• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.8
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• pp.742-745
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• 2001

In this paper, we consider performance assessment methods of mathematics and investigate some difficulties which teachers have been grading of performance assessment of mathematics. And also, using fuzzy theory, we define fuzzy grade sheets for performance assessment of mathematics and discuss some usefulness and simple examples of this new definition.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.767-778
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• 2008

Comparison between two or more fuzzy numbers, along with their ranking, is an important subject discussed in scholarly articles. We endeavor in this paper to present a simple yet effective parametric method for comparing fuzzy numbers. This method offer significant advantages over similar methods, in comparing intersected fuzzy numbers, rendering the comparison between fuzzy numbers possible in different decision levels. In the process, each fuzzy number will be given a parametric value in terms of $\alpha$, which is dependent on the related $\alpha$-cuts. We have compared this method to Cheng's centroid point method [5] (The relation of calculating centroid point of a fuzzy number was corrected later on by Wang [12]). The proposed method can be utilized for all types of fuzzy numbers whether normal, abnormal or negative.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.513-530
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• 2021

The purpose of this paper is to introduce and study a class of coupled systems of fuzzy delay differential equations involving fuzzy initial values and fuzzy source functions of triangular type. We assume that these initial values and source functions are triangular fuzzy functions and define solutions of the coupled systems as a triangular fuzzy function matrix consisting of real functional matrices. The method of triangular fuzzy function, fractional steps and fuzzy terms separation are used to solve the problems. Furthermore, we prove existence and uniqueness of solution for the considered systems, and then a solution algorithm is proposed. Finally, we present an example to illustrate our main results and give some work that can be done later.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.527-545
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• 2021

The aim of this article is to give a numerical method for solving Abel's general fuzzy linear integral equations with arbitrary kernel. The method is based on approximations of fractional integrals and Caputo derivatives. The convergence analysis for the proposed method is also given and the applicability of the proposed method is illustrated by solving some numerical examples. The results show the utility and the greater potential of the fractional calculus method to solve fuzzy integral equations.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.71-82
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• 2023

In this article, we find the approximate solutions of Abel differential equation (ADE) with uncertainty using residual power series (RPS) method. This method helps to calculate the sequence of solutions of ADE. Finally, numerical illustrations demonstrate the applicability of the method.

• Coupled systems mechanics
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• v.2 no.3
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• pp.255-269
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• 2013

This paper targets to investigate the solution of fuzzy quadratic Riccati differential equations with various types of fuzzy environment using Homotopy Perturbation Method (HPM). Fuzzy convex normalized sets are used for the fuzzy parameter and variables. Obtained results are depicted in term of plots to show the efficiency of the proposed method.

• Coupled systems mechanics
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• v.1 no.4
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• pp.345-360
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• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.861-876
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• 2008

This paper concerns a new method called Fuzzy Supervised Method for error matrix, the method has developed based on Adoptive Neuro- Fuzzy Inference Systems(ANFIS). For the performance point of view initially the new method tested with trial data and then this paper applies the proposed method with real world problems. So that this paper generated 1000 random error matrices in programming language [R] and then it tests the new proposed method for the error matrices. The results of Fuzzy Supervised Method given in terms of Kappa Index and Congalton Accuracy Indexes, and performance of Fuzzy Supervised Method has evaluated by using Pearson's test.

• Honam Mathematical Journal
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• v.32 no.2
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• pp.307-331
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• 2010

The notion of intuitionistic fuzzy semi-pre interior (semi-pre closure) is introduced, and several related properties are investigated. Characterizations of an intuitionistic fuzzy regular open set, an intuitionistic fuzzy semi-open set and an intuitionistic fuzzy ${\gamma}$-open set are provided. A method to make an intuitionistic fuzzy regular open set (resp. intuitionistic fuzzy regular closed set) is established. A relation between an intuitionistic fuzzy ${\gamma}$-open set and an intuitionistic fuzzy semi-preopen set is considered. A condition for an intuitionistic fuzzy set to be an intuitionistic fuzzy ${\gamma}$-open set is discussed.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.91-106
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• 2012

In this paper, we prove the Hyers-Ulam stability of the Jensen functional equation in fuzzy Banach algebras by using fixed point method and by using direct method.