Divergence-based cross entropy and uncertainty measures of Atanassov’s intuitionistic fuzzy sets with their application in decision making

• Published in: Applied soft computing Vol. 84; p. 105703
• Main Authors: Song, Yafei, Fu, Qiang, Wang, Yi-Fei, Wang, Xiaodan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2019
• Subjects: Atanassov’s intuitionistic fuzzy sets; Cross entropy; Multi-attribute group decision making; Uncertainty measure; Uncertainty measure; Multi-attribute group decision making; Cross entropy; Atanassov’s intuitionistic fuzzy sets
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2019.105703

The uncertainty measure of Atanassov’s intuitionistic fuzzy sets (AIFSs) is important for information discrimination under intuitionistic fuzzy environment. Although many entropy measures and knowledge measures haven been proposed to depict uncertainty of AIFSs, how to measure the uncertainty of AIFSs is still an open topic. The relation between uncertainty and other measures like entropy measures, fuzziness and intuitionism is not clear. This paper introduces uncertainty measures by using new defined divergence-based cross entropy measure of AIFSs. Axiomatic properties of the developed uncertainty measure are analysis, together with the monotony property of uncertainty degree with respect to fuzziness and intuitionism. To adjust the contribution of fuzzy entropy and intuitionistic entropy on the total uncertainty, the proposed cross entropy and uncertainty measures are parameterized. Numerical examples indicate the effectiveness and agility of the biparametric uncertainty measure in quantifying uncertainty degree. Then we apply the cross entropy and uncertainty measures into an optimal model to determine attribute weights in multi-attribute group decision making (MAGDM) problems. A new method for intuitionistic fuzzy MAGDM problems is proposed to show the efficiency of proposed measures in applications. It is demonstrated by application examples that the proposed measures can get reasonable results coinciding with other existing methods. •A divergence-based cross entropy is defined to discriminate the information conveyed by AIFSs.•An uncertainty measure for AIFS is developed based on the cross entropy measure.•The properties of the proposed uncertainty measure are analyzed mathematically and comparably.•The proposed cross entropy and uncertainty measure are parameterized to reflect the attitudinal influence of decision maker.•The proposed measures are applied in decision making to show their performance.