Two new algorithms for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities
This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solutio...
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| Vydáno v: | Journal of computational and applied mathematics Ročník 233; číslo 8; s. 2090 - 2103 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Kidlington
Elsevier B.V
15.02.2010
Elsevier |
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solution and a finite number of minimal solutions. Also, an efficient algorithm is proposed to solve the model based on the structure of FRI path, the concept of partial solution, and the branch-and-bound approach. The algorithm finds an optimal solution of the model without explicitly generating all the minimal solutions. Some sufficient conditions are given that under them, some of the optimal components of the model are directly determined. Some procedures are presented to reduce the search domain of an optimal solution of the original problem based on the conditions. Then the reduced domain is decomposed (if possible) into several sub-domains with smaller dimensions that finding the components of the optimal solution in each sub-domain is very easy. In order to obtain an optimal solution of the original problem, we propose another more efficient algorithm which combines the first algorithm, these procedures, and the decomposition method. Furthermore, sufficient conditions are suggested that under them, the problem has a unique optimal solution. Also, a comparison between the recently proposed algorithm and the known ones will be made. |
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| AbstractList | This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solution and a finite number of minimal solutions. Also, an efficient algorithm is proposed to solve the model based on the structure of FRI path, the concept of partial solution, and the branch-and-bound approach. The algorithm finds an optimal solution of the model without explicitly generating all the minimal solutions. Some sufficient conditions are given that under them, some of the optimal components of the model are directly determined. Some procedures are presented to reduce the search domain of an optimal solution of the original problem based on the conditions. Then the reduced domain is decomposed (if possible) into several sub-domains with smaller dimensions that finding the components of the optimal solution in each sub-domain is very easy. In order to obtain an optimal solution of the original problem, we propose another more efficient algorithm which combines the first algorithm, these procedures, and the decomposition method. Furthermore, sufficient conditions are suggested that under them, the problem has a unique optimal solution. Also, a comparison between the recently proposed algorithm and the known ones will be made. |
| Author | Molai, Ali Abbasi |
| Author_xml | – sequence: 1 givenname: Ali Abbasi surname: Molai fullname: Molai, Ali Abbasi email: abbasi54@aut.ac.ir, aliabbasimolai@yahoo.com organization: School of Mathematics and Computer Sciences, Damghan University of Basic Sciences, Damghan, P.O. Box 36715-364, Iran |
