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

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.