• Communications of the Korean Mathematical Society
• /
• v.26 no.3
• /
• pp.349-371
• /
• 2011

Using the "belongs to" relation and "quasi-coincident with" relation between a fuzzy point and a fuzzy subgroup, Bhakat and Das, in 1992 and 1996, initiated general types of fuzzy subgroups which are a generalization of Rosenfeld's fuzzy subgroups. In this paper, more general notions of "belongs to" and "quasi-coincident with" relation between a fuzzy point and a fuzzy set are provided, and more general formulations of general types of fuzzy (normal) subgroups by Bhakat and Das are discussed. Furthermore, general type of coset is introduced, and related fundamental properties are investigated.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.9 no.1
• /
• pp.20-29
• /
• 2009

In this paper, by using the definition of fuzzy equivalence relations introduced by Dib and Youssef, we obtain fuzzy analogues of many results concerning ordinary equivalence relations. Moreover, we investigate fuzzy analogues of many results concerning relationships between ordinary equivalence relations and ordinary functions. In particular, we obtain the fuzzy-canonical decomposition of a fuzzy function.

• Communications of the Korean Mathematical Society
• /
• v.23 no.4
• /
• pp.461-468
• /
• 2008

We define an $\epsilon$-fuzzy congruence, which is a weakened fuzzy congruence, find the $\epsilon$-fuzzy congruence generated by the union of two $\epsilon$-fuzzy congruences on a semigroup, and characterize the $\epsilon$-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all $\epsilon$-fuzzy congruences on a semigroup is a complete lattice and that the collection of $\epsilon$-fuzzy congruences under some conditions is a modular lattice.

• Honam Mathematical Journal
• /
• v.28 no.3
• /
• pp.291-315
• /
• 2006

By using the new concepts of fuzzy equivalence relations and fuzzy partitions which Dib and Youssef introduced, we obtains fuzzy analogues of many results concerning ordinary equivalence relations and partitions. Also, we give some examples.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.3
• /
• pp.557-569
• /
• 2013

In this paper we shall introduce the $f$-function in a set, and give some properties of $f$-function of a set. In particular, we establish a relation between $f$-function of a set and fuzzy equivalence relation. We also introduce the notion of $f$-homomorphism on a semigroup S, and prove the generalized fundamental homomorphism theorem of semigroup.

• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.205-213
• /
• 2000

In this paper we introduce the concept of a fuzzy strongly regular relation on a sumihypergroup, and prove a few results concerning this concept.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.13 no.3
• /
• pp.505-513
• /
• 2009

Z. Cao had proposed NFRM(new fuzzy reasoning method) which infers in detail using relation matrix. In spite of the small inference rules, it shows good performance than mamdani's fuzzy inference method. But the most of fuzzy systems are difficult to make fuzzy inference rules in the case of MIMO system. The past days, We had proposed the MIMO fuzzy inference which had extended a Z. Cao's fuzzy inference to handle MIMO system. But many times and effort needed to determine the relation matrix elements of MIMO fuzzy inference by heuristic and trial and error method in order to improve inference performances. In this paper, we propose a MIMO fuzzy inference method with the learning ability witch is used a gradient descent method in order to improve the performances. Through the computer simulation studies for the inverse kinematics problem of 2-axis robot, we show that proposed inference method using a gradient descent method has good performances.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.06a
• /
• pp.556-561
• /
• 1998

This paper deals with our proposed fuzzy inference method, in which the fuzzy relation is represented by the membership functions of the antecedent and consequent parts, it is not used any fuzzy composition. The strong point of this method is that the membership function of an inferred conclusion has a simple shape and thus its meaning can be interpreted easily. Firstly, the proposed method is explained, and then it is applied to fuzzy modeling of distributed data.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.12 no.9
• /
• pp.1591-1598
• /
• 2008

Z. Cao had proposed NFRM(new fuzzy reasoning method) which infers in detail using relation matrix. In spite of the small inference rules, it shows good performance than mamdani's fuzzy inference method. In this paper, we propose Z. Cao's fuzzy inference method with learning ability which is used a gradient descent method in order to improve the performances. It is hard to determine the relation matrix elements by trial and error method. Because this method is needed many hours and effort. Simulation results are applied nonlinear systems show that the proposed inference method using a gradient descent method has good performances.

• East Asian mathematical journal
• /
• v.18 no.2
• /
• pp.225-233
• /
• 2002

In this paper, we obtain the common fixed point for fuzzy mappings satisfying an implicit relation. We improve earlier results of this line.