Intuitionistic Fuzzy Three-Factor Ratio Models and Multi-preference Fusion

Generally, decision-makers (DMs) can provide subjective opinions based on their risk attitude and intuitionistic preference for specific alternatives and attributes, which can be taken as cognitive information. For instance, alternative A is better than alternatives B and C, or attribute 3 is the most important. These multi-dimensional preferences and social cognitive behavior described by DMs based on their subjective evaluation should be taken into account when making a decision. How to fuse multiple, uncertain, imprecise but important preferences and cognitive information and then make a decision in an intuitionistic fuzzy environment is becoming a practical issue. Therefore, this paper defines a three-factor ratio of the intuitionistic fuzzy number and then proposes a basic intuitionistic fuzzy three-factor ratio (IFTR) model. To present DMs’ risk preferences, this paper constructs two extreme IFTR models and describes risk preferences with a risk appetite parameter. For DMs’ alternative preferences, this paper develops a continuous IFTR model in which alternative preferences are fused to calculate the optimal risk appetite parameter. To fully consider DMs’ risk, alternative, and attribute preferences, this paper further proposes a generalized IFTR model. Thus, risk, alternative, and attribute preferences, which can be viewed as the social cognitive information, can be fused in an intuitionistic fuzzy decision-making and group decision-making process simultaneously. An illustrative example to address the problem of demolishing old urban villages is provided to show the effectiveness of the proposed models.