A Generalized p-Norm Knowledge-Based Score Function for an Interval-Valued Intuitionistic Fuzzy Set in Decision Making

This paper addresses the commonly used methods for solving multiple attribute group decision-making problems under an interval-valued intuitionistic fuzzy environment. It is shown that either the most popular score function and its latterly improved versions or other related methods may lead to the undesirable results. Apart from these seemly heuristic methods, we propose a generalized p-norm knowledge-based score function for the interval-valued intuitionistic fuzzy set, which is a generalization of the score function for intuitionistic fuzzy sets as well. The proposed score function is defined as the average amount of knowledge of information depicted in terms of the interval-valued intuitionistic fuzzy sets, that regards their quantitative level of information referred to a reference level, fuzziness and qualitative significance of information. It is proved that the proposed score function has good algebraic properties, such as monotonicity under multiplication or aggregation operator, which are not preserved in the case of existing score functions. We show that the proposed score function is a simple, easily interpreted approach, which provides intuitive results in ranking the IvIFSs as well as IFSs, particularly. Several illustrative examples are performed to demonstrate the superiority of the proposed method in measuring and discriminating the IvIFSs. A comparative analysis with the preceding methods in solving decision-making problems is conducted to show the effectiveness of the proposed method in real-life applications.