Extended version of decision making model for industrial robot selection via fractional continuous fuzzy information

Abstract

Fractional fuzzy sets are widely used in decision-making problems; however, they often face limitations in accurately modeling membership and non-membership values. These sets are considered classical models because they use only specific values from the closed interval [0, 1], which leads to a rigid decision-making structure. To address these challenges, we introduce the concept of fractional continuous fuzzy sets, which integrate continuity into the fuzzy framework and use continuous functions instead of fixed numbers. This allows for a broader and more flexible neighborhood around each decision point. The enhanced structure enables the evaluation of both individual points and their surrounding behavior, improving the sensitivity and precision of the decision-making process. We define multiple types of score and accuracy functions based on the Riemann integral, and utilize function-theoretic tools to analyze the continuous fuzzy data. Two decision-making algorithms are proposed and applied to a real-world industrial robot selection problem. The results are then compared with existing MCDM methods, demonstrating the effectiveness, flexibility, and reliability of the proposed approach.