Systems Engineering and Electronics

Previous Articles     Next Articles

Fundamental definitions and calculation rules of grey mathematics: a review work

Qiaoxing Li1,2, Sifeng Liu2,4, and Jeffrey Yi-Lin Forrest2,3   

  1. 1. School of Management, Guizhou University, Guiyang 550025, China;
    2. School of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
    3. School of Business, Slippery Rock University, Slippery Rock PA 16057, USA;
    4. Centre of Computational Intelligence, De Montfort University, Leicester LE19BH, UK
  • Online:2015-12-25 Published:2010-01-03


Grey mathematics is the mathematical foundation of thegrey system theory. Recently, some important results have beenachieved. In order to accelerate the development of grey mathematics,the results are summarized and redefined. This paperincludes the fundamental definitions and calculation rules of thegrey hazy set, grey number, grey matrix and grey function. Greymathematics includes four types of operation, i.e. the grey operation,the whitened operation, the covered operation and the onlypotential true operation. According to its intrinsic quality, the coveredoperation, which differs from the interval one, is called as thewhole-proximate calculation that means the proximate calculationspreads through the whole range of the covered set of every greynumber, and we confirm that it may be a new branch of computationalor applied mathematics. The overview should develop thegrey system theory and grey mathematics.