• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.831-846
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• 2011

There are several methods, in the literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method (based on fuzzy linear programming formulation) is proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems with a new representation of trapezoidal fuzzy numbers. The advantages of the proposed method over existing method are discussed. Also, it is shown that it is better to use the proposed representation of trapezoidal fuzzy numbers instead of existing representation of trapezoidal fuzzy numbers for finding the fuzzy optimal solution of fuzzy transportation problems. To illustrate the proposed method a fuzzy transportation problem (FTP) is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

• 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.18 no.1_2
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• pp.649-656
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• 2005

In this paper we consider a fuzzy least absolute deviation method in order to construct fuzzy linear regression model with fuzzy input and fuzzy output. We also consider two numerical examples to evaluate an effectiveness of the fuzzy least absolute deviation method and the fuzzy least squares method.

• Structural Engineering and Mechanics
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• v.22 no.4
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• pp.469-481
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• 2006

A new method called fuzzy factor method for the stationary stochastic response analysis of fuzzy truss with global fuzzy structural parameters is presented in this paper. Considering the fuzziness of the structural physical parameters and geometric dimensions simultaneously, the fuzzy correlation function matrix of structural displacement response in time domain is derived by using the fuzzy factor method and the optimization method, the fuzzy mean square values of the structural displacement and stress response in the frequency domain are then developed with the fuzzy factor method. The influences of the fuzziness of structural parameters on the fuzziness of mean square values of the displacement and stress response are inspected via an example and some important conclusions are obtained. Finally, the example is simulated by Monte-Carlo method and the results of the two methods are close, which verified the feasibility of the method given in this paper.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.571-591
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• 2012

To the best of our knowledge, there is no method, in the literature, to find the fuzzy optimal solution of fully fuzzy shortest path (FFSP) problems i.e., shortest path (SP) problems in which all the parameters are represented by fuzzy numbers. In this paper, a new method is proposed to find the fuzzy optimal solution of FFSP problems. Kumar and Kaur [Methods for solving unbalanced fuzzy transportation problems, Operational Research-An International Journal, 2010 (DOI 10.1007/s 12351-010-0101-3)] proposed a new method with new representation, named as JMD representation, of trapezoidal fuzzy numbers for solving fully fuzzy transportation problems and shown that it is better to solve fully fuzzy transportation problems by using proposed method with JMD representation as compare to proposed method with the existing representation. On the same direction in this paper a new method is proposed to find the solution of FFSP problems and it is shown that it is also better to solve FFSP problems with JMD representation as compare to existing representation. To show the advantages of proposed method with this representation over proposed method with other existing representations. A FFSP problem solved by using proposed method with JMD representation as well as proposed method with other existing representations and the obtained results are compared.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.6
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• pp.43-52
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• 1994

A design method of rule-based fuzzy modeling is presented for the model identification of complex and nonlinear systems. The proposed rule-based fuzzy modeling implements system structure and parameter identification in the efficient form of ``IF....,THEN...', using the theories of optimization theory , linguistic fuzzy implication rules and fuzzy c-means clustering. Three kinds of method for fuzzy modeling presented in this paper include simplified inference (type I), linear inference (type 2), and modified linear inference (type 3). In order to identify premise structure and parameter of fuzzy implication rules, fuzzy c- means clustering and modified complex method are used respectively and the least sequare method is utilized for the identification of optimum consequence parameters. Time series data for gas furance and those for sewage treatment process are used to evaluate the performance of the proposed rule-based fuzzy modeling. Comparison shows that the proposed method can produce the fuzzy model with higher accuracy than previous other studies.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.556-561
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• 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 KIISE:Software and Applications
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• v.27 no.7
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• pp.723-730
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• 2000

Fuzzy numbers represent fuzzy numeric values. However, it is difficult to clearly determine whether one fuzzy number is larger or smaller than other fuzzy numbers. Thus it is also difficult to determine the rank which a fuzzy number takes, or to select the k-th largest fuzzy number in a given set of fuzzy numbers. In this paper, we propose a fuzzy set based method to determine the rank of a fuzzy number and the k-th largest fuzzy number. The proposed method uses a given fuzzy greater-than relation which is defined on a set of fuzzy numbers. Our method describes the rank of a fuzzy number with a fuzzy set of ranks that the fuzzy number can take, and the k-th largest fuzzy number with a fuzzy set of fuzzy numbers which can be k-th ranked.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.12
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• pp.139-148
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• 1995

In this paper an electro-hydraulic servo system is designed by using a fuzzy control algorithm. In order to drive an optimal fuzzy control system, a simulation program for the control system has been developed. By this program the fuzzifier and defuzzifier, a fuzzy inference method, a fuzzy relational matrix, and a fuzzy inference method are investigated. As a result, Larsen inference method, 9*9 fuzzy relational matrix, and center of area defuzzifier are turned out the best as parameters. Finally this method is compared with the conventional PID algotithm, and showed that the fuzzy control performs better than PID algorithm. The fuzzy control performs very well adap- tation against uncertain disturbances.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.945-948
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• 1993