Aggregation Through Composition: Unification of Three Principal Fuzzy Theories
This paper shows that the theories of fuzzy rough sets, F-transforms and fuzzy automata can be unified in the framework of fuzzy relational structures. Specifically, the key concepts in such theories are represented as lattice-based aggregations in the form of compositions with suitable fuzzy relations. Furthermore, it is shown that the principal parts of morphisms between all considered fuzzy relational structures coincide.
KeywordsFuzzy relation Fuzzy rough set F-transform Fuzzy automata
This work is supported by University of Ostrava grant lRP201824 “Complex topological structures”. The additional support was also provided by the Czech Science Foundation (GAČR) through the project of No. 18-06915S.
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