Pub. online:27 Mar 2020Type:Research ArticleOpen Access
Volume 31, Issue 2 (2020), pp. 399–433
In this paper, we develop a new flexible method for interval-valued intuitionistic fuzzy decision-making problems with cosine similarity measure. We first introduce the interval-valued intuitionistic fuzzy cosine similarity measure based on the notion of the weighted reduced intuitionistic fuzzy sets. With this cosine similarity measure, we are able to accommodate the attitudinal character of decision-makers in the similarity measuring process. We study some of its essential properties and propose the weighted interval-valued intuitionistic fuzzy cosine similarity measure.
Further, the work uses the idea of GOWA operator to develop the ordered weighted interval-valued intuitionistic fuzzy cosine similarity (OWIVIFCS) measure based on the weighted reduced intuitionistic fuzzy sets. The main advantage of the OWIVIFCS measure is that it provides a parameterized family of cosine similarity measures for interval-valued intuitionistic fuzzy sets and considers different scenarios depending on the attitude of the decision-makers. The measure is demonstrated to satisfy some essential properties, which prepare the ground for applications in different areas. In addition, we define the quasi-ordered weighted interval-valued intuitionistic fuzzy cosine similarity (quasi-OWIVIFCS) measure. It includes a wide range of particular cases such as OWIVIFCS measure, trigonometric-OWIVIFCS measure, exponential-OWIVIFCS measure, radical-OWIVIFCS measure. Finally, the study uses the OWIVIFCS measure to develop a new decision-making method to solve real-world decision problems with interval-valued intuitionistic fuzzy information. A real-life numerical example of contractor selection is also given to demonstrate the effectiveness of the developed approach in solving real-life problems.
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.