An Extended TODIM Method Under Uncertain and Risky Situations

The purpose of this paper is to solve the MADM problem under uncertain and risky situations by proposing an extended TODIM method. After considering about the attitude of decision makers on "risk" sufficiently, we introduce a new measure for IT2FS to describe the uncertain information. Taking into account the complexity of computation using T2FSs, the interval type-2 fuzzy sets can be used to dispose of the vagueness and uncertainty. Moreover, we illustrate the implementation of proposed extended TODIM method based on TrIT2FS by two case studies. The availability and the feasibility of the presented method are validated through a comparative analysis with other methods. Introduction Multi-Attribute Decision Making (MADM)[1] is a part of MCDM problem which is mainly focused on the problem of discrete decision space. The typical MADM problem is concerned with the evaluation of a limited number of predetermined alternatives according as a group of decision criteria. The relevant literature [2] about MADM is very extensive, also its theories and methods are widely applied to many fields such as engineering, technology, economics, management, military, and so on [3-5]. Nevertheless, most existing methods are based on expected utility model of rationality, but some researches about behavioural experiments [6, 7] have illustrated that the decision maker is bounded rational in the decision-making process. Therefore, how to solve the MADM problem when considering decision-maker’s psychological behaviour is always an issue deserving of study. TODIM, a valuable means to resolve the MADM problem, was early introduced by Gomes and Lima [8-13]. It can be effectively applied under the circumstance of risk. This method has been applied in many fields and is empirically validated to be efficient and feasible. However, another difficulty in setting up mathematical models is how to express the DM’s ideas and beliefs in a mathematical form. In reality, as the complexity of society continues to increase, the problems that people met are getting blurred. It is no longer a good solution to solve the decision problem with the exact number. To address this issue, Zadeh proposed T2FSs (the abbreviation for type-2 fuzzy sets) in which the membership function are fuzzy themselves. It uses both primary and secondary membership to provide us with additional degrees of freedom and greater flexibility particularly. This paper will present an TODIM method based on T2FS and introduce a new distance measure based on the signed distance between two interval numbers. At the end of this paper, we will apply this proposed method to a multi-criteria investment selection problem to verify the practical application effect of it. The Measure of IT2FS Considering Risk Preferences The Fuzzy theory provides theoretical basis and technical support for uncertain information representation and organization. [Definition 1] A type-2 fuzzy set, denoted A , is characterized by a type-2 membership function A    , A x  :   , A x     0,1 I  , where x U  ,   0,1 A x J    ,i.e., International Conference on Advanced Education, Management and Humanities (AEMH 2019) Copyright © 2019, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Social Science, Education and Humanities Research, volume 352