• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.79-84
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• 2022

We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T₁-connected fuzzy topological spaces.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.240-245
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• 1998

Fuzzy information retrieval which uses the concept of fuzzy relation is able to retrieve documents in the way based on not morphology but semantics, dissimilar to traditional information retrieval theories. Fuzzy information retrieval logically consists of three sets : the set of documents, the set of terms and the set of queries. It maintains a fuzzy relational matrix which describes the relationship between documents and terms and creates a thesaurus with fuzzy relational product. It also provides the user with documents which are relevant to his query. However, there are some problems on building a thesaurus with fuzzy relational product such that it has big time complexity and it uses fuzzy values to be processed with flating-point. Actually, fuzzy values have to be expressed and processed with floating-point. However, floating-point operations have complex logics and make the system be slow. If it is possible to exchange fuzzy values with binary values, we could expect sp eding up building the thesaurus. In addition, binary value expressions require just a bit of memory space, but floating -point expression needs couple of bytes. In this study, we suggest a new method of building a thesaurus, which accelerates the operation of the system by pre-applying an ${\alpha}$-cut. The experiments show the improvement of performance and reliability of the system.