Volume 32, Issue 4 (2021), pp. 849–864
There exist various types of similarity measures for intuitionistic fuzzy sets in the literature. However, in many studies the interactions among the elements are ignored in the construction of the similarity measure. This paper presents a cosine similarity measure for intuitionistic fuzzy sets by using a Choquet integral model in which the interactions between elements are considered. The proposed similarity measure is applied to some pattern recognition problems and the results are compared with some existing results to demonstrate the effectiveness of this new similarity measure.
Pub. online:1 Jan 2017Type:Research ArticleOpen Access
Volume 28, Issue 3 (2017), pp. 547–564
In this paper, we presented another form of eight similarity measures between PFSs based on the cosine function between PFSs by considering the degree of positive membership, degree of neutral membership, degree of negative membership and degree of refusal membership in PFSs. Then, we applied these weighted cosine function similarity measures between PFSs to strategic decision making. Finally, an illustrative example for selecting the optimal production strategy is given to demonstrate the efficiency of the similarity measures for strategic decision making problem.
Pub. online:1 Jan 2016Type:Research ArticleOpen Access
Volume 27, Issue 1 (2016), pp. 203–229
This paper reviews the existing definitions and formulas of entropy for interval-valued intuitionistic fuzzy sets (IVIFSs) and demonstrates that they cannot fully capture the uncertainty of IVIFSs. Then considering both fuzziness and intuitionism of IVIFSs, we introduce a novel axiomatic definition of entropy for IVIFSs and develop several entropy formulas. Example analyses show that the developed entropy formulas can fully reflect both fuzziness and intuitionism of IVIFSs. Furthermore, based on the entropy formulas of IVIFSs, a method is proposed to solve multi-attribute decision making problems with IVIFSs. Additionally, an investment alternative selection example is provided to validate the practicality and effectiveness of the method.