**Preface to "Fuzzy Sets, Fuzzy Logic and Their Applications 2020"**

A few decades ago, probability theory was the unique tool in the hands of experts for handling situations of the uncertainty appearing in problems of science, technology and everyday life. Probability, which is based on principles of the traditional, bivalent logic, is sufficient for tackling problems of uncertainty connected to randomness, but not those connected with imprecise or vague information. However, nowadays, with the development of fuzzy set theory introduced by Zadeh in 1965, and in extension of fuzzy logic, which is based on it, things have changed. In fact, these new mathematical tools have given the scientists the opportunity to model under conditions which are vague or not precisely defined, thus succeeding to solve mathematically problems whose statements are expressed in our natural language.

As a result, the spectre of their applications has been rapidly extended, covering all physical sciences, economics and management, expert systems, like financial planners, diagnostic, meteorological, information-retrieval, control systems, etc., industry, robotics, decision making, programming, medicine, biology, humanities, education, and almost all the other sectors of human activity, including human reasoning itself. It must be mentioned that fuzzy mathematics has also been significantly developed on a theoretical level, providing important insights even to branches of classical mathematics, like algebra, analysis, geometry, etc.

The present book contains the 24 articles accepted for publication among the 66 total manuscripts submitted to the Special Issue "Fuzzy Sets, Fuzzy Logic and Their Applications, 2020" of the MDPI *Mathematics* journal. This Special Issue is a continuity of last year's successful issue on the same subject, which has also been published in the form of a book containing 20 articles.

The 24 articles, which appear in the present book in the series that they have been published in Volumes 8 (2020) and 9 (2021) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy sets and systems, fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc.

It is hoped that the book will become interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those having the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics and fuzzy logic. As the Guest Editor of the Special Issue, I am grateful to the authors of the papers for their quality contributions, to the reviewers for their valuable comments towards the improvement of the submitted works, and to the administrative staff of the MDPI publications for the support to complete this project. Special thanks must be given to the Managing Editor of the Special Issue Ms. Grace Du for her excellent collaboration and valuable assistance.

> **Michael Gr. Voskoglou** *Editor*
