Detection of the Type of Left and Right Returns-to-Scales Using Envelopment DEA Models in Crisp and Fuzzy Environments: An Application for Predicting Changes in the Stock Market

Abstract

This paper aims to analyze left and right returns-to-scales in crisp and fuzzy data envelopment analysis (DEA). Since all previous envelopment DEA models for assessing left and right returns-to-scales are parametric, they are prone to encountering infeasibility problems, producing incorrect or different solutions for determining the type of returns-to-scale because of the different choices of parameter values. This misdiagnosis will lead to poor management decisions. Due to the mentioned problems, the issue of one-sided returns-to-scale has also not been studied in inaccurate environments. The present paper first proposes an alternative method of left and right returns-to-scales determination with crisp data to address this problem. This approach develops two non-parametric envelopment DEA models for analyzing left and right returns-to-scales. Then, the proposed method is extended to the fuzzy environment where data are considered more realistic. Due to its major advantages, credibility measure is used for solving fuzzy DEA models built to determine left and right returns-to-scales. As an application of the proposed method, data of companies in the Iran stock market are collected for 2014–2019 as fuzzy data and frontier units are analyzed by one-sided returns-to-scale.