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.