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New ranking method for fuzzy numbers by their expansion center

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Based on the area between the curve of the membership function of a fuzzy number and the horizontal real axis, a characteristic as a new numerical index, called the expansion center, for fuzzy numbers is proposed. An intuitive and reasonable ranking method for fuzzy numbers based on this characteristic is also established. The new ranking method is applicable for decision making and data analysis in fuzz environments. An important criterion of the goodness for ranking fuzzy numbers, the geometric intuitivity, is also introduced. It guarantees coinciding with the natural ordering of the real numbers.
Rocznik
Strony
181--187
Opis fizyczny
Bibliogr. 19 poz., rys.
Twórcy
autor
  • Department of Mathematics, University of Nebraska at Omaha, Omaha, USA
  • Department of Economics,University of Nebraska at Omaha, Omaha, USA
Bibliografia
  • [1] S. Abbasbandy and B. Asady, Ranking of fuzzy numbers by sign distance, Information Sciences 176(16), 2405-2416, 2006.
  • [2] G. Bortolan and R. Degani, A review of some methods for ranking fuzzy numbers, Fuzzy Sets and Systems 15, 1-19, 1985.
  • [3] C. H. Cheng, A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems 95, 307-317, 1998.
  • [4] T. C. Chu and C. T. Tsao, Ranking fuzzy numbers with an area between the centroid point and original point, Computers and Mathematics with Applications 43, 111-117, 2002.
  • [5] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980.
  • [6] D. Dubois and H. Prade, Ranking fuzzy numbers in the setting of possibility theory, Information Sciences 30, 183-224, 1983.
  • [7] B. Farhadinia, Ranking fuzzy numbers on lexicographical ordering, International Journal of Applied Mathematics and Computer Sciences 5(4), 248-251, 2009.
  • [8] N. Furukawa, A parametric total order on fuzzy numbers and a fuzzy shortest route problem, Optimization 30, 367-377, 1994.
  • [9] G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, 1995.
  • [10] M. Kurano, M. Yasuda, J Nakagami, and Y. Yoshida, Ordering of convex fuzzy sets − a brief servey and new results, Journal of the Operation Research Society of Japan 43(1), 138-148, 2000.
  • [11] T. S. Liou and M. J. Wang, Ranking fuzzy numbers with integral value, Fuzzy Sets and Systems 50, 247-255, 1992.
  • [12] S. H. Nasseri and M. Sohrabi, Hadi’s method and its advantage in ranking fuzzy numbers, Australian Journal of Basic Applied Sciences 4(10), 4630-4637, 2010.
  • [13] J. Ramk and J. imnek, Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy Sets and Systems 16, 123-138, 1985.
  • [14] K. H. Rosen, Discrete Mathematics and Its Applications (Seventh Edition), McGraw-Hill, 2011.
  • [15] W. Wang and Z. Wang, Total orderings defined on the set of all fuzzy numbers, Fuzzy sets and Systems, 234, 31-41, 2014.
  • [16] Y. J. Wang and H. S. Lee, The revised method of ranking fuzzy numbers with an area between the centroid point and original point, Computers and Mathematics with Applications 55, 2033-2042, 2008.
  • [17] Y. -M. Wang, J. -B. Yang, D. -L. Xu, and K. S. Chin, On the centroid of fuzzy numbers, Fuzzy Sets and Systems, 157, 919-926, 2006.
  • [18] Z. Wang, R. Yang, and K. S. Leung, Nonlinear Integrals and Their Applications in Data Mining, World Scientific, 2010.
  • [19] J. S. Yao and K.Wu, Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems 116, 275-288, 2000
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a7ff399c-5da9-46e6-be87-8bd98c22c8d1
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