DEA-based allocations of fixed costs in a fuzzy environment: fuzzy expected values and max–min satisfaction degree approaches

¹ School of Economics and Management, Chongqing Normal University, Chongqing 401331, P.R. China
² Decision Sciences Institute, Fuzhou University, Fuzhou 350108, P.R. China
³ Key Laboratory of Spatial Data Mining & Information Sharing of Ministry of Education, Fuzhou University, Fuzhou 350108, P.R. China

^* Corresponding author: sugarwang0813@163.com

Received: 3 October 2022
Accepted: 2 July 2025

Abstract

Due to incomplete and unattainable information, the data of inputs and outputs in production often cannot be obtained crisply but are represented by fuzzy data. Therefore, the data envelopment analysis (DEA) approach with precise data to fixed cost allocation is not applicable anymore, and the fuzzy DEA method is necessitated. This paper proposes the fuzzy DEA model based on the fuzzy expected values approach for the first measurement of fixed cost allocation, where the fuzzy inputs and fuzzy outputs are respectively weighted. It proves that there exist feasible allocation schemes that can render each DMU and the collection of all DMUs efficient. Additionally, with the help of the fuzzy expected values approach, the Max-min satisfaction degree principle is utilized to achieve the optimal solution to the fixed cost allocation in the fuzzy scenario. The proposed fuzzy expected values approach based on fuzzy DEA and satisfaction degree for the fixed cost allocation is illustrated by two numerical examples. It shows that the fuzzy DEA approach with the fuzzy expected values can crisply evaluate DMUs and avoid the comparison dilemma of fuzzy efficiencies, as well as determine a precise allocation plan of fixed costs that can make all DMUs DEA efficient.