New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS

Abstract

Abstract In this paper, we first give an example to show that Theorem 1 in Hung and Yang (Inf Sci 178(6):1641–1650, 2008) does not hold, implying that the J-divergence introduced by Hung and Yang does not satisfy the axiomatic definition of intuitionistic fuzzy divergence measure. Inspired by this, a new Jensen–Shannon divergence measure for intuitionistic fuzzy sets (IFSs) is introduced and some basic properties for this new divergence measure are obtained. In particular, this divergence measure, and its induced similarity measure, and induced entropy measure satisfy the axiomatic definitions of divergence, similarity, and entropy for IFSs. Based on our proposed divergence measure, entropy measure, and entropy-weight method, a new TOPSIS method is introduced to deal with multi-attribute decision making (MADM) problems under the intuitionistic fuzzy framework. Finally, a practical example on the credit evaluation of potential strategic partners and a comparative analysis with other TOPSIS methods is developed to illustrate the efficiency of the proposed TOPSIS method.

Keywords

• Fuzzy sets
• Intuitionistic fuzzy sets
• Divergence measures
• Similarity measures
• Entropy
• Multi-attribute decision making (MADM)