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Decision making, reasoning, and analysis in real-world problems are complicated by imperfect information. Real-world imperfect information is mainly characterized by two features. In view of this, Professor 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 its reliability. The concept of distance is one of the important concepts for handling imperfect information in decision making and reasoning. In this paper, we, for the first time, apply the concept of distance of Z-numbers to the approximate reasoning with Z-number based IF-THEN rules. We provide an example on solving problem related to psychological issues naturally characterized by imperfect information, which shows applicability and validity of the suggested approach

The application of z-numbers in fuzzy decision making: The state of the art

A Z-number is very powerful in describing imperfect information, in which fuzzy numbers are paired such that the partially reliable information is properly processed. During a decision-making process, human beings always use natural language to describe their preferences, and the decision information is usually imprecise and partially reliable. The nature of the Z-number, which is composed of the restriction and reliability components, has made it a powerful tool for depicting certain decision information. Its strengths and advantages have attracted many researchers worldwide to further study and extend its theory and applications. The current research trend on Z-numbers has shown an increasing interest among researchers in the fuzzy set theory, especially its application to decision making. This paper reviews the application of Z-numbers in decision making, in which previous decision-making models based on Z-numbers are analyzed to identify their strengths and contributions. The decision making based on Z-numbers improves the reliability of the decision information and makes it more meaningful. Another scope that is closely related to decision making, namely, the ranking of Z-numbers, is also reviewed. Then, the evaluative analysis of the Z-numbers is conducted to evaluate the performance of Z-numbers in decision making. Future directions and recommendations on the applications of Z-numbers in decision making are provided at the end of this review

Application of fuzzy sets in data-to-text system

This PhD dissertation addresses the convergence of two distinct paradigms: fuzzy sets and natural language generation. The object of study is the integration of fuzzy set-derived techniques that model imprecision and uncertainty in human language into systems that generate textual information from numeric data, commonly known as data-to-text systems. This dissertation covers an extensive state of the art review, potential convergence points, two real data-to-text applications that integrate fuzzy sets (in the meteorology and learning analytics domains), and a model that encompasses the most relevant elements in the linguistic description of data discipline and provides a framework for building and integrating fuzzy set-based approaches into natural language generation/data-to-ext systems