• 대한수학회논문집
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• 제18권2호
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• pp.385-392
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• 2003

The sum Of L - R fuzzy numbers With Unbounded Supports based on Archimedean continuous f-norm T is considered. Results are more simple than those of the case for bounded supports.

• 제어로봇시스템학회논문지
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• 제8권11호
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• pp.941-947
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• 2002

Two methods of constructing T-S fuzzy model which is equivalent to a given nonlinear system are presented. The first method is to obtain an equivalent T-S fuzzy model by using the sum of linearly independent scalar functions with constant real matrix coefficients. The sum of products of linearly independent scalar functions is used in the second method. The former method is to formulate the procedures of T-S fuzzy modeling dealt in many examples of previous publications; the latter is a new method. By comparing the number of linearly independent functions used in the two methods, we can easily find out which method makes fewer rules than the other. The nonlinear dynamics of an inverted Pendulum on a cart is used as an equivalent T-5 fuzzy modeling example.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2006년도 추계 학술발표회 논문집
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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.

• 한국지능시스템학회논문지
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• 제17권6호
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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.

• 제어로봇시스템학회논문지
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• 제8권11호
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• pp.916-921
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• 2002

We presents a new method of constructing an equivalent T-S fuzzy model by using the sum of products of linearly independent scalar functions from nonlinear dynamics. This method exactly expresses nonlinear systems and automatically determines the number of rules. We design a stabilizing controller f3r ul inverted pendulum system by using the concep of parallel distributed compensation (PDC) and linear matrix inequalities (LMIs) based on the proposed T-S fuzzy modeling method. We show effectiveness of a systematically designed fuzzy controller based on the proposed T-S fuzzy modeling method through the simulation and experiment of an inverted pendulum system.