A Novel Distance Measure and CRADIS Method in Picture Fuzzy Environment

Abstract

Abstract Picture fuzzy set (PFS) is an extension of intuitionistic fuzzy set, providing a more realistic representation of information characterized by fuzziness, ambiguity, and inconsistency. Distance measure plays a crucial role in organizing diverse strategies for addressing multi-attribute decision-making (MADM) problems. In this paper, we provide a novel distance measure on the basis of Jensen–Shannon divergence in a picture fuzzy environment. This newly proposed PF distance measure not only satisfies the four properties of metric space, but also has good differentiation. Numerical example and pattern recognition are used to compare the proposed PF distance measure with some existing PF distance measures to illustrate that the new PF distance has effectiveness and superiority. Then, we develop a maximum deviation method in association with the proposed distance measure to evaluate the weight of the attribute with picture fuzzy information in the MADM problem. Subsequently, a new MADM method is proposed under picture fuzzy environment, which is on the basis of new PF distance measure and the compromise ranking of alternatives from distance to ideal solution (CRADIS) method. Finally, we furnish an illustrative example and perform a comparative analysis with various decision-making methods to confirm the validity and practicability of the improved MADM method.

Keywords

• Picture fuzzy set (PFS)
• Multi-attribute decision-making (MADM)
• Picture fuzzy distance measure
• Compromise ranking of alternatives from distance to ideal solution (CRADIS) method