Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
권호 표지

Fuzzy Partitioning with Fuzzy Equalization Given Two Points and Partition Cardinality

두 점과 분할 카디날리티가 주어진 퍼지 균등화조건을 갖는 퍼지분할

  • Kim, Kyeong-Taek (Department of Industrial and Management Engineering, Hannam University) ;
  • Kim, Chong-Su (Department of Industrial and Management Engineering, Hannam University) ;
  • Kang, Sung-Yeol (College of Business Administration, Hongik University)
  • 김경택 (한남대학교 공과대학 산업경영공학과) ;
  • 김종수 (한남대학교 공과대학 산업경영공학과) ;
  • 강성열 (홍익대학교 상경대학 상경학부)
  • Published : 2008.12.31
Download PDF
⟨ Previous Next ⟩

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.

Keywords

References

  1. 김경택, 김종수; "퍼지 균등화조건을 갖는 2단 퍼 지분할", 산업경영시스템학회지, 25(6)：54-59, 2002
  2. Au, W. H., Chan, K. C. C., and Wong A. K. C.; "A Fuzzy Approach to Partitioning Contonuous Attributes for Classification," IEEE Transactions on Systems, Man,and Cybernetics, 18(5)：715-719, 2006 https://doi.org/10.1109/21.21599
  3. Foulloy, L. and Benoit, E.; "Building a Class of Fuzzy Equivalence Relations," Fuzzy Sets and Systems, 15 7：1417-1437, 2006
  4. Guillaume, S. and Magdalena, S.; "Expert Guided Integration of Induced Knowledge into a Fuzzy Knowledge base," Soft Computing, 10：773-784, 2006 https://doi.org/10.1007/s00500-005-0007-9
  5. Hirota, K. and Pedrycz, W.; "Fuzzy Computing for Data Mining," Proceeding of the IEEE, 87(9)：1575- 1600, 1999
  6. Pedrycz, W.; "Fuzzy Sets Framework for development of Perception Perspective," Fuzzy Sets and Systems, 37：123-137, 1990 https://doi.org/10.1016/0165-0114(90)90037-7
  7. Pedrycz, W.; "Selected Issues of Frame of Knowledge Representation Realized by Means of Linguistic Labels," International Journal of Intelligent System, 7： 155-170, 1992 https://doi.org/10.1002/int.4550070205
  8. Pedrycz, W. and Gomide, F.; An Introduction to Fuzzy Sets: Analysis and Design, MIT Press, Cambridge, MA, 1998
  9. Pedrycz, W.; "Fuzzy Equalization in the Construction of Fuzzy Sets,"　Fuzzy Sets and Systems, 119：329- 335, 2001 https://doi.org/10.1016/S0165-0114(99)00135-9
  10. Pedrycz, W. and Bargiela, A.; "Granular Clustering: A Granular Signature of Data,"　IEEE Transactions on Systems, Man, and Cybernetics, 32(2)：212-224, 2002 https://doi.org/10.1109/3477.990878
  11. Zadeh, L. A.; "The Concept of a Linguistic Variable and its Application to Approximate Reasoning," Information Science, 8(3)：199-249, 1975 https://doi.org/10.1016/0020-0255(75)90036-5
  12. Zadeh, L. A.;　"Fuzzy Sets and Information Granularity," Advances in Fuzzy Set Theory and Applications, (ed.) M.M. Gupta, R. K. Ragade, and R. R. Yager, North Holland, Amsterdam, 3-18, 1979
  13. Zadeh, L. A.;　"Toward a Theory of Fuzzy Information Granulation and its Uncertainty in Human Reasoning and Fuzzy Logic," Fuzzy Sets and Systems, 90： 11-127, 1997 https://doi.org/10.1016/S0165-0114(96)00137-6
  14. Zhuang, H. and Wu, X.; "Membership Function Modification of Fuzzy Logic Controllers with Histogram Equalization," IEEE Transactions on Systems, Man, and Cybernetics, 31(1)：125-132, 2001 https://doi.org/10.1109/3477.907571
  15. Zimmermann, H. J.; Fuzzy Set Theory and Its Applications, Kluwer, Boston, MA, 1991