Development of prospect theory in decision making with different types of fuzzy sets: A state-of-the-art literature review

Abstract

Decision making is undertaken by individuals whose perceptions for the objectives are vague due to the dynamics of decision-making objectives, the complexity of decision-making situation and the limitations of individuals’ education backgrounds, experiences, etc. Therefore, decision making which uses fuzzy set (FS) and its variants to describe the individuals’ vague perceptions has become more and more popular. Furthermore, in real-life decision-making situations, individuals are always bounded rationality, which is clearly described by prospect theory (PT). Thus, PT has been integrated into fuzzy decision making (FDM). Since then, FDM with PT have been rapidly developed. In this paper, we systematically analyze the existing FDM with prospect framework. Firstly, a detailed analysis about the existing research on this topic is given separately, including how to determine the reference point, how to express the value function and weighting function in PT under vague conditions. With this in mind, the applications and challenges of the existing methods are described and some possible directions for future research are provided. According to our review, it is worth mentioning that the FDM with psychological factors of decision makers will surely receive much more attention from researchers and practitioners in the future.