Three-way decisions with decision-theoretic rough sets based on covering-based q-rung orthopair fuzzy rough set model

Based on decision theory rough sets (DTRSs), three-way decisions (TWDs) provide a risk decision method for solving multi-attribute decision making (MADM) problems. The loss function matrix of DTRS is the basis of this method. In order to better solve the uncertainty and ambiguity of the decision problem, we introduce the q-rung orthopair fuzzy numbers (q-ROFNs) into the loss function. Firstly, we introduce concepts of q-rung orthopair fuzzy beta-covering (q-ROF beta-covering) and q-rung orthopair fuzzy beta-neighborhood (q-ROF beta-neighborhood). We combine covering-based q-rung orthopair fuzzy rough set (Cq-ROFRS) with the loss function matrix of DTRS in the q-rung orthopair fuzzy environment. Secondly, we propose a new model of q-ROF beta-covering DTRSs (q-ROFCDTRSs) and elaborate its relevant properties. Then, by using membership and non-membership degrees of q-ROFNs, five methods for solving expected losses based on q-ROFNs are given and corresponding TWDs are also derived. On this basis, we present an algorithm based on q-ROFCDTRSs for MADM. Then, the feasibility of these five methods in solving the MADM problems is verified by an example. Finally, the sensitivity of each parameter and the stability and effectiveness of these five methods are compared and analyzed.

Automated summary

This paper introduces the q-rung orthopair fuzzy numbers (q-ROFNs) to provide a method for solving multi-attribute decision making problems by combining Cq-ROFRS with the loss function matrix of DTRS. The aim is to improve the ability to solve uncertainties and ambiguities in decision making problems, and verify the feasibility of the methods through an algorithm.