A fuzzy two person interval game problem is proposed and treated in this paper which is not easily tackled by the conventional methods. First, with respect to this pay-off values, a necessary and sufficient condition for the existence of a saddle point is proved. Based on interval value model, we are to find the value of interval game without saddle point. Finally, example is given to illustrate the procedure and to indicate the performance of the proposed method. 285 Asia Pac. J. Oper. Res. 2009.26:285-305. Downloaded from www.worldscientific.com by MCMASTER UNIVERSITY on 02/05/15. For personal use only.The set of all interval numbers in is denoted by I( ).
Basic interval arithmeticAn extension of ordinary arithmetic to intervals is known as interval arithmetic. Let A = [a 1 , a 2 ] and B = [b 1 , b 2 ] ∈ I( ) be two interval numbers. The arithmetic and multiplication by a real number c are defined as follows:(i) The sum of two interval numbers is A + B = [a 1 + b 1 , a 2 + b 2 ].(ii) The subtraction of these two numbers isIf c = 0 be a scalar then, cA = [ca 1 , ca 2 ] if c ≥ 0, and cA = [ca 2 , ca 1 ] if c < 0. Asia Pac. J. Oper. Res. 2009.26:285-305. Downloaded from www.worldscientific.com by MCMASTER UNIVERSITY on 02/05/15. For personal use only.
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