An (R, S)-norm information measure for hesitant fuzzy sets and its application in decision-making

To characterize the uncertainty of a hesitant fuzzy set, a new entropy, which is called (R, S)-norm information measure, is proposed in this paper. It is proved that the proposed measure satisfies the axiomatic definition of entropy measures for hesitant fuzzy sets, and then, some properties of the proposed measure are also explored. Furthermore, several examples are presented to show the advantages of the (R, S)-norm information measure compared with some existing entropy measures. Then, based on the new information measure, we utilize decision-making method by combining prospect theory with technique for order preference by similarity to an ideal solution to address multi-attribute decision-making problems. Finally, a concrete example of business investment is provided to illustrate the effectiveness of our proposed information measure, and comparative analysis is also completed to verify the validity of the (R, S)-norm information measure.