Intuitionistic Fuzzy Possibility Degree Measure for Ordering of IVIFNs with Its Application to MCDM

Abstract

In this article, the concept of an intuitionistic fuzzy possibility degree (IFPD) for ordering several interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced. The IFPD ranks IVIFNs by distinguishing the comparable and non-comparable components of the joint intervals of membership and non-membership degrees. The incomparable cases of nested joint intervals can also rank respective IVIFNs through the proposed IFPD approach. An intuitionistic fuzzy possibility preference relation based on the proposed IFPD measure for IVIFNs is defined as a more effective tool for modelling uncertainty than existing intuitionistic preference relations. Further, an approach for solving multicriteria interval-valued intuitionistic fuzzy decision-making problems based on IFPD measure of IVIFNs is advanced also provides a possibility degree as supplementary information to the ranking of alternatives. The validity and effectiveness of the advanced approach are demonstrated through two illustrative examples.