두 점과 분할 카디날리티가 주어진 퍼지 균등화조건을 갖는 퍼지분할 = Fuzzy Partitioning with Fuzzy Equalization Given Two Points and Partition Cardinality

다국어 초록 (Multilingual Abstract)

Fuzzy partition is a conceptual vehicle that encapsulates data into information granules. Fuzzy equalization concerns a process of building information granules that are semantically and experimentally meaningful. A few algorithms generating fuzzy partitions with fuzzy equalization have been suggested. Simulations and experiments have showed that fuzzy partition representing more characteristics of given input distribution usually produces meaningful results. In this paper, given two points and cardinality of fuzzy partition, we prove that it is not true that there always exists a fuzzy partition with fuzzy equalization in which two of points having peaks fall on the given two points. Then, we establish an algorithm that minimizes the maximum distance between given two points and adjacent points having peaks in the partition. A numerical example is presented to show the validity of the suggested algorithm.

참고문헌 (Reference)

1 김경택, "퍼지 균등화조건을 갖는 2단 퍼지분할" 한국산업경영시스템학회 25 (25): 54-58, 2002

2 Zadeh, L. A., "Toward a Theory of Fuzzy Information Granulation and its Uncertainty in Human Reasoning and Fuzzy Logic" 90 : 11-127, 1997

3 Zadeh, L. A., "The Concept of a Linguistic Variable and its Application to Approximate Reasoning" 8 (8): 199-249, 1975

4 Pedrycz, W., "Selected Issues of Frame of Knowledge Representation Realized by Means of Linguistic Labels" 7 : 155-170, 1992

5 Zhuang, H., "Membership Function Modification of Fuzzy Logic Controllers with Histogram Equalization" 31 (31): 125-132, 2001

6 Pedrycz, W., "Granular Clustering: A Granular Signature of Data" 32 (32): 212-224, 2002

7 Zadeh, L. A., "Fuzzy Sets and Information Granularity In: Advances in Fuzzy Set Theory and Applications" 3-18, 1979

8 Pedrycz, W., "Fuzzy Sets Framework for development of Perception Perspective" 37 : 123-137, 1990

9 Zimmermann, H. J., "Fuzzy Set Theory and Its Applications" Kluwer 1991

10 Pedrycz, W., "Fuzzy Equalization in the Construction of Fuzzy Sets" 119 : 329-335, 2001

11 Hirota, K, "Fuzzy Computing for Data Mining" 1575-1600, 1999

12 Guillaume, S., "Expert Guided Integration of Induced Knowledge into a Fuzzy Knowledge base" 10 : 773-784, 2006

13 Foulloy, L., "Building a Class of Fuzzy Equivalence Relations" 157 : 1417-1437, 2006

14 Pedrycz, W., "An Introduction to Fuzzy Sets: Analysis and Design" MIT Press 1998

15 Au, W. H., "A Fuzzy Approach to Partitioning Contonuous Attributes for Classification" 18 (18): 715-719, 2006