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Mathematical aspects of fuzzy sets and fuzzy logic. Some reflections after 40 years. (English) Zbl 1088.03024
This survey paper considers some of the main trends of the development of mathematical fuzzy logic and of formalized fuzzy set theory. In four decades of fuzzy set theory and fuzzy logic, the last one has seen a tremendous wealth of new and important approaches and results which paved the way for the future success. Especiall BL-algebras, introduced by P. Hájek, brought a qualitative jump in the fuzzy logic theory and they have initiated several new streams of research. Some important open problems for further research are mentioned in the concluding remarks of this interesting paper that is worth reading for any scientist interested in logic, artificial intelligence or soft computing.

MSC:
03B52 Fuzzy logic; logic of vagueness
03E72 Theory of fuzzy sets, etc.
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03-03 History of mathematical logic and foundations
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