EXTENSION OF FUZZY IMPLICATIONS TO Z-IMPLICATION

The effectiveness of any management process in technical, organizational and other systems depends on the quality of the decisions used.Decisions are more useful if they are made on the basis of reliable information.The description of the reliability of information is not always possible within the framework of strict mathematical regularities, because it is based on perception, expressed by words .Considering that information processing in computers is based on binary logic, it turns out that there are numerous problems in this area.There are numerous approaches to information processing based on probability theory, fuzzy logic, and Zadeh's latest theory-Z-number theory.Zadeh introduced the concept of fuzzy implication in 1965, Atanassov introduced the concept of intuitionistic fuzzy implication in 1983, Torra introduced the concept of hesitant fuzzy implication in 2010, Przemyslaw Grzegorzewski introduced the concept of new probabilistic implication in 2011, and Zadeh introduced the concept of Z-number theory into science.Thus, fundamental knowledge was accumulated for the development of new approaches in this field.Based on the analytical analysis, it can be noted that the solution to the information processing problem by using probability and fuzzy implications together can be solved with a new approach based on Z-number theory.It was this idea that gave impetus to the formation of the new Z-implication (in 2025) and the creation of the Z-conditional reasoning algorithm based on it.In this work, we will prove that 3 fuzzy implications-Fodor, Gödel, Rescher implications are probabilistic implications.This also proves that these implications are Z-implications.