On a New Model for Solving B ilevel Leader2follower Decision2making Problem s

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1 ( ) Journal of Yunnan Nationalities University(Natural Sciences Edition) Vol. 17 No. 2 Ap r [ ] (, ).,,.,.,,,,,,. ; ; TP181 A (2008) On a New Model for Solving B ilevel Leader2follower Decision2making Problem s Zheng Zheng ( School of Autom ation Science and Electrical Engineering, Beijing University of Aeronautics and A stronautics, Beijing , China) Abstract: H ierarchical leader2follower decision is a common issue in organizational management. U sually or2 ganizational decisions involve entities at several levels and the decision entities have different p riorities. The hierar2 chical nature of organizational decisions often requires comp rom ised solutions between the entities but w ithin guide2 lines determ ined by decision entities at upper levels. Due to m any uncertain factors in real decision2making situa2 tions, it is rather difficult to formulate objective functions and constraints of the two entities to simp ly app ly bilevel p rogramm ing. In this paper, after analyzing some existent bilevel leader2follower decision2making models, a rule set based on the bilevel leader2follower decision2m aking model is p roposed. B esides, we develop a modeling ap2 p roach; thus a rule set based on the bilevel leader2follower decision2making model can be constructed from real p roblem s. Finally, some suggestions about the future work related to this research are p roposed. Key words: leader2follower decision; bilevel leader2follower decision; rule set 0,,,,, ( ) ( ), ( ), 3 : : ( ). : (1980 ),,,,, : , , Expert Systems with Applications Fundamenta Informaticae ( ) 20, SCI 7, EI 11 ; ; :. 97

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3 2 : ( ), ( input, state), (output, tape move2 ment, state)., [ 18 ].,,,,.,,.,., : 1), ; 2),,,,. 3 [ 19 ] ( ) L, a = v, a A t v V a. <, <, < <. 4 [ 19 ] ( ) x < ( x 5 S < x 5< ), S : 1) x 5a = v iff I a ( x) = v, 2) x 5 < iff not x 5<, 3) x 5< iff x 5< and x 5. 4) x 5< iff x 5< or x 5. S < m S ( <), m S ( < ) = { x U x 5< }., m ( <). A t}, 5 ( ) [ 15 ] S = (U, A t, L, { V a a { I a a A t} } ), r <], < S, x U x 5<] iff x 5 <. 6 ( ) [ 15 ] S = (U, C D, L, {V a a A t}, { I a a C D } } ), dr <], <, ( ), < c = v c C, d = v d D.., 5 ( a 1,, a 5 ) 1 d, ( a 1 = 1) ( a 3 = 1) ( a 4 = 1) ϖ d = 4 2. a 1, a 3, a 4 1, 1, 1, d 1. 7 ( ) [ 15 ] X Y rs X Y. X x, RS y, y Y, ( x, y) rs., x, y, X, Y., [15, 16 ]. 8 ( ) [ 15 ] x, RS, cf ( x, RS ) cf ( x, RS ) = True, if forπ r RS, x =m ( r). False, else cf ( x, RS ) : x RS. 2,,,.,.,. 2, [15 ]. 9 ( ) : m in x f L ( x, y) s. t. cf ( x, G L ) = True; m in y f F ( x, y) s. t. cf ( y, G F ) = True, x y. f L f F, 99

4 ( ) 17 cf. G L G F,?. :, ; ; 1 ; 2 F L,, ; 3 F L, F L ; 4 G L,, ; 5 G L, F L ; 6 F F,, ; 7 F F, F F ; 8 G F,, ; 9 G F, G F ; ,, 2, 4, 6 8, 4.,,, [ 20 ]. 5, 7 9,. 3 : 1),. ; 2).,, ; 3),,, [ 17, 21 ]., ROSETTA [ 22 ], R I2 DAS [ 23 ], RSES [ 24 ],. [ 20 ]. 3,,,,,,..,.,.,. :,

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