Scaled Prioritized Operators Based on the Linguistic Intuitionistic Fuzzy Numbers and Their Applications to Multi-Attribute Decision Making

Abstract

Linguistic intuitionistic fuzzy number (LIFN) is a special intuitionistic fuzzy number which can describe the vagueness existing in the real decision making more easily. The scaled prioritized operator is a special prioritized operator which can express the prioritized relationships for different criteria by prioritized labels in knowable situation and unknowable situation. In this paper, in order to add up the advantages of them together, we propose the scaled prioritized averaging operator for LIFNs (SPLIFA) and the scaled prioritized geometric averaging operator for LIFNs (SPGLIFA) which are suitable for the problems in which the priority relationship between different categories of the attributes are known. Further, we proposed the scaled prioritized weighted averaging operator for LIFNs (SPLIFWA) and the scaled prioritized geometric weighted averaging operator for LIFNs (SPGLIFWA) which are suitable for the problems in which the priority relationship between different categories of the attributes are completely unknown. In the meantime, we discussed some characteristics of them, including idempotency, monotonicity and boundedness. Further we proposed an approach for the multi-attribute decision making on the basis of these operators. In the end, we give an example to illustrate the computing procedure and validity of our proposed method.