Data Envelopment Analysis (DEA) as a data-oriented benchmarking tool is considered a powerful and promising instrument for performance evaluation in various application areas. In DEA, the set of all decision-making units (DMUs) is divided into efficient and inefficient subsets. Inefficient DMUs are improved by reducing the input and/or increasing the output, and as far as we know, efficient DMUs are abandoned with the conclusion that they are all technically and relatively efficient, and no further analysis has been suggested in the literature. In this article, we first show that there is a gap between the actual efficiency and the efficiency estimated using benchmarking tools such as DEA. This means that there is no guarantee that the efficient DMUs characterized by DEA are really efficient. Thus, there is a gap in improving the technical efficiency of efficient DMUs. In this paper, we attempt to close this gap by introducing a method to improve efficient DMUs. First, we introduce a random variable as a corrector of efficiency evaluation, and then an inverse DEA model (IDEA) is proposed to improve efficient DMUs. To demonstrate the actual applicability of the proposed approach, we present an illustrative empirical application using 106 Chinese bank data from 2021.

This paper introduces two processes of ranking methods on Z-numbers that are effectively able to deal with uncertain decision-making data. Decision making is based on recommended Z- numbers. For this purpose first, the Z-number is transformed to a fuzzy number and then the ranking method by using the sigmoid function and the sign method is used to mention fuzzy numbers. For the next step, the method is extended to related Z-numbers. Finally, we use it to prioritize the items and solve some examples.

In this paper, the parametric form of Z-numbers is introduced and it is followed by defining arithmetic operations on them. To suggest Z-number initial value problem (ZIVP), definition of derivative of Z-process is necessary. For this purpose, the generalized Hukuhara differentiation and generalized differentiation are defined in details. To solve the mentioned ZIVP, the characterization theorem is proved. Finally, for more illustrations of the subject, some examples are solved and expounded.