# Integration of MULTIMOORA algorithm combined with circular q-rung orthopair fuzzy information for optimizing player positioning

## TL;DR

This paper introduces a new method using fuzzy logic and optimization to improve player positioning decisions in sports.

## Contribution

A novel integration of MULTIMOORA with circular q-rung orthopair fuzzy sets and Dombi operators for multi-objective decision-making.

## Key findings

- The proposed Cq-ROFSDPWA and Cq-ROFSDPWG operators show logical and consistent results in decision-making scenarios.
- Comparative analysis demonstrates advantages of the new operators over existing methods.
- Empirical experiments validate the practical relevance of the methodology.

## Abstract

The following paper presents a new analytical framework for the optimization of player positioning, a methodology with significant practical implications. The method implements the multi-objective optimization by ratio analysis with full multiplicative form (MULTIMOORA) in a decision-making context in which several non-commensurable performance variables have to be combined. The application of Dombi operationalizes the framework by prioritizing weighted aggregation operators coupled with circular q-rung orthopair fuzzy sets (Cq-ROFSs). The Cq-ROFSs allow multidimensional representation of uncertainty, and allow dynamic actions upon the fuzzy parameter q, such that both intuitionistic fuzzy sets and Pythagorean fuzzy sets are subsets. Two Dombi prioritized operators on Cq-ROFSs are thereby devised a Cq-ROFSs Dombi prioritized weighted averaging operator (Cq-ROFSDPWA) and a Cq-ROFSs Dombi prioritized weighted geometric operator (Cq-ROFSDPWG). Results from empirical experiments are reported that demonstrate the performance of the resulting methodology, highlighting its practical relevance. The fundamental properties of these operators are also examined. The proposed aggregation operators are applied within the MULTIMOORA technique to assess their effectiveness. Numerical examples demonstrate that the methods yield logical and consistent results across different decision-making scenarios. Comparative analyses further highlight the advantages of the Cq-ROFSDPWA and Cq-ROFSDPWG operators over existing approaches.

The online version contains supplementary material available at 10.1038/s41598-025-18795-0.