A new approach to the comparison of real, interval and fuzzy-valued intuitionistic fuzzy and Belief-Plausibility numbers

Recently the useful redefinition of the intuitionistic and interval-valued intuitionistic fuzzy set theories (A−IFS, A−IVIFS) based on the Dempster-Shafer theory of evidence (DST) was developed. It was named the “Belief-Plausibility” (BP) approach as only the basic mathematical tools of the DST were used for its foundation. In this paper, a new approach to compare the real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers is proposed. Among known approaches to compare intuitionistic fuzzy objects, most justified and used in applications are those based on the so-called score and accuracy functions. The observed multiplicity of these functions treatments and modifications indicates that the source of such a divergence is the impossibility to solve this problem exclusively in the framework of the A−IFS. Therefore, to develop the reliable methods for the considered types of comparison, a redefinition of this problem based on the BP approach is proposed. This redefinition allows us to develop new two and three criteria methods for comparison of real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers, based on the local criteria with transparent interpretation in the framework of the BP approach.