Based on the prospect theory, a novel linguisticdecision method under risk is proposed. First, the alternativesunder each risk state are rated using linguistic terms, and＇ thelinguistic decision matrix is constructed. Secondly, thelinguistic terms are transformed into triangular fuzzy numbers,so that the linguistic evaluations can be changed into numericalforms. Thirdly, with the aid of the prospect theory, theprobability weight functions and the linguistic value functionscan be computed, based on which the prospective values of thealternatives are obtained. Finally, the alternatives are rankedwith respect to the prospective values combined of probabilityweight and linguistic value functions. Thus, the optimalchoice is made. The decision process takes the psychologicalpreferences of the decision maker into consideration. Thepracticality of the proposed method is illustrated through anapplication on stock selection problems.
The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.
