A parametric similarity measure for extended picture fuzzy sets and its application in pattern recognition

This article advances the idea of extended picture fuzzy set (E-PFS), which is especially an augmentation of generalised spherical fuzzy set (GSFS) by releasing the restricted selection of $p$ in the description of GSFSs.Moreover, by the use of triangular conorm term in the description of E-PFS, it indeed widens the scope of E-PFS not only compared to picture fuzzy set (PFS) and spherical fuzzy set (SFS), but also to GSFS. In the sequel, a given fundamental theorem concerning E-PFS depicts its more ability in comparison with the special types to deal with the ambiguity and uncertainty.Further, we propose a parametric E-PFS similarity measure which plays a critical role in information theory.In order for revealing the advantages and authenticity of E-PFS similarity measure, we exhibit its applicability in multiple criteria decision making entitling the recognition of building material, the recognition of patterns, and the selection process of mega project(s) in developing countries.Furthermore, through the experimental studies, we demonstrate that E-PFS is able to handle uncertain information in real-life decision procedures with no extra parameter, and it has a prominent role in decision making whenever the concepts of  PFS, SFS and GSFS do not make sense.