Fuzzy Mathematics

Dear Colleagues,

Exactly today, 7 September, 2017, the founder of fuzzy set theory, Prof. Lotfi Zadeh, passed away at the age of 97. We would like to dedicate this Special Issue to our scientific father. In his 1965 seminal paper, entitled “Fuzzy sets” Zadeh extended Cantor’s binary set theory to a gradual model by introducing degrees of belonging and relationship. Very soon, this extension has been applied to almost all domains of contemporary mathematics giving birth to new disciplines, such as fuzzy topology, fuzzy arithmetic, fuzzy algebraic structures, fuzzy differential calculus, fuzzy geometry, fuzzy relational calculus, fuzzy databases and fuzzy decision making. In the beginning, mostly direct fuzzyfications of the classical mathematical domains have been launched by simply changing Cantor’s set-theoretic operations by Zadeh’s max-min extensions. The 1980s were characterized by an explosion of the possible fuzzyfications due to the discovery of triangular norms and co-norms. Starting from the nineties more profound analysis has been performed by studying the axiomatization of fuzzy structures and searching for links between the different models to represent imprecise and uncertain information. It is our aim to have in this Special Issue a healthy mix of excellent state-of-the-art papers, as well as brand-new material that can serve as a starting point for newcomers in the field to further develop this wonderful domain of fuzzy mathematics.

Prof. Dr. Etienne E. Kerre
Prof. Dr. John Mordeson
Guest Editors

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