Title: A new fuzzy multi-objective optimisation method with desirability function under uncertainty

Authors: P. Soleymani; S. Meysam Mousavi; Behnam Vahdani; A. Aboueimehrizi

Addresses: Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran ' Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran ' Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran ' Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran

Abstract: Step method (STEM) is one of the most efficient and usable method of multi-objective decision making (MODM), and it is in the interactive category which uses decision makers (DMs) preference information during problem solving. In recent years, step method (STEM) has been developed based on the desirability function, namely D-STEM, in which the shortcoming of the STEM has been removed. To confront the problem in the real-world, paying attention to imprecision and uncertainty in decision making should be considered; however, in such status, D-STEM is unable to solve complex problem under uncertainty. In this paper, a new version of multi-objective optimisation method under a fuzzy environment with desirability function concept, namely FD-STEM, is proposed to deal with uncertain and imprecise conditions. Fuzzy uncertainties and imprecisions are considered in all parameters including objective coefficient, technologic coefficient, resources and decision variables as a fully fuzzy multi-objective optimisation. Finally, in an application example, decision making in manufacturing industry is presented and discussed based on consequents of fuzzy desirability function and with a fuzzy ranking function. Also, by using transformation method, the application example is solved and based on the overall desirability they are compared.

Keywords: fuzzy multi-objective optimisation; fuzzy desirability; fuzzy D-STEM; interactive methods; desirability function; uncertainty; fuzzy logic; multi-objective decision making; manufacturing industry; fuzzy ranking.

DOI: 10.1504/IJADS.2016.078225

International Journal of Applied Decision Sciences, 2016 Vol.9 No.1, pp.100 - 120

Received: 05 Feb 2016
Accepted: 02 Jul 2016
Published online: 08 Aug 2016 *

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