A picture fuzzy similarity measure based on direct operations and novel multi-attribute decision-making method

Picture fuzzy set (PFS) is a direct generalization of the fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) and is quite powerful in modelling the situations that involve more answers of the type yes, no, abstain, and refuse. In this study, we introduce a novel picture fuzzy (PF) similarity measure on the basis of direct operation on the function of membership, the function of non-membership, the function of neutrality, the function of refusal, and the upper bound of the function of membership of two PFSs instead on the basis of distance measure or the association between the functions of membership, non-membership, and neutrality. The comparison of the proposed PF similarity measure with the existing PF similarity measures reveals that it does not give unreasonable results and also overcomes the drawbacks of the existing PF similarity measures. The application of the proposed measure in pattern recognition is also discussed. Moreover, we also introduce a new multi-attribute decision-making (MADM) method using the proposed PF similarity measure that overcomes a major drawback of the technique for order preference by similarity to ideal solution (TOPSIS). Finally, we contrast the performance of the proposed MADM method with several existing MADM methods in the PF environment.