An interactive satisficing method for solving multiobjective mixed fuzzy-stochastic programming problems
In this paper an interactive satisficing method (named PRELIME) is proposed for solving mixed fuzzy-stochastic multiobjective programming problems. The proposed method can be used to solve linear as well as a class of nonlinear multiobjective problems in mixed fuzzy-stochastic environment wherein va...
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| Veröffentlicht in: | Fuzzy sets and systems Jg. 117; H. 1; S. 61 - 79 |
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| Sprache: | Englisch |
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Elsevier B.V
2001
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| Abstract | In this paper an interactive satisficing method (named PRELIME) is proposed for solving mixed fuzzy-stochastic multiobjective programming problems. The proposed method can be used to solve linear as well as a class of nonlinear multiobjective problems in mixed fuzzy-stochastic environment wherein various kinds of uncertainties related to fuzziness and/or randomness are present. In this method a fuzzifying approach has been proposed which treats the stochastic objectives on the basis of extended E-model and the stochastic constraints as fuzzified chance constraints. As a result of this the stochastic objectives as well as the stochastic constraints are treated in a fuzzy environment providing an opportunity to the decision maker (DM) to trade-off fuzzy as well as stochastic objectives and constraints during the interactive process of search for a satisficing solution. The use of the method has been illustrated on some test examples taken from literature. |
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| AbstractList | In this paper an interactive satisficing method (named PRELIME) is proposed for solving mixed fuzzy-stochastic multiobjective programming problems. The proposed method can be used to solve linear as well as a class of nonlinear multiobjective problems in mixed fuzzy-stochastic environment wherein various kinds of uncertainties related to fuzziness and/or randomness are present. In this method a fuzzifying approach has been proposed which treats the stochastic objectives on the basis of extended E-model and the stochastic constraints as fuzzified chance constraints. As a result of this the stochastic objectives as well as the stochastic constraints are treated in a fuzzy environment providing an opportunity to the decision maker (DM) to trade-off fuzzy as well as stochastic objectives and constraints during the interactive process of search for a satisficing solution. The use of the method has been illustrated on some test examples taken from literature. |
| Author | Nguyen, H.T. Mohan, C. |
| Author_xml | – sequence: 1 givenname: C. surname: Mohan fullname: Mohan, C. email: maths@rukiu.ernet.in organization: Department of Mathematics, University of Roorkee, Roorkee 247667, U.P., India – sequence: 2 givenname: H.T. surname: Nguyen fullname: Nguyen, H.T. organization: Section of Mathematics, Agricultural University, Hanoi, Viet Nam |
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| Cites_doi | 10.1007/BF03398512 10.1007/978-3-642-45700-5_2 10.1016/0165-0114(91)90093-6 10.1016/0165-0114(89)90017-1 10.1016/S0377-2217(97)00161-6 10.1007/BF00933504 10.1016/0165-0114(94)00364-7 10.1007/978-94-009-2111-5 |
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| Keywords | Interactive methods Decision making Multicriteria analysis Fuzzified chance constraints Fuzzy goals Multiobjective mixed fuzzy-stochastic programming Mathematical programming |
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| References | Slowinski, Teghem (BIB17) 1990 Price (BIB10) 1983; 40 R. Slowinski, J. Teghem (Eds.), Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertainty, Kluwer Academic Publishers, Dordrecht, 1990. C. Mohan, H.T. Nguyen, A controlled random search technique incorporating simulated annealing concept for solving integer and mixed integer global optimization problems, Comput. Optim. Appl. (1997), accepted for publication. Mohan, Shanker (BIB8) 1994; 11 D. Delgalo, J. Kacprzyk, J.L. Verdegay, M.A. Vila (Eds.), Fuzzy optimization: Recent advances, Physica Verlag, Germany, 1994. M. Fedrizzi, J. Kacprzyk, M. Roubens (Eds.), Interactive fuzzy optimization, Lecture Notes in Economics and Mathematical Systems, vol. 368, 1991. Roubens, Teghem (BIB13) 1991; 42 Sakawa, Yano (BIB15) 1989; 30 Inuiguchi, Sakawa (BIB5) 1995; 76 Chakraborty, Rao, Tiwari (BIB1) 1994; 31 Rommelfanger (BIB11) 1990 Sakawa (BIB14) 1993 Slowinski (BIB16) 1990 Nguyen (BIB9) 1996 Rommelfanger (BIB12) 1991; 12 Stancu-Minasian (BIB19) 