A New Uncertainty Measure of Discrete Z-numbers

摘要

Today's modern decision-making problem is designated by not being the most effective fuzziness; however, additionally partial reliability also plays a crucial role. The incomplete and unreliable information may also affect the selection maker to earn inaccurate decisions, ensuing in monetary losses and wastes of resources. Thus, it is vital to describe the reliability of the facts. To cope with it entirely, a notion of Z-number, i.e., a pair of fuzzy sets modeling a probability-qualified fuzzy statement, is the most suitable medium to access it. In this paper, we spout a new technique to measure the uncertainty of discrete Z-numbers based on Shannon entropy. In the given approach, by using characteristics of Z-number, all the potential probability distributions are estimated by the maximum entropy method. Then, a new fuzzy subset of the Z-number is formed based on the probability distributions and the membership functions of the fuzzy number. Finally, the centroid of the formulated set is determined to rank the degree of the uncertainty of Z-number. The applicability of the delivered approach is read with some numerical examples related to the decision-making process.