• Journal of the Korean Institute of Intelligent Systems
• /
• v.18 no.4
• /
• pp.543-548
• /
• 2008

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in $E_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$. Main tool is successive iteration method.

• Korean Journal of Mathematics
• /
• v.4 no.2
• /
• pp.117-124
• /
• 1996

In this paper we define a new fuzzy metric $\tilde{\theta}$ of fuzzy number sequences, and prove that the space of convergent sequences of fuzzy numbers is a fuzzy complete metric space in the fuzzy metric $\tilde{\theta}$.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.333-341
• /
• 2004

In the real world there are many linear programming problems where all decision parameters are fuzzy numbers. Several approaches exist which use different ranking functions for solving these problems. Unfortunately when there exist alternative optimal solutions, usually with different fuzzy value of the objective function for these solutions, these methods can not specify a clear approach for choosing a solution. In this paper we propose a method to remove the above shortcoming in solving fuzzy number linear programming problems using the concept of expectation and variance as ranking functions

• Industrial Engineering and Management Systems
• /
• v.13 no.4
• /
• pp.357-368
• /
• 2014

Since its birth in 1993, fuzzy time series have seen different classes of models designed and applied, such as fuzzy logic relation and rule-based models. These models have both advantages and disadvantages. The major drawbacks with these two classes of models are the difficulties encountered in identification and analysis of the model. Therefore, there is a strong need to explore new alternatives and this is the objective of this paper. By transforming a fuzzy number to a real number via integrating the inverse of the membership function, new autoregressive models can be developed to fit the observation values of a fuzzy time series. With the new models, the issues of model identification and parameter estimation can be addressed; and trends, seasonalities and multivariate fuzzy time series could also be modeled with ease. In addition, asymptotic behaviors of fuzzy time series can be inspected by means of characteristic equations.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.2
• /
• pp.277-286
• /
• 2014

We define the pentagonal fuzzy sets and generalize the results of addition, subtraction, multiplication, and division based on the Zadeh's extension principle for two pentagonal fuzzy sets. In addtion, we find the condition that the result of addition or subtraction for two pentagonal fuzzy sets becomes a triangular fuzzy number and give some example.

• Journal of Mechanical Science and Technology
• /
• v.15 no.11
• /
• pp.1482-1489
• /
• 2001

Thermally-induced errors originating from machine tool errors have received significant attention recently because high speed and precise machining is now the principal trend in manufacturing proce sses using CNC machine tools. Since the thermal error model is generally a function of temperature, the thermal error compensation system contains temperature sensors with the same number of temperature variables. The minimization of the number of variables in the thermal error model can affect the economical efficiency and the possibility of unexpected sensor fault in a error compensation system. This paper presents a thermal error model with minimum number of variables using a fuzzy logic strategy. The proposed method using a fuzzy logic strategy does not require any information about the characteristics of the plant contrary to numerical analysis techniques, but the developed thermal error model guarantees good prediction performance. The proposed modeling method can also be applied to any type of CNC machine tool if a combination of the possible input variables is determined because the error model parameters are only calculated mathematically-based on the number of temperature variables.

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

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.05a
• /
• pp.1-4
• /
• 2003

This paper we study the existence of a global solution for the nonlinear fuzzy differential equations in E$_{N}$$^{n}$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in R$^{n}$ . .

• The Journal of Korean Association of Computer Education
• /
• v.6 no.4
• /
• pp.95-113
• /
• 2003

We introduce an AFES(Adaptive Fuzzy Evaluation System) that applies an evaluation system used to existing LCMS(Learning Contents Management System) to a fuzzy reasoning rule. The AFES confers a course level on the learner through a fuzzy diagnostic evaluation before the learner enters a learning course. After the learner completes a learning course through the tailored learning path that is suitable for the learner's level, the AFES confers a final grade on the learner by means of fuzzy final evaluation. The biggest characteristic of the AFES is a grade rule of the final grade. Although different learners get the same number of correct answers to the same number of Questions, AFES flexibly confers the different final grade on the learner by means of the number of 125's fuzzy reasoning rules.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.2 no.2
• /
• pp.159-165
• /
• 2002

This paper proposes a GA and Gradient Descent Method-based method for choosing an appropriate set of fuzzy rules for classification problems. The aim of the proposed method is to fond a minimum set of fuzzy rules that can correctly classify all training patterns. The number of inference rules and the shapes of the membership functions in the antecedent part of the fuzzy rules are determined by the genetic algorithms. The real numbers in the consequent parts of the fuzzy rules are obtained through the use of the descent method. A fitness function is used to maximize the number of correctly classified patterns, and to minimize the number of fuzzy rules. A solution obtained by the genetic algorithm is a set of fuzzy rules, and its fitness is determined by the two objectives, in a combinatorial optimization problem. In order to demonstrate the effectiveness of the proposed method, computer simulation results are shown.