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CONVEXITY AND SEMICONTINUITY OF FUZZY MAPPINGS USING THE SUPPORT FUNCTION
홍덕헌,문은호,Jae Duck Kim 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.5
Since Goetschel and Voxman [5] proposed a linear order on fuzzy numbers, several authors studied the concept of semicontinuity and convexity of fuzzy mappings defined through the order. Since the order is only defined for fuzzy numbers on R, it is natural to find a new order for normal fuzzy sets on Rⁿ in order to study the concept of semicontinuity and convexity of fuzzy mappings on normal fuzzy sets. In this paper, we introduce a new order □ for normal fuzzy sets on Rⁿ with respect to the support function. We define the semicontinuity and convexity of fuzzy mappings with this order. Some issues which are related with semicontinuity and convexity of fuzzy mappings will be discussed..
A Note to the Stability of Fuzzy Closed-Loop Control Systems
홍덕헌,Hong, Dug-Hun The Korean Data and Information Science Society 2001 한국데이터정보과학회지 Vol.12 No.1
Chen and Chen(FSS, 1993, 159-168) presented a reasonable analytical model of fuzzy closed-loop systems and proposed a method to analyze the stability of fuzzy control by the relational matrix of fuzzy system. Chen, Lu and Chen(IEEE Trans. Syst. Man Cybern., 1995, 881-888) formulated the sufficient and necessary conditions on stability of fuzzy closed-loop control systems. Gang and Chen(FSS, 1996, 27-34) deduced a linguistic relation model of a fuzzy closed loop control system from the linguistic models of the fuzzy controller and the controlled process and discussed the linguistic stability of fuzzy closed loop system by a linguistic relation matrix. In this paper, we study more on their models. Indeed, we prove the existence and uniqueness of equilibrium state $X_e$ in which fuzzy system is stable and give closed form of $X_e$. The same examples in Chen and Chen and Gang and Chen are treated to analyze the stability of fuzzy control systems.
Convergence of interval-valued choquet integrals
홍덕헌,김경태 한국지능시스템학회 2005 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.5 No.3
Recently, many types of set-valued fuzzy integrals are studied by many authors. In this paper, we consider various types of convergence theorems of Choquet integrals of interval-valued function with respect to an autocontinuous fuzzy measure.
Entropy and information energy arithmeticoperations
홍덕헌 한국지능시스템학회 2005 한국지능시스템학회논문지 Vol.15 No.7
There have been several tipical methods being used tomeasure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. Recently, Wang and Chiu [FSS103(1999) 443-455] and Pedrycz [FSS 64(1994) 21-30] showed the relationship(addition, subtraction, multiplication) between the entropies of the resultant fuzzy number and the original fuzzy numbers of same type. In this paper, using Lebesgue-Stieltjes integral, we generalize results of Wang and Chiu [FSS 103(1999) 443-455] concerning entropy arithmetic operations without the condition of same types of fuzzy numbers. And using this results and trade-off relationship between information energy and entropy, we study more properties of information energy of fuzzy numbers.
Convergence of Choquet integral
홍덕헌,Kyung Tae Kim 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1-2
In this paper, we consider various types of convergence theorems of Choquet integral. We also show that the autocontinuity of finite fuzzy measure is equivalent to a convergence theorem with respect to convergence in measure.
홍덕헌,Hong, Dug-Hun Korean Data and Information Science Society 1991 한국데이터정보과학회지 Vol.2 No.-
Petrov (1968) gave two theorems on the law of the iterated logarithm without any assumptions about the existence of moments of independent random variables. In the present paper we show that the same holds true for sign-invariant random variables.
On entropy for intuitionistic fuzzy sets applying the Euclidean distance
홍덕헌 한국지능시스템학회 2002 한국지능시스템학회논문지 Vol.12 No.6
Recently, Szmidt and Kacprzyk[Fuzzy Sets and Systems 118(2001) 467-477] proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets. It is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them. They showed that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F BIGCAP F^c