This chapter describes the evolution of different multi-objective decision-making (MODM) models with their historical backgrounds. Starting from MODM models in deterministic environments along with various solution techniques, the chapter presents how different kinds of uncertainties may be associated with such decision-making models. Among several types of uncertainties, it has been found that probabilistic and possibilistic uncertainties are of special interests. A brief literature survey on different existing methods to solve those types of uncertainties, independently, is discussed and focuses on the need of considering simultaneous occurrence of those types of uncertainties in MODM contexts. Finally, a bibliographic survey on several approaches for MODM under hybrid fuzzy environments has been presented. Through this chapter the readers can be able to get some concepts about the historical development of MODM models in hybrid fuzzy environments and their importance in solving various real-life problems in the current complex decision-making arena.
Top1.2 Historical Developments Of Multi-Objective Decision Making
The concept of optimization theory in MODM was introduced by Kuhn and Tucker (1951). Thereafter, Charnes (1952) extended the concept and developed a methodology for solving optimization problems with several conflicting objectives. Subsequently, several researchers (Arrow et al., 1958; Charnes and Cooper, 1961; Briskin, 1966; Cochrane and Zeleny, 1973; Steuer 1977; Leitmann, 1976; Keeney and Raiffa 1976) made a significant impact in the field of MODM. Hwang and Masud (1979), Naccache (1979), Corley (1981) and other researchers scientifically classified and discussed the methodologies for solving MODM problems. Other methodological development in the field of optimization problems were presented in the books and monographs written by Goicoechea et al. (1982), Sawaragi et al. (1985), Yu (1985) and others. Due to the significant contribution of the pioneer researchers (Chiang and Tzeng, 2000; Chiou and Tzeng, 2003; Yu et al., 2004; Tzeng et al., 2007; Faulkenberg, 2009; Baky, 2010; Huang et al., 2012) MODM problems were applied to various real life decision making problems. Recently, Qu et al. (2018) developed an efficient multi-objective evolutionary algorithm as an effective tool to solve highly constrained complex bi-objective optimization problems.