Computation and Reasoning with Z-Numbers

In most cases the information relevant to the real-world decision is partially reliable. This can be explained by the unreliability of the source of information, misinterpretation, inexperience etc. Z-numbers-based formalization of information (Z-information) represents a Natural Language (NL)-based value of a variable of interest in line with the related NL-based reliability. The necessary point that needs to be considered is that a Z-information generally represents the imperfect information specific to real-world, but at the same time a Z-information has a powerful description from perception point of view of human compared to fuzzy number. In this thesis two conversion methods are given to convert the Z-number into the fuzzy number and also, to convert the fuzzy number into the crisp number. An approach to decision making under Z-information based on direct computation over Z-numbers is presented. This approach utilizes the expected utility paradigm and is applied to a benchmark decision problem in the field of economics. Keywords: Z-numbers, Fuzzy number, Discrete Z-numbers, Discrete fuzzy number, Utility value, Defuzzification, Decision making, Expected utility