Special Relationship among Decision Making Units based on Partially Ordered Set and New Evaluation and Projection Methods

Abstract

This paper provides data envelopment analysis methods based on partially ordered set theory. These methods reveal the special relationships between two decision making units from the perspective of mathematical theory and offer the classification, projection and improvement methods of decision making units. It is proved that an efficient decision making unit must be a maximal element of the related poset, and the maximal element may not be efficient. For this, we introduce the concepts of minimum envelope and efficiency envelope which further reveal the special relationship among efficient and inefficient decision making units. Compared with the previous methods, this method not only reveals theoretically the complex relationship among decision making units and the causes of the ineffectiveness, but also gives a new importance and competitiveness measurement method to each decision making unit. Finally, related algorithm and examples are given for the application of these methods to complex decision making problems.

Keywords

Data envelopment analysis / partially ordered set / returns to scale / projection / maximal element

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