Novel score function and non-dominance prioritisation method for intuitionistic fuzzy preference relations

Since Atanassov introduced the concept of intuitionistic fuzzy set (IFS) in 1986, much work has been done to develop decision making models with it as the information representation format. A problem that needs to be addressed in this type of decision making environment is the ranking of intuitionistic fuzzy numbers (IFNs). However, it is well known that there is no unique best approach to achieve this. A widely used approach to rank IFNs is to convert them into a representative crisp value, and perform the comparison on them. The representative crisp value developed for IFNs is known with the name of score degree. This contribution presents a novel IFS score function which is further used to derive a fuzzy preference relation (FPR) from an intuitionistic FPR (IFPR). This result has the potential of being exploited to develop prioritisation methods for intuitionistic preferences relations based on their associated score preference relations. In particular, for IFPRs we define the intuitionistic quantifier guided dominance and intuitionistic quantifier guided non-dominance degree and propose a new prioritisation methodology for decision making problems with information represented using IFPRs. We prove that this methodology is an extension of the widely accepted methodology developed for the case of using FPRs to model information in decision making problems.