A hesitant fuzzy multiplicative Base-criterion multi-criteria group decision making method
Abstract
Hesitant fuzzy sets have a unique characteristic that its basic element could manifest the assessment values of different decision makers on the same option under a certain criterion. Base-criterion method is a very significant tool for calculating the weights of the criteria in multiple criteria decision-making. In this paper, we developed a novel approach hesitant fuzzy BCM based on hesitant fuzzy multiplicative preference relation for multiple criteria group decision making. The base-comparison of the preferential criterion relative to other criteria is expressed as linguistic terms, which might be converted into hesitant multiplicative elements (HMEs). HMEs are extended along the same length according to the attitude of the decision makers. Then normalized optimal hesitant fuzzy weights are calculated. The normalized optimal hesitant fuzzy weights of criteria may be transferred to crisp values by employing score function. To illustrate the applicability and suitability of hesitant fuzzy BCM, we analyse the optimal transportation mode selection problem and car selection problem under hesitant fuzzy environment. The outcomes of the proposed model indicate that the hesitant fuzzy BCM is highly consistent and can yield appreciable preference ranking of criteria and alternatives.
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Parreiras, R., Pedrycz, W., Ekel, P.: Fuzzy Multicriteria Decision‐Making: Models, Methods and Applications. John Wiley & Sons. (2011)
Yoon, K., Hwang, C.L.: Multiple Attribute Decision Making: Methods and Applications. A State‐of‐the‐Art Survey. New York, Springer‐Verlag. (1981)
Rao, R.V.: Decision Making in The Manufacturing Environment Using Graph Theory and Fuzzy Multiple Attribute Decision Making. 2. London, Springer‐Verlag. (2013)
Duckstein, L., Opricovic, S.: Multiobjective optimization in river basin development. Water Resources Research. 16(1):14-20 (1980)
Benayoun, R., Roy, B., Sussman, N.: Manual de, du programme ELECTRE. Note Synth. Form. 25 (1996)
Hwang, C.L., Yoon, k.: Multiple attribute decision making, methods and applications. Springer, New York (1981)
Yoon, K.: A reconciliation among discrete compromise solutions. Journal of the Operational Research Society. 38(3):277-86 (1987)
Zavadskas, E.K.: "The new method of multicriteria complex proportional assessment of projects," Technological and Economic Development of Economy. 131-139 (1994)
Zavadskas, E.K., Kaklauskas, A. & Kvederytė, N.: Multivariant design and multiple criteria analysis of building life cycle. Informatica. 12(1):169–188 (2001)
Keršuliene, V., Zavadskas, E.K., Turskis, Z.: Selection of rational dispute resolution method by applying new step‐wise weight assessment ratio analysis (SWARA). Journal of Business Economics and Management. 11(2):243-58 (2010)
Satty, T.L.: Decision making with dependence and feedback: The analytic network process. RWS Publication. (1996)
Saaty, T.L.: Theory and applications of the analytic network process: decision making with benefits, opportunities, costs, and risks. RWS publications. (2005)
Saaty, L.: The Analytical Hierarchy Process. McGraw-Hill, New York (1980)
Rezaei, J.: Best-worst multi-criteria decision-making method. Omega. 53:49–57 (2015)
Rezaei, J.: Best-worst multi-criteria decision-making method: Some properties and a linear model. Omega. 64:126–130 (2016)
Haseli, G., Sheikh, R., Sana, S.S.: Base-criterion on multi-criteria decision-making method and its applications. International journal of management science and engineering management. 15(2):79-88 (2019)
Zadeh, L.A.: Fuzzy sets. Information Control. 8:338-353 (1965)
Pramanik, T., Samanta, S., Pal, M., Mondal, S., Sarkar, B.: Interval-valued fuzzy φ-tolerance competition graphs. SpringerPlus. 5(1):1981 (2016)
Rashmanlou, H., Pal, M., Borzooei, R.A., Mofidnakhaei, F., Sarkar, B.: Product of interval-valued fuzzy graphs and degree. Journal of Intelligent Fuzzy System. 35(6):6443–6451 (2018)
Dubois, D., Prade, H.: Systems of linear fuzzy constraints. Fuzzy Sets and System. 3(1):37–48 (1980)
Atanassov, K.T.: Intuitionistic fuzzy sets. In: Intuitionistic fuzzy sets. Physica Heidelberg. 1-137 (1999)
Torra, V.: Hesitant fuzzy sets. International Journal of Intelligent Systems 25:529–539 (2010)
Torra, V., Narukawa, Y.: Modeling decisions: Information fusion and aggregation operators. Springer (2007)
Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea. 1378–1382 (2009)
Xia, M.M., Xu, Z.S.: Managing hesitant information in GDM problems under fuzzy and multiplicative preference relations. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems. 21:865–897 (2013)
Xia, M.M., Xu, Z.S.: Studies on the aggregation of intuitionistic fuzzy and hesitant fuzzy information. Technical Report (2011a)
Ali, A., Rashid, T.: Hesitant fuzzy best worst multi-criteria decision-making method and its applications. International Journal of Intelligent Systems. 34:1953‐1967 (2019)
Xu, Z., Zhang, S.: An overview on the applications of the hesitant fuzzy sets in group decision-making: Theory, support and methods. Frontiers of Engineering Management. 6(2):163-182 (2019)
Xu, Z. S., & Zhang, X. L.: Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems. 52:53–64 (2013)
DOI: https://doi.org/10.31449/inf.v46i2.3452
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