Research On Fuzzy Multi-attribute Decision Making Based On TODIM

Multi-criteria decision making(MCDM)is a hot topic in the decision-making research community.Note that the existing MCDM methods are usually based on the expected utility theory,where the DMs are assumed to be completely rational.In real-life situations,due to the uncertainty of the decision problems and to limited human cognition,the DM is associated with bounded rationality.TODIM(an acronym in Portuguese of interactive and multi-criteria decision making),which is a recently developed method that based on prospect theory can capture the decision-maker's psychological behaviour,can address this problem effectively.The classical TODIM method can only handle information in the form of crisp numbers,but it has no capability to deal with fuzzy information,which are flexible in reflecting the uncertainty and hesitation of the DM's opinions.Therefore,in order to make the behavioural decision making methods more guiding value in reality,this paper introduces the fuzzy information into TODIM method.Meanwhile,due to the increasing complexity of society,a single DM is difficult to take in account all relevant aspects of a decision problem.Thus,many of the decision processes that are made in the real world occur in group settings to make the decision-making more comprehensive and reasonable.Based on these ideas,a serious works is conducted and the contributions are as follows:First,to better reflect the uncertainty of the environment and the DM's preference information,this paper extends the TODIM method to multi-granularity linguistic term sets,2-dimension fuzzy linguistic variables and triangular intuitionistic fuzzy numbers(TIFNs).In addition,the TODIM method is extended to group decision making area under the triangular intuitionistic fuzzy environment,to make the decision more comprehensive.Second,in order to deal with linguistic information,this paper transform the linguistic terms into intuitionistic fuzzy numbers,interval-valued intuitionistic fuzzy numbers(IVIFNs).Compared with standard IVIFNs provide a flexible model which helps to elaborate uncertainty and imprecision when dealing with the uncertainty of MCDM problems.In addition,the hesitation degree of IVIFNs is a more appropriate mean of measuring the vagueness of the linguistic information.We propose a concept of multi-granularity 2-dimension fuzzy linguistic variable,which can describe the evaluation values provided by DM to the given alternatives and the subjective assessment about the dependability of the provided results simultaneously with fuzzy linguistic variables.Third,from the probability point of view,we propose some new operational laws on triangular intuitionistic fuzzy sets,and two triangular intuitionistic fuzzy interaction averaging operators are presented based on the new operational laws for triangular intuitionistic fuzzy sets,including the weighted arithmetic interaction averaging operator of TIFN and the weighted geometric interaction averaging operator of TIFN.Finally,when considering the situation of completely unknown weights of criteria,this research determines the weights of the criteria with entropy method with linguistic information,but employs the similarity method to obtain the weights of criteria under triangular intuitionistic environment.Additionally,a consensus model based on the rank orders of grey relational coefficients between individual decision makers and the ideal decision maker and a mathematical programming model based on similarity are designed to obtain the weights of all decision makers.