The order structure of fuzzy numbers based on the level characteristics and its application to optimization problems

Ranking and comparing fuzzy numbers is an important part in many fuzzy optimization problems such as intelligent control and manufacturing system production line scheduling with uncertainty environments. In this paper, based on the level characteristic function andα-average of level cut sets of fuzzy number, we establish the IMα-metric method for measuring fuzzy number as a whole, and introduce the concept of IDα-difference that describes the reliability of IMα-metric value. Further, the basic properties and the separability of IMα-metric and IDα-difference are discussed. Finally, we give a mathematical model to solve fuzzy optimization problems by means of IMα-metric.

[1]  Gregory T. Adams,et al.  The fuzzy integral , 1980 .

[2]  K. Kim,et al.  Ranking fuzzy numbers with index of optimism , 1990 .

[3]  E. Lee,et al.  Comparison of fuzzy numbers based on the probability measure of fuzzy events , 1988 .

[4]  R. Goetschel,et al.  Topological properties of fuzzy numbers , 1983 .

[5]  G. Bortolan,et al.  A review of some methods for ranking fuzzy subsets , 1985 .

[6]  Congxin Wu,et al.  Fuzzy metric and convergences based on the symmetric difference , 1999, Fuzzy Sets Syst..

[7]  P. Kloeden,et al.  Metric Spaces Of Fuzzy Sets Theory And Applications , 1975 .

[8]  Kaoru Hirota,et al.  On fuzzy number lattice (R̄, ⩽) , 1997, Fuzzy Sets Syst..

[9]  Mao-Jiun J. Wang,et al.  Ranking fuzzy numbers with integral value , 1992 .

[10]  Mohamed Abd El-Hady Kassem,et al.  Stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraints , 1995, Fuzzy Sets Syst..

[11]  Peter E. Kloeden,et al.  Characterization of compact subsets of fuzzy sets , 1989 .

[12]  Tong Shaocheng,et al.  Interval number and fuzzy number linear programmings , 1994 .

[13]  H. Tanka Fuzzy data analysis by possibilistic linear models , 1987 .

[14]  Hiroaki Kuwano,et al.  On the fuzzy multi-objective linear programming problem: Goal programming approach , 1996, Fuzzy Sets Syst..

[15]  W. Congxin,et al.  The Supremum and Infimum of the Set of Fuzzy Numbers and Its Application , 1997 .

[16]  Shan-Huo Chen Ranking fuzzy numbers with maximizing set and minimizing set , 1985 .

[17]  Hung T. Nguyen,et al.  A note on the extension principle for fuzzy sets , 1978 .