Study on uniform for ten types of preference information in multi-attribute group decision making

The problem of uniform for the existing preference information in multi-attribute group decision making is discussed in this paper. A method is proposed based on the λ-cut of fuzzy mathematics to convert triangular fuzzy numbers and trapezoidal fuzzy numbers to interval number complementary judgment matrix. Means of converting interval-valued intuitionistic fuzzy judgment matrix and linguistic variables to interval number complementary judgment matrix are also presented. An approach of uniform for the following ten types of preference information is obtained: real number utility values, preference orderings, reciprocal judgment matrix and complementary judgment matrix, interval number utility values, interval number complementary judgment matrix, fuzzy number utility values, intuitionistic fuzzy judgment matrix, interval-valued intuitionistic fuzzy judgment matrix and linguistic variable utility values. A group decision making method is provided to integrate the ten types of preference information. Finally, a numerical example about emergency plans is used to illustrate the practicality and effectiveness of the proposed approach.