Multi-Layer Decision Methodology For Ranking Z-Numbers

The new concept of a Z - number has been recently introduced in decision making analysis. This concept is capable of effectively dealing with uncertainty in information about a decision. As this concept is relatively new in fuzzy sets, its underlying theoretical aspects have not been established yet. In this paper, a multi-layer methodology for ranking Z - numbers is proposed for the first time. This methodology consists of two layers: Z - number conversion as the first layer and fuzzy number ranking as the second layer. In this study, the conversion methodology of Z - numbers into fuzzy numbers is extended to conversion into standardised generalised fuzzy number so that the methodology is applicable to both positive and negative data values. The methodology is validated by means of thorough comparison with some established ranking methods for consistency purposes. This methodology is considered as a generic decision making procedure, especially when Z - numbers are applied to real decision making problems.