Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters
In this paper, we present interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Using the level sets of fuzzy parameters, the corresponding nonfuzzy two-level linear fractional programming problem is introduced. In our interactive method, after det...
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| Vydáno v: | Fuzzy sets and systems Ročník 115; číslo 1; s. 93 - 103 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.10.2000
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| ISSN: | 0165-0114, 1872-6801 |
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| Abstract | In this paper, we present interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Using the level sets of fuzzy parameters, the corresponding nonfuzzy two-level linear fractional programming problem is introduced. In our interactive method, after determining fuzzy goals of decision makers at both levels, a satisfactory solution is derived efficiently by updating a minimal satisfactory level of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. The satisfactory solution well-balanced between both levels is easily computed by combined use of the bisection method, the phase one of the simplex method and the variable transformation method by Charnes and Cooper. An illustrative numerical example for two-level linear fractional programming problems with fuzzy parameters is provided to demonstrate the feasibility of the proposed method. |
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| AbstractList | In this paper, we present interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Using the level sets of fuzzy parameters, the corresponding nonfuzzy two-level linear fractional programming problem is introduced. In our interactive method, after determining fuzzy goals of decision makers at both levels, a satisfactory solution is derived efficiently by updating a minimal satisfactory level of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. The satisfactory solution well-balanced between both levels is easily computed by combined use of the bisection method, the phase one of the simplex method and the variable transformation method by Charnes and Cooper. An illustrative numerical example for two-level linear fractional programming problems with fuzzy parameters is provided to demonstrate the feasibility of the proposed method. |
| Author | Uemura, Yoshio Sakawa, Masatoshi Nishizaki, Ichiro |
| Author_xml | – sequence: 1 givenname: Masatoshi surname: Sakawa fullname: Sakawa, Masatoshi email: sakawa@msl.sys.hiroshima-u.ac.jp organization: Department of Industrial and Systems Engineering, Faculty of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, 739-8527 Japan – sequence: 2 givenname: Ichiro surname: Nishizaki fullname: Nishizaki, Ichiro organization: Department of Industrial and Systems Engineering, Faculty of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, 739-8527 Japan – sequence: 3 givenname: Yoshio surname: Uemura fullname: Uemura, Yoshio organization: Products Projects Development Department, Juken Sangyou Co., Ltd., 1-1 Mokuzaikouminami, Hatsukaichi, Hiroshima, 738-8502 Japan |
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| Keywords | Interactive methods Fuzzy goals Two-level linear fractional programming problems Fuzzy parameters Fuzzy programming |
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| References | Zimmermann (BIB21) 1978; 1 Sakawa, Yumine (BIB17) 1983; 5 Steuer (BIB19) 1986 Sakawa (BIB11) 1993 Kornbluth, Steuer (BIB7) 1981; 8 Sakawa, Nishizaki, Uemura (BIB13) 2000; 109 Sakawa, Yano (BIB16) 1990; 35 Bitran, Novaes (BIB5) 1973; 21 Bellman, Zadeh (BIB3) 1970; 17 Charnes, Cooper (BIB6) 1962; 9 Luhandjula (BIB10) 1984; 13 Lai (BIB9) 1996; 77 Bard, Falk (BIB2) 1982; 9 Sakawa, Yano (BIB15) 1988; 28 Bard (BIB1) 1983; 38 Shih, Lai, Lee (BIB18) 1996; 23 Kornbluth, Steuer (BIB8) 1981; 27 Sakawa, Yano (BIB14) 1985; 16 Bialas, Karwan (BIB4) 1984; 30 Sakawa, Nishizaki, Uemura (BIB12) 1998; 36 White, Anandalingam (BIB20) 1993; 3 Sakawa (10.1016/S0165-0114(99)00027-5_BIB11) 1993 Steuer (10.1016/S0165-0114(99)00027-5_BIB19) 1986 Sakawa (10.1016/S0165-0114(99)00027-5_BIB17) 1983; 5 White (10.1016/S0165-0114(99)00027-5_BIB20) 1993; 3 Bellman (10.1016/S0165-0114(99)00027-5_BIB3) 1970; 17 Sakawa (10.1016/S0165-0114(99)00027-5_BIB14) 1985; 16 Sakawa (10.1016/S0165-0114(99)00027-5_BIB12) 1998; 36 Sakawa (10.1016/S0165-0114(99)00027-5_BIB16) 1990; 35 Shih (10.1016/S0165-0114(99)00027-5_BIB18) 1996; 23 Bialas (10.1016/S0165-0114(99)00027-5_BIB4) 1984; 30 Lai (10.1016/S0165-0114(99)00027-5_BIB9) 1996; 77 Zimmermann (10.1016/S0165-0114(99)00027-5_BIB21) 1978; 1 Sakawa (10.1016/S0165-0114(99)00027-5_BIB13) 2000; 109 Luhandjula (10.1016/S0165-0114(99)00027-5_BIB10) 1984; 13 Sakawa (10.1016/S0165-0114(99)00027-5_BIB15) 1988; 28 Bitran (10.1016/S0165-0114(99)00027-5_BIB5) 1973; 21 Charnes (10.1016/S0165-0114(99)00027-5_BIB6) 1962; 9 Kornbluth (10.1016/S0165-0114(99)00027-5_BIB7) 1981; 8 Bard (10.1016/S0165-0114(99)00027-5_BIB1) 1983; 38 Bard (10.1016/S0165-0114(99)00027-5_BIB2) 1982; 9 Kornbluth (10.1016/S0165-0114(99)00027-5_BIB8) 1981; 27 |
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