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| Cites_doi | 10.1016/S0165-0114(98)00417-5 10.1007/s10700-008-9029-y 10.1016/j.camwa.2004.10.049 10.1016/0165-0114(95)00221-9 10.1007/s10700-009-9059-0 10.1016/S0165-0114(99)00117-7 10.1016/j.fss.2009.01.012 10.1016/S0019-9958(76)90446-0 10.1109/TFUZZ.2002.806322 10.1016/j.ins.2003.05.007 10.1016/S0165-0114(01)00052-5 10.1016/0022-247X(85)90329-4 10.1016/j.fss.2009.03.007 10.1016/0165-0114(81)90081-6 10.1109/91.784204 10.1016/j.fss.2004.09.010 10.1109/TFUZZ.2002.800657 10.1016/0022-247X(84)90144-6 10.1016/S0165-0114(97)00184-X 10.1023/A:1022800330844 10.1109/FUZZY.1995.409860 10.1016/j.fss.2004.10.002 10.1016/S0165-0114(96)00246-1 10.1016/S0165-0114(98)00471-0 10.1016/0022-247X(91)90222-L 10.1023/A:1020955112523 10.1016/0165-0114(91)90047-T 10.1016/0165-0114(88)90199-6 10.1016/j.aml.2005.11.001 10.1016/0165-0114(91)90170-U 10.1016/j.fss.2005.02.010 10.1007/s10700-005-4914-0 10.1016/0165-0114(85)90036-3 10.1002/mcda.4020040103 10.1007/s00500-001-0157-3 10.1016/j.ins.2004.04.003 |
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| Keywords | Minimum solution Fuzzy optimization Max-Einstein composition Partial solution Fuzzy relation inequality Solution uniqueness Fuzzy system Optimal algorithm Decomposition method Optimization method Linear model Numerical analysis Sufficient condition Applied mathematics Optimal solution Inequality constraint Problem solving Variational calculus Mathematical programming |
| Language | English |
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| References | Pedrycz (b38) 1988; 28 S.-M. Guu, Y.-K. Wu, Minimizing a linear objective function under a max-t-norm fuzzy relational equation constraint, Fuzzy Sets and Systems Di Nola, Sessa, Pedrycz, Sanchez (b8) 1989 Loetamonphong, Fang (b25) 2001; 118 Sanchez (b43) 1977 Wu, Guu, Liu (b51) 2002; 10 Baets (b3) 2000; vol. 1 Chen, Wang (b4) 2002; 6 Czogala, Predrycz (b6) 1981; 6 Gottwald (b13) 2000 W.B. Vasantha Kandasamy, F. Smarandache, Fuzzy relational maps and neutrosophic relational maps, hexis church rock (2004). (see Chapters one and two) at Guo, Xia (b14) 2006; 5 W.-L. Xu, Fuzzy relation equation, Reports on Beijing Fuzzy Math. Meeting, 1978 Wang (b48) 1983 Stamou, Tzafestas (b30) 2001; 120 Pedrycz (b41) 1989 Guu, Wu (b15) 2002; 1 Wang (b44) 1984; 4 Wu, Guu (b52) 2005; 150 Bourke, Fisher (b2) 1998; 94 Lu, Fang (b32) 2001; 119 Pedrycz (b39) 1985; 107 Luoh, Wang, Liaw (b35) 2003; 11 Wang, Fang, Nuttle (b46) 2003; 2 Loetamonphong, Fang (b27) 1998; 7 Pappis, Sugeno (b37) 1985; 15 Xiong, Wang (b54) 2005; 151 Hu (b19) 1998; 146 Klir, Folger (b21) 1988 Peeva, Kyosev (b42) 2004 Li, Fang (b23) 2008; 7 Loetamonphong, Fang, Young (b26) 2002; 127 P.Z. Wang, D.Z. Zhang, Fuzzy decision making, Beijing Normal University Lectures, 1987 Klir, Yuan (b22) 1995 Sanchez (b1) 1976; 30 Wang, Sessa, Di Nola, Pedrycz (b49) 1984; 18 Loia, Sessa (b28) 2005; 171 Fernandez, Gil (b11) 2004; 164 Li, Miao, HAN, Wang (b29) 2005; 50 Zhang, Dong, Ren (b56) 2003; 3 Di Nola, Pedrycz, Sessa, Sanchez (b9) 1991; 40 Fang, Li (b10) 1999; 103 Gottwald (b12) 1993 Han, Li, Wang (b17) 2006; 19 Luo (b33) 1984; 103 Luo (b34) 1989 Wang, Zhang, Sachez, Lee (b45) 1991; 159 Di Nola, Pedrycz, Sessa, Wang (b7) 1984; 8 Zimmermann (b57) 1991 Hirota, Pedrycz (b20) 1996; 81 Lin (b31) 2009; 160 Markovskii (b36) 2005; 153 Chen, Wang (b5) 2006 Pedrycz (b40) 1991; 40 Wang (b47) 1995; 4 S.Z. Han, A.H. Song, T. Sekiguchi, Fuzzy inequality relation system identification via sign matrix method, in: Proceeding of 1995 IEEE International Conference 3, 1995, pp. 1375–1382 Li, Fang (b24) 2009; 8 Loetamonphong (10.1016/j.cam.2009.09.042_b27) 1998; 7 Gottwald (10.1016/j.cam.2009.09.042_b13) 2000 Lin (10.1016/j.cam.2009.09.042_b31) 2009; 160 Markovskii (10.1016/j.cam.2009.09.042_b36) 2005; 153 Di Nola (10.1016/j.cam.2009.09.042_b8) 1989 Pedrycz (10.1016/j.cam.2009.09.042_b41) 1989 Zhang (10.1016/j.cam.2009.09.042_b56) 2003; 3 Wang (10.1016/j.cam.2009.09.042_b44) 1984; 4 Guu (10.1016/j.cam.2009.09.042_b15) 2002; 1 Li (10.1016/j.cam.2009.09.042_b24) 2009; 8 Pedrycz (10.1016/j.cam.2009.09.042_b40) 1991; 40 Luo (10.1016/j.cam.2009.09.042_b33) 1984; 103 Klir (10.1016/j.cam.2009.09.042_b21) 1988 Wu (10.1016/j.cam.2009.09.042_b51) 2002; 10 Czogala (10.1016/j.cam.2009.09.042_b6) 1981; 6 Di Nola (10.1016/j.cam.2009.09.042_b9) 1991; 40 Zimmermann (10.1016/j.cam.2009.09.042_b57) 1991 Pappis (10.1016/j.cam.2009.09.042_b37) 1985; 15 Luoh (10.1016/j.cam.2009.09.042_b35) 2003; 11 Fernandez (10.1016/j.cam.2009.09.042_b11) 2004; 164 Di Nola (10.1016/j.cam.2009.09.042_b7) 1984; 8 Wang (10.1016/j.cam.2009.09.042_b49) 1984; 18 Guo (10.1016/j.cam.2009.09.042_b14) 2006; 5 Hu (10.1016/j.cam.2009.09.042_b19) 1998; 146 Wang (10.1016/j.cam.2009.09.042_b48) 1983 Han (10.1016/j.cam.2009.09.042_b17) 2006; 19 Luo (10.1016/j.cam.2009.09.042_b34) 1989 Wang (10.1016/j.cam.2009.09.042_b47) 1995; 4 Lu (10.1016/j.cam.2009.09.042_b32) 2001; 119 Pedrycz (10.1016/j.cam.2009.09.042_b38) 1988; 28 Wu (10.1016/j.cam.2009.09.042_b52) 2005; 150 10.1016/j.cam.2009.09.042_b55 Wang (10.1016/j.cam.2009.09.042_b46) 2003; 2 10.1016/j.cam.2009.09.042_b53 Sanchez (10.1016/j.cam.2009.09.042_b43) 1977 Stamou (10.1016/j.cam.2009.09.042_b30) 2001; 120 10.1016/j.cam.2009.09.042_b18 Loetamonphong (10.1016/j.cam.2009.09.042_b26) 2002; 127 Sanchez (10.1016/j.cam.2009.09.042_b1) 1976; 30 10.1016/j.cam.2009.09.042_b16 Chen (10.1016/j.cam.2009.09.042_b5) 2006 Li (10.1016/j.cam.2009.09.042_b23) 2008; 7 Bourke (10.1016/j.cam.2009.09.042_b2) 1998; 94 Baets (10.1016/j.cam.2009.09.042_b3) 2000; vol. 1 10.1016/j.cam.2009.09.042_b50 Wang (10.1016/j.cam.2009.09.042_b45) 1991; 159 Klir (10.1016/j.cam.2009.09.042_b22) 1995 Peeva (10.1016/j.cam.2009.09.042_b42) 2004 Li (10.1016/j.cam.2009.09.042_b29) 2005; 50 Loia (10.1016/j.cam.2009.09.042_b28) 2005; 171 Loetamonphong (10.1016/j.cam.2009.09.042_b25) 2001; 118 Gottwald (10.1016/j.cam.2009.09.042_b12) 1993 Hirota (10.1016/j.cam.2009.09.042_b20) 1996; 81 Chen (10.1016/j.cam.2009.09.042_b4) 2002; 6 Xiong (10.1016/j.cam.2009.09.042_b54) 2005; 151 Pedrycz (10.1016/j.cam.2009.09.042_b39) 1985; 107 Fang (10.1016/j.cam.2009.09.042_b10) 1999; 103 |
| References_xml | – volume: 120 start-page: 395 year: 2001 end-page: 407 ident: b30 article-title: Resolution of composite fuzzy relation equations based on Archimedean triangular norms publication-title: Fuzzy Sets and Systems – reference: P.Z. Wang, D.Z. Zhang, Fuzzy decision making, Beijing Normal University Lectures, 1987 – volume: 15 start-page: 79 year: 1985 end-page: 90 ident: b37 article-title: Fuzzy relation equations and the inverse problem publication-title: Fuzzy Sets and Systems – reference: S.Z. Han, A.H. Song, T. Sekiguchi, Fuzzy inequality relation system identification via sign matrix method, in: Proceeding of 1995 IEEE International Conference 3, 1995, pp. 1375–1382 – volume: 119 start-page: 1 year: 2001 end-page: 20 ident: b32 article-title: Solving nonlinear optimization problems with fuzzy relation equations constraints publication-title: Fuzzy Sets and Systems – volume: 18 start-page: 67 year: 1984 end-page: 74 ident: b49 article-title: How many lower solutions does a fuzzy relation equation have? publication-title: BUSEFAL – volume: 146 start-page: 198 year: 1998 end-page: 203 ident: b19 article-title: Generalized variational inequalities with fuzzy relation publication-title: Journal of Computational and Applied Mathematics – year: 1989 ident: b41 article-title: Fuzzy Control and Fuzzy Systems – volume: 118 start-page: 509 year: 2001 end-page: 517 ident: b25 article-title: Optimization of fuzzy relation equations with max-product composition publication-title: