A Novel Multiobjective Game IDEA Cross-Efficiency Method Based on Boolean Possibility Degree for Ranking Biomass Materials With Interval Data

Abstract

The concept of processing biomass materials into charcoal briquettes is a viable solution for every developing nation’s energy crisis problem. However, the important properties of each biomass material must first be considered, in order to find suitable biomass materials for processing into charcoal briquettes. Sometimes these qualities are measured with imprecise values, making it exceedingly challenging to rank biomass materials’ decision-making units (DMUs). This problem is one of the interval data envelopment analysis (IDEA) ranking problems that make it difficult to calculate and rank all DMUs. In this paper, the concepts of the Game IDEA cross-efficiency method and Boolean possibility degree were utilized to solve the IDEA ranking problems. Unlike existing IDEA ranking models, a new multi-objective Game IDEA cross-efficiency (MO-G-IDEA-CE) method was used to obtain the Game interval cross-efficiency (GICE) scores of each DMU simultaneously. After that, the Boolean possibility degree was used to transform GICE scores into crisp values for ranking all DMUs. Three numerical examples including a simple numerical example, China’s primary schools and seven biomass materials problems are provided to demonstrate and validate the effectiveness of the proposed model. For the case study of seven biomass materials, after the Spearman correlation test, the correlation coefficients ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r_s</i> ) for the proposed method and Wang’s method and Wu <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i> .’s method are calculated as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r_s</i> = 1.000 and 0.964 respectively. In addition, it is worth noting that the proposed MO-G-IDEA-CE method has a very high correlation with the other ranking methods for all three numerical examples.