New Distance and Entropy for Linguistic Intuitionistic Fuzzy Set and their Application to Linguistic Decision Making

In order to handle the multi-attribute group decision making(MAGDM) problems with linguistic intuitionistic fuzzy (LF) information, a modified TOPSIS method is proposed with LF entropy and LF distance measure. Firstly, the linguistic metric function(LMF) is defined as a tool to quantity LF information, and the new LF entropy is further introduced to derive the attribute weights. Secondly, based on the classical cosine similarity, the new distance measure between linguistic intuitionistic fuzzy sets(LIFSs) is developed, which is called the LF induced ordered weighted distance(LIFIOWD) measure. Subsequently, a modified TOPSIS method based on LF entropy and the LFIOWD measure is presented for linguistic decision making(LDM). Finally, the example of a car company choosing a wheel manufacturer is used to demonstrate this approach.