Compromise ratio method for fuzzy multi-attribute group decision making

The aim of this paper is to develop a compromise ratio (CR) methodology for fuzzy multi-attribute group decision making (FMAGDM), which is an important part of decision support system. Owing to fuzziness being inherent in decision data and group decision making processes, the crisp values are inadequate to model real-life situations. In this paper, the weights of all attributes and the ratings of each alternative with respect to each attribute are described by linguistic terms which can be expressed in trapezoid fuzzy numbers. A fuzzy distance measure is developed to calculate difference between trapezoid fuzzy numbers. The compromise ratio method for FMAGDM is developed by introducing the ranking index based on the concept that the chosen alternative should be as close as possible to the ideal solution and as far away from the negative-ideal solution as possible simultaneously. The computation principle and procedure of the compromise ratio method are described in detail in this paper. Moreover the TOPSIS method which was developed for multi-attribute decision making (MADM) with crisp decision data is analyzed and extended to multi-attribute group decision making (MAGDM) under fuzzy environments. A comparative analysis of the compromise ratio method and the extended fuzzy TOPSIS method is illustrated with a numerical example, showing their similarity and some differences.