• Journal of the Korean Data and Information Science Society
• /
• v.9 no.2
• /
• pp.105-111
• /
• 1998

In this paper a fuzzy regression model based on the weakest t-norm is introduced. The model shows a regression model which has fuzzy coefficients and fuzzy variables.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.7 no.1
• /
• pp.85-89
• /
• 2007

Many authors considered the computational aspect of sup-min convolution when applied to weighted average operations. They used a computational algorithm based on a-cut representation of fuzzy sets, nonlinear programming implementation of the extension principle, and interval analysis. It is well known that $T_W$(the weakest t-norm)-based addition and multiplication preserve the shape of L-R type fuzzy numbers. In this paper, we consider the computational aspect of the extension principle by the use of $T_W$ when the principle is applied to fuzzy weighted average operations. We give the exact solution for the case where variables and coefficients are L-L fuzzy numbers without programming or the aid of computer resources.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.8 no.3
• /
• pp.170-174
• /
• 2008

The measurement of performance of a process considering both the location and the dispersion of information about the process is referred to as the process capacity indices (PCIs) of interest, $C_{pk}$. This information is presented by the mean and standard deviation of the producing process. Linguistic variables are used to express the evaluation of the quality of a product. Consequently, $C_{pk}$ is defined with fuzzy numbers. Lee [Eur. J. Oper. Res. 129(2001) 683-688] constructed the definition of the $C_{pk}$ index estimation presented by fuzzy numbers and approximated its membership function using the "min" - norm based Zadeh's extension principle of fuzzy sets. However, Lee's result was shown to be invalid by Hong [Eur. J. Oper. Res. 158(2004) 529-532]. It is well known that $T_w$ (the weakest t-norm)-based addition and multiplication preserve the shape of L-R fuzzy numbers. In this paper, we allow that the fuzzy numbers are of L-R type. The object of the present study is to propose a new method to calculate the $C_{pk}$ index under $T_w-based$ fuzzy arithmetic operations.

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

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2000.11a
• /
• pp.139-144
• /
• 2000

Recently, a homogeneous fuzzy time series model was proposed by means of defining some new operations on fuzzy numbers. In this paper, we consider expanding the results to the nonhomogeneous fuzzy time series and the general fuzzy time series using Tw, the weakest t-norm, based algebraic fuzzy operations.