Ranking of Z-Numbers and Its Application in Decision Making

• Published in: International journal of information technology & decision making Vol. 15; no. 6; pp. 1503 - 1519
• Main Authors: Aliev, R. A., Huseynov, O. H., Serdaroglu, R.
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 01.11.2016; World Scientific Publishing Co. Pte., Ltd
• Subjects: Decision analysis; Decision making; Ecological monitoring; Economic analysis; Ranking; Reliability; Systems analysis; probability measure; Ranking; uncertainty aversion; fuzzy optimality; Z-number; fuzzy number
• ISSN: 0219-6220; 1793-6845
• DOI: 10.1142/S0219622016500310

Real-world decision problems in decision analysis, system analysis, economics, ecology, and other fields are characterized by fuzziness and partial reliability of relevant information. In order to deal with such information, Prof. Zadeh suggested the concept of a Z-number as an ordered pair Z = ( A , B ) of fuzzy numbers A and B , the first of which is a linguistic value of a variable of interest, and the second one is a linguistic value of probability measure of the first one, playing a role of reliability of information. Decision making under Z-number based information requires ranking of Z-numbers. In this paper we suggest a human-like fundamental approach for ranking of Z-numbers which is based on two main ideas. One idea is to compute optimality degrees of Z-numbers and the other one is to adjust the obtained degrees by using a human being’s opinion formalized by a degree of pessimism. Two examples and a real-world application are provided to show validity of the suggested research. A comparison of the proposed approach with the existing methods is conducted.