• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.187-199
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• 2009

In this paper, we introduce the concept of fuzzy weakly (r,s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in Sostak's sense. The relations among various kinds of fuzzy mappings on intuitionistic fuzzy topological spaces in $\check{S}ostak^{\prime}s$ sense are displayed. The characterization for the fuzzy weakly (r,s)-semicontinuous mapping is obtained. Also, we introduce the notion of fuzzy weakly (r,s)-semicontinuous mappings at a given intuitionistic fuzzy point. The relation between fuzzy weakly (r,s)- semicontinuous mappings and fuzzy weakly (r,s)-semicontinuous mappings at an intuitionistic fuzzy point is discussed.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.177-196
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• 2022

The Elzaki Transform method is fuzzified to fuzzy Elzaki Transform by Rehab Ali Khudair. In this article, we propose a Double fuzzy Elzaki transform (DFET) method to solving fuzzy partial differential equations (FPDEs) and we prove some properties and theorems of DFET, fundamental results of DFET for fuzzy partial derivatives of the n^th order, construct the Procedure to find the solution of FPDEs by DFET, provide duality relation of Double Fuzzy Laplace Transform (DFLT) and Double Fuzzy Sumudu Transform(DFST) with proposed Transform. Also we solve the Fuzzy Poisson's equation and fuzzy Telegraph equation to show the DFET method is a powerful mathematical tool for solving FPDEs analytically.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.4 no.2
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• pp.135-141
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• 2004

This paper proposes a new heuristic search technique for obstacle avoidance of autonomous underwater vehicles equipped with a looking ahead obstacle avoidance sonar. We suggest the fuzzy relation between the sonar sections and the properties of real world environment. Bandler and Kohout's fuzzy relational method are used as the mathematical implementation for the analysis and synthesis of relations between the partitioned sections of sonar over the real-world environmental properties. The direction of the section with optimal characteristics would be selected as the successive heading of AUVs for obstacle avoidance. For the technique using in this paper, sonar range must be partitioned into multi equal sections; membership functions of the properties and the corresponding fuzzy rule bases are estimated heuristically. With the two properties Safety, Remoteness and sonar range partitioned in seven sections, this study gives the good result that enables AUVs to navigate through obstacles in the optimal way to goal.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1181-1198
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• 2022

In this paper we are concerned with the number of fuzzy subgroups of a finite abelian p-group ℤ_p^m × ℤ_pⁿ × ℤ_p^ℓ of rank three with order p^m+n+ℓ. We obtain a recurrence relation for the number of fuzzy subgroups of a finite abelian p-group ℤ_p^m × ℤ_pⁿ × ℤ_p^ℓ. In order to show that using this recurrence relation, one can find explicit formulas for the number of fuzzy subgroups of ℤ_p^m × ℤ_pⁿ × ℤ_p^ℓ consecutively, we give explicit formulas for the number of fuzzy subgroups of ℤ_p^m × ℤ_pⁿ × ℤ_p^ℓ where (n, ℓ) = (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (2, 2), (3, 2), (4, 2), (5, 2).

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.155-164
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• 1998

In this paper, the fuzzy $T_2$-axioms due to Hutton and Reilly, Ganguly and Saha and Sinha are characterized by using the notion of fuzzy closure. As consequences, we study the relation between the fuzzy $T_2$-axioms and give some examples which show that the axiom of fuzzy compactness, due to Ganguly and Saha, is not compatible with the fuzzy $T_2$-axioms.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.51-62
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• 2002

The present paper gives a new construction of a quotient BCI(BCK)-algebra X/${\mu}$ by a fuzzy ideal ${\mu}$ in X and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if ${\mu}$ is a fuzzy ideal (closed fuzzy ideal) of X, then X/${\mu}$ is a commutative (resp. positive implicative, implicative) BCK(BCI)-algebra if and only if It is a fuzzy commutative (resp. positive implicative, implicative) ideal of X Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra of X We show that if the period of every element in a BCI-algebra X is finite, then any fuzzy ideal of X is closed. Especiatly, in a well (resp. finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.

• Journal of Intelligence and Information Systems
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• v.3 no.1
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• pp.69-81
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• 1997

In this paper, first we propose an architecture of fuzzy neural networks with triangular fuzzy weights. The proposed fuzzy neural network can handle fuzzy input vectors. In both cases, outputs from the fuzzy network are fuzzy vectors. The input-output relation of each unit of the fuzzy neural network is defined by the extention principle of Zadeh. Also we define a cost function for the level sets(i. e., $\alpha$-cuts)of fuzzy outputs and fuzzy targets. Then we derive a learning algorithm from the cost function for adjusting three parameters of each triangular fuzzy weight. Finally, we illustrate our a, pp.oach by computer simulation examples.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.623-634
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• 2006

Various methods have been studied to construct a fuzzy regression model in order to present a fuzzy relation between a dependent variable and an independent variable. However, in the fuzzy regression analysis the value of the center point of estimated fuzzy output may be either greater than the value of the right endpoint or smaller than the value of the left endpoint. In the case, we cannot predict the fuzzy output properly. This paper presents sufficient conditions to construct the fuzzy regression model using several methods investigated by some authors and then introduces the censored fuzzy regression model using the censored samples to manipulate the problem of crossing of the center and the end points of the estimated fuzzy number. Examples show that the censored fuzzy regression model is an extension of the fuzzy regression model and also it improves the problem of crossing.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.195-211
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• 2024

In this paper, we introduce the concept of a fuzzy lattice ordered group, which is based on a fuzzy lattice that Chon developed in his paper "Fuzzy Partial Order Relations and Fuzzy Lattice". We will also discuss fuzzy lattice-ordered groups in detail, provide several results that are analogous to the classical theory of lattice-ordered groups, and characterize the relationship between a fuzzy lattice-ordered group using its level set and support. Moreover, we define the concepts of fl-subgroups, quotients, and cosets of fl-groups and obtain some fundamental results for these fuzzy algebraic structures.

• The Journal of the Korea Contents Association
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• v.8 no.12
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• pp.1-9
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• 2008

Fuzzy Cognitive Map, one of ways to model, describe and infer reasoning relations, is widely used in the field of reasoning knowledge engineering. Despite of the natural and easy understanding of decision and smooth explanation of relation between front and rear, reasoning relation is organized with mathematical haziness and complex algorithm and rarely has an interactive user interface. This paper suggests an interactive Fuzzy Cognitive Map(FCM) construction support system. It builds a FCM increasingly concerning multiple experts' knowledge. Futhermore, it supports user-supportive environment by dynamically displaying the structure of Fuzzy Cognitive Map which is constructed by the interaction between experts and the system.