𝑍-Distance Based IF-THEN Rules

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.