Complex Diophantine interval-valued Pythagorean normal set for decision-making processes

Abstract

A novel method for solving the multiple-attribute decision-making problem is proposed using the complex Diophantine interval-valued Pythagorean normal set (CDIVPNS). This study aims to discuss aggregating operations and how they are interpreted. We discuss the concept of CDIVPN weighted averaging (CDIVPNWA), CDIVPN weighted geometric (CDIVPNWG), generalized CDIVPN weighted averaging (CGDIVPNWA) and generalized CGDIVPN weighted geometric (CGDIVPNWG). This study aimed to examine several aggregation operators using complex Diophantine interval-valued Pythagorean normal sets. We calculated the weighted average and geometric distance based on an aggregating model. We demonstrate that complex Diophantine interval-valued Pythagorean normal sets satisfy algebraic structures such as associative, distributive, idempotent, bounded, commutative and monotonic properties. In this study, we discuss the mathematical properties of the score and accuracy values. We provide an example of how enhanced score and accuracy values are used in the real world. Machine tool technology and computer science play essential roles in robots. To evaluate robotic systems, four factors must be considered such as tasks, precision, speed and completion of the work. Consequently, it is evident that the models are significantly influenced by the natural number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla$$\end{document}. To further demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and applied to a numerical example. Additionally, a comparative study has been carried out to demonstrate the better results that the proposed approach provides when compared to current approaches.