Decision based algorithm for circular pythagorean fuzzy framework and advanced petroleum exploration methods.

This presentation articulates different terminologies of fuzzy mathematical approaches and decision-making techniques for handling vague-type human opinions. To achieve this purpose, we explore a novel approach of circular pythagorean fuzzy set (Cr-PyFS), which is an extended framework of intuitionistic and pythagorean fuzzy sets. A Cr-PyFS expresses expert opinion with an additional term radius of a circle among an element's membership grade and non-membership grade. Moreover, we also illustrate the theory of Hamy mean (HM) models to define correlation among different input arguments and preferences. By combining theories of HM models and Cr-PyFSs, we derived new mathematical methodologies, including circular pythagorean fuzzy HM (Cr-PyFHM), circular pythagorean fuzzy weighted HM (Cr-PyFWHM), circular pythagorean fuzzy Dual HM (Cr-PyFDHM) and circular pythagorean fuzzy weighted Dual HM (Cr-PyFDHM) operators. All aggregation operators (AOs) are verified through different mathematical properties and special cases. An intelligent decision algorithm of the multi-attribute decision-making (MADM) problem is modified considering circular pythagorean fuzzy information. To show the reliability and effectiveness of developed approaches, we discussed an application related to the exploration and production of the petroleum industry. An experimental case study is resolved using derived mathematical approaches and decision-making terminologies. The setting of different parametric variables in sensitivity analysis verifies the advantages and reliability of designed approaches. A comparison approach is conducted to compare the results of pioneered approaches with existing AOs.