• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.5
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• pp.571-575
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• 2003

In this paper, we describe a method for fuzzy polynomial regression analysis for fuzzy input--output data using shape preserving operations for least-squares fitting. Shape preserving operations simplifies the computation of fuzzy arithmetic operations. We derive the solution using mixed nonlinear program.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.869-880
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• 2001

In this paper, we describe a method for fuzzy polynomial regression analysis for fuzzy input-output data using shape preserving operations based on Tanaka’s approach. Shape preserving operations simplifies the computation of fuzzy arithmetic operations. We derive the solution using general linear program.

• Proceedings of the IEEK Conference
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• 2004.08c
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• pp.867-871
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• 2004

In this paper, a new analytic approach for shape preserving contrast enhancement is presented. Contrast enhancement is achieved by means of segmental histogram stretching modification which preserves the given image shape, not distorting the original shape. After global stretching, the image is partitioned into several level-sets according to threshold condition. The image information of each level-set is represented as typical value based on grouped differential values. The basic property is modified into common local schemes, thereby introducing the enhanced effect through extreme discrimination between subsets. The scheme is based on stretching the histogram of subsets in which the intensity gray levels between connected pixels are approximately same In spite of histogram widening, stretched by local image information, it neither creates nor destroys the original image, thereby preserving image shape and enhancing the contrast. By designing local histogram stretching operations, we can preserve the original shape of level-sets of the image, and also enhance the global intensity. Thus it can hold the main properties of both global and local image schemes, which leads to versatile applications in the field of digital epigraphy.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.6
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• pp.804-806
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• 2007

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.

• 한국데이터정보과학회:학술대회논문집
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• 2006.11a
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• pp.81-95
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• 2006

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with a particular type of fuzzy intervals. Recently Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. A result proved by Mesiar on a strict t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is recalled. As applications, we define a broader class of bell-shaped fuzzy intervals. Then we study t-norms which are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.

• Journal of Electrical Engineering and information Science
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• v.3 no.2
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• pp.131-138
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• 1998

We derive a back-propagation learning algorithm of fuzzy neural networks using fuzzy operations, which preserves the shapes of fuzzy numbers, in order to utilize fuzzy if-then rules as well as numerical data in the learning of neural networks for classification problems and for fuzzy control problems. By introducing the shape preseving fuzzy operation into a neural network, the proposed network simplifies fuzzy arithmetic operations of fuzzy numbers with exact result in learning the network. And we illustrate our approach by computer simulations on numerical examples.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.306-310
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• 2008

Fuzzy regression, a nonparametric method, can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise. It can also serve as a sound methodology that can be applied to a variety of management and engineering problems where variables are interacting in an uncertain, qualitative, and fuzzy way. A close examination of the fuzzy regression algorithm reveals that the resulting possibility distribution of fuzzy parameters, which makes this technique attractive in a fuzzy environment, is dependent upon an h parameter value. The h value, which is between 0 and 1, is referred to as the degree of fit of the estimated fuzzy linear model to the given data, and is subjectively selected by a decision maker (DM) as an input to the model. The selection of a proper value of h is important in fuzzy regression, because it determines the range of the posibility ditributions of the fuzzy parameters. In this paper, we discuss the interdependent relationship among the h value, membership function shape, and the spreads of fuzzy parameters in fuzzy linear regression with fuzzy input-output using shape-preserving operations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.4
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• pp.306-311
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• 2008

Fuzzy regression, a nonparametric method, can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise. It can also serve as a sound methodology that can be applied to a variety of management and engineering problems where variables are interacting in an uncertain, qualitative, and fuzzy way. A close examination of the fuzzy regression algorithm reveals that the resulting possibility distribution of fuzzy parameters, which makes this technique attractive in a fuzzy environment, is dependent upon an h parameter value. The h value, which is between 0 and 1, is referred to as the degree of fit of the estimated fuzzy linear model to the given data, and is subjectively selected by a decision maker (DM) as an input to the model. The selection of a proper value of h is important in fuzzy regression, because it determines the range of the posibility ditributions of the fuzzy parameters. In this paper, we discuss the interdependent relationship among the h value, membership function shape, and the spreads of fuzzy parameters in fuzzy linear regression with fuzzy input-output using shape-preserving operations.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.131-141
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• 2003

In this paper, we prove that multi-variate fuzzy polynomials are universal approximators for multi-variate fuzzy functions which are the extension principle of continuous real-valued function under $T_W-based$ fuzzy arithmetic operations for a distance measure that Buckley et al.(1999) used. We also consider a class of fuzzy polynomial regression model. A mixed non-linear programming approach is used to derive the satisfying solution.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.643-654
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• 2000

In this paper, we review some class of t-norms on which fuzzy arithmetic operations preserve the shapes of fuzzy numbers and the Hausdorff-distance between fuzzy numbers as the measure of distance between fuzzy numbers. And we suggest the least Hausdorff-distance square method for fuzzy linear regression model using shape preserving fuzzy arithmetic operations.