A novel possibility measure to interval-valued intuitionistic fuzzy set using connection number of set pair analysis and its applications

The aim of this paper is to give a multi-attribute decision-making (MADM) method for the interval-valued intuitionistic fuzzy (IVIF) set using the set pair analysis (SPA) theory. IVIF set can express the uncertain information in a more valuable manner, while the connection number (CN) based on the identity, discrepancy and contrary degrees of the SPA theory handles the uncertainties and certainties systems. Based on these features, in this paper, we develop a new possibility degree measure based on the CNs to rank the different IVIF numbers. The properties and advantages of the measure are described in details. Later on, we present a novel MADM method and illustrate with several examples to validate it. A comparative as well as superiority analysis is performed to show the feasibility and validity of the approach.