Abstract
Picture fuzzy set (PFS) is a direct generalization of the fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). The concept of PFS is suitable to model the situations that involve more answers of the type yes, no, abstain, and refuse. In this study, we introduce a novel picture fuzzy (PF) distance measure on the basis of direct operation on the functions of membership, non-membership, neutrality, refusal, and the upper bound of the function of membership of two PFSs. We contrast the proposed PF distance measure with the existing PF distance measures and discuss the advantages in the pattern classification problems. The application of fuzzy and non-standard fuzzy models in the real data is very challenging as real data is always found in crisp form. Here, we also derive some conversion formulae to apply proposed method in the real data set. Moreover, we introduce a new multi-attribute decision-making (MADM) method using the proposed PF distance measure. In addition, we justify necessity of the newly proposed MADM method using appropriate counterintuitive examples. Finally, we contrast the performance of the proposed MADM method with the classical MADM methods in the PF environment.
Highlights
The comparison of the two distinct objects from various viewpoints is necessary to deal with various real-life problems concerning machine learning, pattern recognition, image processing, decision-making, etc
With the help of the novel PF distance measure, we propose a new method known as the picture fuzzy inferior ratio (PFIR) method for solving multi-attribute decision-making (MADM) problems in the PF environment that is based on the same idea as TOPSIS considering the distance from the positive ideal solution (PIS) as well as from the negative ideal solution (NIS)
To overcome this major drawback, we introduce a new MADM method in the PF environment known as the picture fuzzy inferior ratio (PFIR) method based on the same concept as in TOPSIS that the chosen alternative should be closest to picture fuzzy positive ideal solution (PFPIS) and farthest from picture fuzzy negative ideal solution (PFNIS)
Summary
The comparison of the two distinct objects from various viewpoints is necessary to deal with various real-life problems concerning machine learning, pattern recognition, image processing, decision-making, etc. Nhung et al [53] proposed some new dissimilarity measures involving PF-information and applied them in pattern recognition and multi-criteria decision-making (MCDM). With the help of the novel PF distance measure, we propose a new method known as the picture fuzzy inferior ratio (PFIR) method for solving MADM problems in the PF environment that is based on the same idea as TOPSIS considering the distance from the positive ideal solution (PIS) as well as from the negative ideal solution (NIS). In “Experiments and analysis”, we run some experiments on synthetic dataset as well as on real dataset regarding problems of pattern recognition These numerical experiments facilitate us to contrast the performance of our proposed PF distance measure with various existing PF compatibility measures. The section “Conclusion” includes the main findings of this paper and the scope for the future research
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