A Sample Survey Based Linguistic MADM Method with Prospect Theory for Online Shopping Problems

In MADM problems, the attributes are often rated in linguistic variables, some researchers transform them into numerical values through some formulas. However, it might be inconsistent with real human thinking in some extent. In order to deal with such problems, a sample survey based MADM method with prospect theory is proposed. Firstly, through sampling survey, we collect the data in single point format corresponding to the words, and establish the codebook by mapping words into fuzzy sets, after that fuzzy operation rules are suitable for them. Secondly, based on the reference points, the gain and/or loss matrix is obtained, in accordance with the value function, the prospect value matrix is constructed. Finally, if the attributes are independent, the weighted prospect value of each alternative is computed, if the attributes are dependent, the Choquet integral based prospect value of each alternative is computed. The alternatives are ranked in descending order respect to the defuzzified values. The first alternative is chosen as the best decision result. The feasibility of the proposed method is illustrated through an application in online shopping problem from real life.