XOR data envelopment analysis and its application to renewable energy sector

The conventional data envelopment analysis (DEA) method suffers from its inability to incorporate the decision -makers' preferences and cope with the uncertainty that exists in real-life decision problems. Exclusive-or (XOR for short) is an uncertain logic that describes a situation in which there is only one choice between two or more competitive actions and neither is strong enough to overcome the others. In this paper, a new research thread of the DEA paradigm, named XOR-DEA, is proposed to deal with decision-making problems under xorness (or XOR input/output data). To incorporate decision-makers' preferences in the optimization process, three types of preferences are proposed: positive, negative, and neutral. To cope deeply with uncertainty, a new concept of "the output mechanism of the XOR function"is developed to support the analyst in controlling this phenomenon based on two channels: controlled and uncontrolled. Moreover, to enrich the analysis of practical applications, a new visual analytic material is designed to detect the behavior of the XOR functions during the optimization process. To show the models' applicability, an illustrative example and an application of ranking renewable energy technologies are presented.