On entropy function and reliability indicator for D numbers

As an extension of Dempster-Shafer evidence theory, D numbers theory is developed with two more generalized properties that the elements in its frame of discernment do not require to be mutually exclusive strictly and the completeness constraint is released in its framework, which make it an effective tool for expressing and handling uncertain information. As a form of information representation and processing, there exists a certain amount of uncertainty in D numbers. How to reasonably measure the uncertainty of D numbers is still an open issue, and it is crucial to its further development and application. To address this issue, in this paper, a novel entropy function is defined to measure the uncertainty of D numbers, and based on which, the reliability indicator of D numbers is proposed motivated by TOPSIS method. Some numerical examples are given to illustrate the process of the proposed entropy function and reliability indicator, and in order to further demonstrate their effectiveness, a real-life application is conducted for bridge condition assessment problem using the developed D numbers approach.

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