• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.135-148
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• 2023

We prove that for any preordered intuitionistic fuzzy approximation space, an intuitionistic fuzzy topology can be created, and conversely, for any intuitionistic fuzzy topology, a reflexive intuitionistic fuzzy relation can be constructed. We also show that there is a relationship, called Galois correspondence, between the functors of these categories. Additionally, by applying certain limitations on the category of intuitionistic fuzzy topological spaces, we obtain an isomorphism between these categories.

• Journal of Korean Society of Transportation
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• v.22 no.3 s.74
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• pp.179-201
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• 2004

Online traffic flow modeling is attracting more attention due to intelligent transport systems and technologies. The flow-density relation plays an important role in traffic flow modeling and provides a basic way to illustrate traffic flow behavior under different traffic flow and traffic density conditions. Until now the research effort has focused mainly on the shape of the relation. The time series of the relation has not been identified clearly, even though the time series of the relation reflects the upstream/downstream traffic conditions and should be considered in the traffic flow modeling. In this paper the flow-density relation is analyzed dynamically and interpreted as a states diagram. The dynamic flow-density relation is quantified by applying fuzzy logic. The quantified dynamic flow-density relation builds the basis for online application of a macroscopic traffic flow model. The new approach to online modeling of traffic flow applying the dynamic flow-density relation alleviates parameter calibration problems stemming from the static flow-density relation.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1109-1118
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• 2019

In this paper, we introduce the notion of residuated and Galois connections on adjoint triples and investigate their properties. Using the properties of residuated and Galois connections, we solve fuzzy relation equations and give their examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.6
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• pp.48-52
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• 1998

We introduce the concepts of fuzzy s-continuous mappings, s-open mappings, and s-closed mappings. We investigate several properties of such mappings. In particular, we study the relation between fuzzy s-continuous mappings and fuzzy s-open mappings(s-closed mappings).

• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.3
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• pp.89-93
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• 1996

In this paper, we investigated the relation between the ideals of BCK-algebras and fuzzy ideals. We defined the weakly implicative ideals of BCK-algebras and obtained some properties. We proved some results for the fuzzy weakly implicative ideals of bounded commutative BCK-algebras. We also investigated that the weakly implicative ideals are similar to the fuzzy positive implicative ideals.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.425-431
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• 2009

By using the notion of interval-valued fuzzy relations, we forms the poset (IVFR (X), $\leq$) of interval-valued fuzzy relations on a given set X. In particular, we forms the subposet (IVFE (X), $\leq$) of interval-valued fuzzy equivalence relations on a given set X and prove that the poset (IVFE(X), $\leq$) is a complete lattice with the least element and greatest element.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.1
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• pp.145-152
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• 2011

By using the notion of interval-valued intuitionistic fuzzy relations, we form the poset (IVIR(X), $\leq$) of interval-valued intuitionistic fuzzy relations on a given set X. In particular, we form the subposet (IVIE(X), $\leq$) of interval-valued intuitionistic fuzzy equivalence relations on a given set X and prove that the poset (IVIE(X), $\leq$) is a complete lattice with the least element and greatest element.

• Journal of the Ergonomics Society of Korea
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• v.16 no.2
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• pp.1-14
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• 1997

In conventional probability-based human reliability analysis, the basic human error rates are modified by experts to consider the influences of many factors that affect human reliability. However, these influences are not easily represented quantitatively, because the relation between human reliability and each of these factors in not clear. In this paper, the relation is expressed quantitatively. Furthermore, human reliability is represented by error possibilities proposed by Onisawa, which is a fuzzy set on the interval [0,1]. Fuzzy reasoning is used in this method in order to obtain error possibilities. And, it is supposed that many basic events affected by the above factors are connected to the top event through Fault Tree structure, and an estimate of the top event expressed by a member- ship function is obtained by using the fuzzy measure and fuzzy integral. Finally, a numerical example of human reliability analysis obtained by this method is given.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.201-211
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• 2017

The notion of falling fuzzy filters of a BE-algebra is introduced based on the theory of falling shadows and fuzzy sets. Relation between fuzzy filters and falling fuzzy filters are presumed and characterized them interms of subsets of a sample space.

• East Asian mathematical journal
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• v.22 no.1
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• pp.93-109
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• 2006

The concept of intuitionistic fuzzy set was first introduced by Atanassov in 1986. In this paper, we define the intuitionistic(S,T)-fuzzy left h-ideals of a hemiring by using an s-norm S and a t-norm T and study their properties. In particular, some results of fuzzy left h-ideals in hemirings recently obtained by Jun, $\"{O}zt\"{u}rk$, Song, and others are extended and generalized to intuitionistic (S,T)-fuzzy ideals over hemirings.