1984 Teghem (BIB20) 1990 (a) C. Mohan, H.T. Nguyen, A fuzzifying approach to stochastic programming, Opsearch 34 (1997) 73–96. (b) C. Mohan, H.T. Nguyen, Reference direction interactive method for solving multiobjective fuzzy programming problems, European J. Oper. Res. 107 (1998) 599–613. Zimmermann (BIB21) 1987 Goicoechea, Hansen, Duckstein (BIB4) 1982 10.1016/S0165-0114(98)00269-3_BIB7 Mohan (10.1016/S0165-0114(98)00269-3_BIB8) 1994; 11 Rommelfanger (10.1016/S0165-0114(98)00269-3_BIB11) 1990 10.1016/S0165-0114(98)00269-3_BIB3 cr-split#-10.1016/S0165-0114(98)00269-3_BIB6.1 cr-split#-10.1016/S0165-0114(98)00269-3_BIB6.2 Nguyen (10.1016/S0165-0114(98)00269-3_BIB9) 1996 Sakawa (10.1016/S0165-0114(98)00269-3_BIB14) 1993 Chakraborty (10.1016/S0165-0114(98)00269-3_BIB1) 1994; 31 Roubens (10.1016/S0165-0114(98)00269-3_BIB13) 1991; 42 Teghem (10.1016/S0165-0114(98)00269-3_BIB20) 1990 10.1016/S0165-0114(98)00269-3_BIB2 10.1016/S0165-0114(98)00269-3_BIB18 Rommelfanger (10.1016/S0165-0114(98)00269-3_BIB12) 1991; 12 Price (10.1016/S0165-0114(98)00269-3_BIB10) 1983; 40 Slowinski (10.1016/S0165-0114(98)00269-3_BIB16) 1990 Goicoechea (10.1016/S0165-0114(98)00269-3_BIB4) 1982 Inuiguchi (10.1016/S0165-0114(98)00269-3_BIB5) 1995; 76 Stancu-Minasian (10.1016/S0165-0114(98)00269-3_BIB19) 1984 Sakawa (10.1016/S0165-0114(98)00269-3_BIB15) 1989; 30 Slowinski (10.1016/S0165-0114(98)00269-3_BIB17) 1990 Zimmermann (10.1016/S0165-0114(98)00269-3_BIB21) 1987 |
| References_xml | – year: 1993 ident: BIB14 article-title: Fuzzy Sets and Interactive Multiobjective Optimization – volume: 76 start-page: 309 year: 1995 end-page: 317 ident: BIB5 article-title: A possibilistic linear program is equivalent to a stochastic linear program in a special case publication-title: Fuzzy Sets and Systems – start-page: 103 year: 1990 end-page: 116 ident: BIB20 article-title: STRANGE – an interactive method for multiobjective stochastic linear programming and STRANGE-MONIX – its extension to integer variables publication-title: Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertainty – reference: R. Slowinski, J. 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Roubens (Eds.), Interactive fuzzy optimization, Lecture Notes in Economics and Mathematical Systems, vol. 368, 1991. – year: 1982 ident: BIB4 article-title: Multiobjective Decision Making with Engineering and Business Applications – year: 1984 ident: BIB19 article-title: Stochastic Programming with Multiple Objective Functions – volume: 40 start-page: 333 year: 1983 end-page: 348 ident: BIB10 article-title: Global optimization by controlled random search publication-title: J. Optim. Theory Appl. – reference: D. Delgalo, J. Kacprzyk, J.L. Verdegay, M.A. Vila (Eds.), Fuzzy optimization: Recent advances, Physica Verlag, Germany, 1994. – volume: 11 start-page: 93 year: 1994 end-page: 101 ident: BIB8 article-title: A controlled random search technique for global optimization using quadratic approximation publication-title: Asia-Pacific J. Oper. 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Oper. Res. – year: 1987 ident: 10.1016/S0165-0114(98)00269-3_BIB21 – year: 1996 ident: 10.1016/S0165-0114(98)00269-3_BIB9 – start-page: 365 year: 1990 ident: 10.1016/S0165-0114(98)00269-3_BIB17 article-title: Comparison study of STRANGE and FLIP – year: 1982 ident: 10.1016/S0165-0114(98)00269-3_BIB4 – volume: 40 start-page: 333 year: 1983 ident: 10.1016/S0165-0114(98)00269-3_BIB10 article-title: Global optimization by controlled random search publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00933504 – year: 1993 ident: 10.1016/S0165-0114(98)00269-3_BIB14 – volume: 76 start-page: 309 year: 1995 ident: 10.1016/S0165-0114(98)00269-3_BIB5 article-title: A possibilistic linear program is equivalent to a stochastic linear program in a special case publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(94)00364-7 – ident: 10.1016/S0165-0114(98)00269-3_BIB18 doi: 10.1007/978-94-009-2111-5 – ident: 10.1016/S0165-0114(98)00269-3_BIB7 – volume: 12 start-page: 213 year: 1991 ident: 10.1016/S0165-0114(98)00269-3_BIB12 article-title: Stochastic programming with vague data publication-title: Ann. Univ. Sci. Budapest, Sect. Comput. – ident: 10.1016/S0165-0114(98)00269-3_BIB2 – year: 1984 ident: 10.1016/S0165-0114(98)00269-3_BIB19 |
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| SubjectTerms | Decision making Fuzzified chance constraints Fuzzy goals Interactive methods Mathematical programming Multicriteria analysis Multiobjective mixed fuzzy-stochastic programming |
| Title | An interactive satisficing method for solving multiobjective mixed fuzzy-stochastic programming problems |
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