Abstract
In the first place, the paper proves that the reasonable and significant binary operation in [0, 1] for membership functions of type O of fuzzy sets of type O will be ∧ (or ∨) if the reasonable and significant binary operations in [0, 1] for membership functions of type O are triangular norms (or triangular conorms). Secondly, the definition of fuzzy equivalent relations of type O of fuzzy sets of type O is given, and we discuss the feasibility and meaning of making fuzzy clustering based on transitive closures of strongly reflexive and symmetric fuzzy relations of type O.
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