI: 10.3390/sym15020559.
19. Wang Y.G., Yang J.B., Xu D.L., Chin K.S. On the centroids of fuzzy numbers, Fuzzy Sets and Systems, 2006, Vol. 157, No. 7, pp. 919-926. DOI: 10.1016/j.fss.2005.11.006.
20. Hsu H.M., Chen C.T. Aggregation of fuzzy opinions under group decision making, Fuzzy Sets and Systems, 1996, Vol. 79, No. 13, pp. 279-285. DOI: 10.1016/0165-0114(95)00185-9.
21. Anbarkhan S.H. A Fuzzy-TOPSIS-Based Approach to Assessing Sustainability in Software Engineer-ing: An Industry 5.0 Perspective, Sustainability, 2023, Vol. 15, No. 18, 13844. DOI: 10.3390/su151813844.