Fuzzy Sets and Systems – volume: 7 start-page: 441 year: 1998 end-page: 445 ident: b27 article-title: An efficient solution procedure for fuzzy relational equations with max-product composition publication-title: IEEE Transactions on Fuzzy Systems – start-page: 271 year: 1989 end-page: 285 ident: b34 article-title: Fuzzy relation equalities (Chapter 6) publication-title: Introduction of Fuzzy Sets – year: 1988 ident: b21 article-title: Fuzzy Sets, Uncertainty, and Information – volume: 40 start-page: 77 year: 1991 end-page: 106 ident: b40 article-title: Processing in relational structures: Fuzzy relation equations publication-title: Fuzzy Sets and Systems – volume: 171 start-page: 145 year: 2005 end-page: 172 ident: b28 article-title: Fuzzy relation equations for coding/decoding processes of images and videos publication-title: Information Sciences – volume: 7 start-page: 169 year: 2008 end-page: 214 ident: b23 article-title: On the resolution and optimization of a system of fuzzy relational equations with sup-T composition publication-title: Fuzzy optimization and Decision making – volume: 94 start-page: 61 year: 1998 end-page: 69 ident: b2 article-title: Solution algorithms for fuzzy relational equations with max-product composition publication-title: Fuzzy Sets and Systems – volume: 4 start-page: 67 year: 1984 end-page: 73 ident: b44 article-title: How many lower solutions of finite fuzzy relation equations publication-title: Fuzzy Mathematics – volume: 28 start-page: 183 year: 1988 end-page: 202 ident: b38 article-title: Approximate solutions of fuzzy relational equations publication-title: Fuzzy Sets and Systems – reference: W.-L. Xu, Fuzzy relation equation, Reports on Beijing Fuzzy Math. Meeting, 1978 – year: 1995 ident: b22 article-title: Fuzzy Sets and Fuzzy Logic: Theory and Applications – volume: 160 start-page: 2328 year: 2009 end-page: 2344 ident: b31 article-title: On the relation between fuzzy max-Archimedean publication-title: Fuzzy Sets and Systems – year: 1983 ident: b48 article-title: Fuzzy Sets Theory and its Applications – volume: vol. 1 start-page: 291 year: 2000 end-page: 340 ident: b3 article-title: Analytical solution methods for fuzzy relational equations publication-title: Fundamentals of Fuzzy Sets – start-page: 221 year: 1977 end-page: 234 ident: b43 article-title: Solutions in composite fuzzy relation equations publication-title: Fuzzy Automata and Decision Processes – year: 2006 ident: b5 article-title: Fuzzy relation equations (II): The branch-point-solutions and the categorized minimal solutions publication-title: Soft Computing – volume: 103 start-page: 107 year: 1999 end-page: 113 ident: b10 article-title: Solving fuzzy relation equations with a linear objective function publication-title: Fuzzy Sets and Systems – start-page: 401 year: 2000 end-page: 430 ident: b13 article-title: Generalized solvability behaviour for systems of fuzzy equations publication-title: Discovering the World with Fuzzy Logic – volume: 40 start-page: 415 year: 1991 end-page: 429 ident: b9 article-title: Fuzzy relation equations theory as a basis of fuzzy modeling: An overview publication-title: Fuzzy Sets and Systems – volume: 50 start-page: 623 year: 2005 end-page: 636 ident: b29 article-title: A new kind of fuzzy relation equations based on inner transformation publication-title: Computers and Mathematics with Applications – year: 2004 ident: b42 article-title: Fuzzy Relational Calculus: Theory, Applications and Software – volume: 127 start-page: 141 year: 2002 end-page: 164 ident: b26 article-title: Multi-objective optimization problems with fuzzy relation equation constraints publication-title: Fuzzy Sets and Systems – reference: S.