A New Distance Measure Between Atanassov's Intuitionistic Fuzzy Sets Based on Mapping

Fang Su, Jing Li, Dongxuan Xiao, Chengrui Duan

Abstract: A new trapezoidal approximation of Atanassov’s intuitionistic fuzzy sets (AIFSs) and a new distance measure between AIFSs based on the area relations of membership function graphs of their corresponding trapezoidal fuzzy sets are proposed. By the conversion from Atanassov’s intuitionistic fuzzy numbers (AIFNs) to trapezoidal fuzzy numbers, the measurement of distance between AIFSs can be transformed into the calculation of area relations of the corresponding trapezoidal fuzzy sets. Then the new distance measurement can integrate continuous information rather than only taking discrete variables into consideration as before. The main innovation of our distance is that it can integrate comprehensive and continuous information in calculation instead of partial discrete variables, which can efficiently avoid information loss. The contrastive tests demonstrate the efficiency and practicality of the approach.