General grey numbers and their operations

Grey Systems

Volumn 2, Issue 3, 2012, Pages 341-349

  Liu, Sifeng ^a   Fang, Zhigeng ^a   Yang, Yingjie ^b   Forrest, Jeffrey ^c  

^a NANJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS   (China)

^b DE MONTFORT UNIVERSITY   (United Kingdom)

^c SLIPPERY ROCK UNIVERSITY   (United States)

Author keywords

Basic element; General grey numbers; Greyness; Kernel; Mathematical programming; Number theory; Operations

Indexed keywords

EID: 85136353597     PISSN: 20439377     EISSN: 20439385     Source Type: Journal    
DOI: 10.1108/20439371211273230     Document Type: Article

References (15)

1. Alefeld, G. and Herzberger, J. (1983), Introduction to Interval Computations, Academic Press, New York, NY (Transl. by J. Rokne from the original German “Einf¨hrung In Die Intervallrechnung”).
2. Deng, J.L. (1982), “Control problems of grey systems”, Systems & Control Letters, Vol. 1 No. 5, pp. 288‐94.
3. Ishihuchi, H. and Tanaka, M. (1990), “Multiobjective programming in optimization of the interval objective function”, European Journal of Operation Research, Vol. 48, pp. 219‐25.
4. Liu, S. (1989), “On Perron‐Frobenius Theorem of grey nonnegative matrix”, Journal of Grey System, Vol. 1 No. 2, pp. 157‐66.
5. Liu, S. and Lin, Y. (2006), Grey Information: Theory and Practical Applications, Springer, London.
6. Liu, S. and Lin, Y. (2011), Grey Systems: Theory and Applications, Springer‐Verlag, Berlin.
7. Liu, S.F. (1996), “Axioms on grey degree”, The Journal of Grey System, Vol. 8 No. 4, pp. 397‐400.
8. Moore, R.E. (1979), Method and Application of Interval Analysis, Prentice‐Hall, London.
9. Yang, Y. (2007), “Extended grey numbers and their operations”, Proceedings of 2007 IEEE International Conference on Systems, Man and Cybernetics, Montreal, Canada, pp. 2181‐6.
10. Yang, Y. and Liu, S. (2011), “Reliability of operations of grey numbers using kernels”, Grey Systems: Theory and Application, Vol. 1 No. 1, pp. 57‐71.
11. Young, R.C. (1931), “The algebra of many‐valued quantities”, Annals of Mathematics, Vol. 31, pp. 260‐90.
12. Liu, S., Fang, Z. and Xie, N. (2010), “Algorithm rules of interval grey numbers based on the kernel and the degree of greyness of grey numbers”, Systems Engineering and Electronics, Vol. 32 No. 2, pp. 313‐16.
13. Liu, S.F. and Lin, Y. (2006), “On measures of information content of grey numbers”, Kybernetes: The International Journal of Systems & Cybernetics, Vol. 35 No. 6, pp. 899‐904.
14. Liu, S.F., Dang, Y.G., Fang, Z.G. and Xie, N.M. (2010), Grey System: Theory and Application, 5th ed., Science Press, Beijing.
15. Yang, Y. and John, R. (2012), “Grey sets and greyness”, Information Sciences, Vol. 185 No. 1, pp. 249‐64.