퍼지집합을 이용한 퍼지숫자의 순위 결정 방법

A Fuzzy Set based Method for Determining the Ranks of Fuzzy Numbers

  • 이지형 (한국과학기술원 전자전산학과) ;
  • 이광형 (한국과학기술원 전자전산학과)
  • 발행 : 2000.07.15

초록

퍼지숫자는 보통숫자와는 달리 애매모호한 값을 표현하기 때문에, 어느 퍼지숫자가 다른 퍼지숫자보다 큰지 작은지를 명확히 기술하기 어렵다. 따라서, 주어진 퍼지숫자의 집합 내에서, 어느 퍼지숫자가 몇 번째로 큰지, 또는 k번째로 큰 퍼지숫자가 어느 것인지 역시 애매모호할 수밖에 없다. 본 논문에서는 퍼지숫자의 순위와 k번째로 큰 퍼지숫자를 결정하기 위하여 퍼지집합을 이용하는 방법을 제안한다. 제안하는 방법은 퍼지숫자들 사이에 퍼지대소관계가 주어졌다고 가정하며, 이를 이용하여 퍼지숫자의 순위와 k번째 큰 퍼지숫자를 결정한다. 제안하는 방법은 어느 한 퍼지숫자가 취할 수 있는 모든 순위를 퍼지집합으로 표현하며, k번째로 큰 퍼지숫자가 될 수 있는 모든 퍼지숫자들을 퍼지집합으로 표현한다.

Fuzzy numbers represent fuzzy numeric values. However, it is difficult to clearly determine whether one fuzzy number is larger or smaller than other fuzzy numbers. Thus it is also difficult to determine the rank which a fuzzy number takes, or to select the k-th largest fuzzy number in a given set of fuzzy numbers. In this paper, we propose a fuzzy set based method to determine the rank of a fuzzy number and the k-th largest fuzzy number. The proposed method uses a given fuzzy greater-than relation which is defined on a set of fuzzy numbers. Our method describes the rank of a fuzzy number with a fuzzy set of ranks that the fuzzy number can take, and the k-th largest fuzzy number with a fuzzy set of fuzzy numbers which can be k-th ranked.

키워드

참고문헌

  1. A. Kaufmann, M. M. Gupta, Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold, New York, 1991
  2. V. Peneva, I. Popchev, 'Comparison of clusters from fuzzy numbers,' Fuzzy Sets and Systems, vol.97, pp.75-81, 1998 https://doi.org/10.1016/S0165-0114(96)00360-0
  3. C. H. Cheng, 'A new approach for ranking fuzzy numbers by distance method,' Fuzzy Sets and Systems, vol.95, pp.307-317, 1998 https://doi.org/10.1016/S0165-0114(96)00272-2
  4. K. Kim, K. S. Park, 'Ranking fuzzy numbers with index of optimism,' Fuzzy Sets and Systems, vol.35, pp.143-150, 1990 https://doi.org/10.1016/0165-0114(90)90189-D
  5. S.-H. Chen, 'Ranking fuzzy numbers with maximizing set and minimizing set,' Fuzzy Sets and Systems, vol.17, pp.113-129, 1985 https://doi.org/10.1016/0165-0114(85)90050-8
  6. G. Bortolan, R. Degani, 'A review of some methods for ranking fuzzy subsets,' Fuzzy Sets and Systems, vol.15, pp.1-19, 1985 https://doi.org/10.1016/0165-0114(85)90012-0
  7. L. M. Campos Ibanes, A. Gonzalez Munoz, 'A subjective approach for ranking fuzzy numbers,' Fuzzy Sets and Systems, vol.29, pp.145-153, 1989 https://doi.org/10.1016/0165-0114(89)90188-7
  8. S. A. Orlovsky, 'Decision-making with a fuzzy preference relation,' Fuzzy Sets and Systems, vol.1, pp.155-167, 1978 https://doi.org/10.1016/0165-0114(78)90001-5
  9. T. S. Liou, M. J. Wang, 'Ranking fuzzy numbers with integral value,' Fuzzy Sets and Systems, vol.50, pp.247-255, 1992 https://doi.org/10.1016/0165-0114(92)90223-Q
  10. P. Fortemps, M. Roubens, 'Ranking and defuzzification methods based on area compensation,' Fuzzy Sets and Systems, vol.82, pp.319-330, 1996 https://doi.org/10.1016/0165-0114(95)00273-1
  11. K. P. Yoon, 'A probabilistic approach to rank complex fuzzy numbers,' Fuzzy Sets and Systems, vol.80, pp.167-176, 1996 https://doi.org/10.1016/0165-0114(95)00193-X
  12. A. Gonz?ez, 'A study of the ranking function approach through mean values,' Fuzzy Sets and Systems, vol.35, pp.29-41, 1990 https://doi.org/10.1016/0165-0114(90)90016-Y
  13. R. R. Yager, 'A procedure for ordering fuzzy subsets of the unit interval,' Information Science, vol.24, pp.141-161, 1981
  14. J. F. Baldwin, N. C. F. Guild, 'Comparison of fuzzy sets on the same decision space,' Fuzzy Sets and Systems, vol.2, pp.213-231, 1979 https://doi.org/10.1016/0165-0114(79)90028-9
  15. J. H. Lee, H. Lee-Kwang, 'A method for ranking fuzzy numbers based on a given viewpoint and its application to decision-making,' IEEE trans. Fuzzy Systems, 1999 (to appear) https://doi.org/10.1109/91.811235
  16. K. M. Lee, C. H. Cho, H. Lee-Kwang, 'Ranking fuzzy values with satisfaction function,' Fuzzy Sets and Systems, vol.64, pp.295-309, 1994 https://doi.org/10.1016/0165-0114(94)90153-8
  17. J. H. Lee, H. Lee-Kwang, 'Comparison of fuzzy values on a continuous domain,' Fuzzy Sets and Systems, 1999(to appear) https://doi.org/10.1016/S0165-0114(98)00381-9