• Korean Journal of Mathematics
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• v.14 no.2
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• pp.241-248
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• 2006

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, and characterize the G-fuzzy congruence generated by a left and right compatible fuzzy relation on a semigroup.

• Journal of the Korean Society for Railway
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• v.9 no.4 s.35
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• pp.432-440
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• 2006

Prior to the service evaluation, many kinds of its attributes must be identified on the basis of rational decision owing to complexity and ambiguity inherent in logistics service. there are so many evaluation methods but they are not applicable to logistics service the have property of non-additivity and overlapped attributes. Therefore, probability measure can not used to evaluate logistics service but Fuzzy Measure is required. And the method should be easy to calculate it Recently Fuzzy theory has been applied in Various evaluation problem. Fuzzy evaluation based on Fuzzy theory can accommodate fuzziness in judgement with people through introducing Fuzzy Measure. In this paper, Hierarchical Fuzzy Process is applied to evaluate level of logistics service in Korail and the biggest six logistics companies in the korea which is called 3PL Company. Also Fuzzy Relation Equation which is problem identifying evaluation value at these fuzzy evaluation is applied to verify relation between Input and Output data through @-operation. Therefore, we apply this Fuzzy Relation Equation to Hierarchical Fuzzy Process and verify evaluation value which objects of evaluation are able to possess.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.5
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• pp.451-459
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• 2013

In this paper we analyze the Korean foods and sensory adjectives that can be used for the taste expression of corresponding food based on the fuzzy relation. In order to construct fuzzy relation we gathered and chose 87 related Korean adjectives for expressing not only taste but also smell from foods. After then we performed a sensory evaluation for 51 Korean foods with 20 subjects to check the proper adjectives when they take a food. Based on the data collected by the evaluation a fuzzy relation is constructed and used for the analysis of the properties of food and adjectives. In addition the composition of the fuzzy relation provides the fuzzy tolerance(compatibility) relation among foods as well as that among adjectives. From the fuzzy complete ${\alpha}$-cover of the relations we could explore the taxonomy of food or adjectives. We expect that the fuzzy relation-based scheme in the paper can be utilized for analysis of the sensory adjectives like smelling and tactile sensation.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.4
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• pp.832-839
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• 2009

In this paper, we introduce an design of fuzzy relation-based fuzzy neural networks with multi-output. Fuzzy relation-based fuzzy neural networks comprise the network structure generated by dividing the entire input space. The premise part of the fuzzy rules of the network reflects the relation of the division space for the entire input space and the consequent part of the fuzzy rules expresses three types of polynomial functions such as constant, linear, and modified quadratic. For the multi-output structure the neurons in the output layer were connected with connection weights. The learning of fuzzy neural networks is realized by adjusting connections of the neurons both in the consequent part of the fuzzy rules and in the output layer, and it follows a back-propagation algorithm. In addition, in order to optimize the network, the parameters of the network such as apexes of membership functions, learning rate and momentum coefficient are automatically optimized by using real-coded genetic algorithm. Two examples are included to evaluate the performance of the proposed network.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.106.2-106
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• 2001

The two typical composite operations of fuzzy relation are the max-min and the min-max composite operations. It is known that the two operations can be completely dual. This paper pays attention to the nature that these two typical operations are completely dual and investigates the correlation between the max-min composite relation equation and the min-max composite relation equation. An important scheme of correlation is in the characteristic of solution sets derived from these two fuzzy relation equations. The paper explains that one of the composite fuzzy relation equations is solvable using the solution method of the other fuzzy relation equation. The above-mentioned duality plays an important role in this solution procedure. Since it is not necessary to build the solution method separately like before, calculation efficiency can be raised. Moreover, the solution for the relation ...

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.343-356
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• 2010

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, discuss some of its basic properties, and characterize the G-fuzzy congruence generated by a fuzzy relation on a semigroup. We also give certain lattice theoretic properties of G-fuzzy congruences on semigroups.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.563-577
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• 2017

We define a weak fuzzy equivalence relation and a weak fuzzy congruence and develop some properties of the weak fuzzy equivalence relations and the weak fuzzy congruences on semigroups.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.683-691
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• 2014

We redefine a fuzzy congruence, discuss some properties of the fuzzy congruences, find the fuzzy congruence generated by a fuzzy relation on a semigroup, and give some lattice theoretic properties of the fuzzy congruences on semigroups.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1071-1084
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• 2008

The notion of intuitionistic fuzzy filters in ordered semigroups is introduced and relation between intuitionistic fuzzy filters and intuitionistic fuzzy prime ideals is investegated. The notion of intuitionistic fuzzy bi-ideal subsets and intuitionistic fuzzy bi-filters are provided and relation between intuitionistic fuzzy bi-filters and intuitionistic fuzzy prime bi-ideal subsets is established. The concept of intuitionistic fuzzy right filters(1eft filters) is given and their relation with intuitionistic fuzzy prime right (left) ideals is discussed.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.219-234
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• 2020

The fundamental relation on a fuzzy hyperring is defined as the smallest equivalence relation, such that the quotient would be the ring, that is not commutative necessarily. In this paper, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings, where the ring is commutative with respect to both sum and product. With considering this relation on fuzzy hyperring, the set of the quotient is a commutative ring. Also, we introduce fundamental functor between the category of fuzzy hyperrings and category of commutative rings and some related properties. Eventually, we introduce α-part in fuzzy hyperring and determine some necessary and sufficient conditions so that the relation α is transitive.