An extension of TOPSIS method using interval bipolar linguistic neutrosophic set and its application

Abstract

TOPSIS, known as the “Technique for Order of Preference by Similarity to Ideal Solution” (TOPSIS), is one of the well-known methods for solving “multi-criteria decision-making” (MCDM) problems. Many TOPSIS methods have been developed to solve real-life problems using neutrosophic sets. However, no study has developed the TOPSIS method under interval bipolar linguistic neutrosophic environments. Therefore, this study aims to present a new concept of “interval bipolar linguistic neutrosophic set” (IBL_NS). IBL_NS is more flexible and adaptable to real-world applications than other sets. Some set-theoretic operations, such as “union”, “intersection”, and “complement”, and the “operational rules” of IBL_NS are defined. Then, a new TOPSIS procedure in IBL_NS is developed. In the proposed IBL_NS-TOPSIS method, ratings of alternatives and importance weights of criteria are expressed in IBL_NS. An application is presented demonstrating the advantages of the proposed IBL_NS-TOPSIS approach.