• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.3
• /
• pp.242-246
• /
• 2010

It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

• Proceedings of the KIEE Conference
• /
• 1999.07g
• /
• pp.2876-2878
• /
• 1999

There have been several tipical methods being used to measure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. This paper studies the entropy variation on the fuzzy numbers with arithmetic operations(addition, subtraction, multiplication). It is shown that through the arithmetic operations, the entropy of the resultant fuzzy number has the arithmetic relation with the entropy of each original fuzzy number. This paper generalize earlier results of Pedrycz [FSS 64(1994) 21-30] and Wang and Chiu [FSS 103(1999) 443-455].

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.1
• /
• pp.75-82
• /
• 2003

In this paper, a general convergence theorem of fuzzy random variables is considered. Using this result, we can easily prove the recent result of Joo et al. (2001) and generalize the recent result of Kim(2000).

• Proceedings of the KSRS Conference
• /
• 2005.10a
• /
• pp.675-677
• /
• 2005

This study proposes a fuzzy classification using EM algorithm. For cluster validation, this approach iteratively estimates the class-parameters in the fuzzy training for the sample classes and continuously computes the log-likelihood ratio of two consecutive class-numbers. The maximum ratio rule is applied to determine the optimal number of classes.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.221-233
• /
• 2004

In this paper we introduce the concept of the McShane-Stieltjes integrals of interval-valued functions and fuzzy-number-valued functions and investigate some of their properties.

• Proceedings of the Korean Statistical Society Conference
• /
• 2003.10a
• /
• pp.183-188
• /
• 2003

In this paper, we establish some results on strong convergence for weighted sums of uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.

• Journal of the Korean Data and Information Science Society
• /
• v.12 no.1
• /
• pp.99-101
• /
• 2001

In this note, we show that a linear regression model, using entropy and degree of nearness of fuzzy numbers, suggested by Wang and Li[FSS 36, 125-136] seems to be unreasonable by an example.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2002.09a
• /
• pp.13.1-13
• /
• 2002

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.409-420
• /
• 2006

In this paper we consider the set of all n + 1-tuples of real numbers, not necessarily all distinct, in the decreasing order from the unit interval under the usual ordering of real numbers, always including 1. Such n + 1-tuples inherently arise as the membership values of fuzzy subsets and are called keychains. An natural equivalence relation is introduced on this set and the equivalence classes of keychains are studied here. The number of such keychains is finite and the set of all keychains is a lattice under the coordinate-wise ordering. Thus keychains are subchains of a finite chain of real numbers in the unit interval. We study some of their properties and give some applications to counting fuzzy subsets of finite sets.

• International Journal of Reliability and Applications
• /
• v.1 no.2
• /
• pp.123-131
• /
• 2000

This paper concerns with the consistent estimator for the fuzzy expectation of a random variable taking values in the space F($R^p$) of upper semicontinuous convex fuzzy subsets of $R^p$ with compact support. We introduce the concept of a fuzzy sample mean and show that the fuzzy sample mean is a strong consistent estimator for the fuzzy expectation. Some examples are given to illustrate the main result.