-M. Guu, Y.-K. Wu, Minimizing a linear objective function under a max-t-norm fuzzy relational equation constraint, Fuzzy Sets and Systems, – volume: 30 start-page: 38 year: 1976 end-page: 48 ident: b1 article-title: Resolution of composite fuzzy relation equations publication-title: Information and Control – volume: 153 start-page: 261 year: 2005 end-page: 273 ident: b36 article-title: On the relation between equations with max-product composition and the covering problem publication-title: Fuzzy Sets and Systems – volume: 81 start-page: 355 year: 1996 end-page: 363 ident: b20 article-title: Solving fuzzy relational equations through logical filtering publication-title: Fuzzy Sets and Systems – volume: 19 start-page: 752 year: 2006 end-page: 757 ident: b17 article-title: Resolution of finite fuzzy relation equations based on strong pseudo-t-norms publication-title: Applied Mathematics Letters – volume: 159 start-page: 72 year: 1991 end-page: 87 ident: b45 article-title: Lattecized linear programming and fuzzy relational inequalities publication-title: Journal of Mathematical Analysis and Applications – volume: 150 start-page: 147 year: 2005 end-page: 162 ident: b52 article-title: Minimizing a linear function under a fuzzy max–min relational equation constraint publication-title: Fuzzy Sets and Systems – volume: 107 start-page: 520 year: 1985 end-page: 536 ident: b39 article-title: On generalized fuzzy relational equations and their applications publication-title: Journal of Mathematical Analysis and Applications – volume: 1 start-page: 347 year: 2002 end-page: 360 ident: b15 article-title: Minimizing a linear objective function with fuzzy relation equation constraints publication-title: Fuzzy Optimization and Decision Making – volume: 3 start-page: 231 year: 2003 end-page: 233 ident: b56 article-title: Programming problem with fuzzy relation inequality constraints publication-title: Journal of Liaoning Normal University – year: 1989 ident: b8 article-title: Fuzzy Relation Equations and their Applications to Knowledge Engineering – year: 1993 ident: b12 article-title: Fuzzy Sets and Fuzzy Logic: The Foundations of Application—From a Mathematical Point of View – volume: 10 start-page: 552 year: 2002 end-page: 558 ident: b51 article-title: An accelerated approach for solving fuzzy relation equations with a linear objective function publication-title: IEEE Transactions on Fuzzy Systems – volume: 103 start-page: 524 year: 1984 end-page: 532 ident: b33 article-title: Reachable equation of a fuzzy relation equation publication-title: Journal of Mathematical Analysis and Applications – volume: 6 start-page: 428 year: 2002 end-page: 435 ident: b4 article-title: Fuzzy relation equations (I): The general and specialized solving algorithms publication-title: Soft Computing – volume: 8 start-page: 99 year: 1984 end-page: 145 ident: b7 article-title: Fuzzy relation equations under a class of triangular norms: A survey and new results publication-title: Stochastica – volume: 5 start-page: 33 year: 2006 end-page: 47 ident: b14 article-title: An algorithm for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities publication-title: Fuzzy Optimization and Decision Making – volume: 11 start-page: 100 year: 2003 end-page: 108 ident: b35 article-title: Matrix-pattern-based computer algorithm for solving fuzzy relation equations publication-title: IEEE Transactions on Fuzzy Systems – volume: 4 start-page: 23 year: 1995 end-page: 35 ident: b47 article-title: A multi-objective mathematical programming problem with fuzzy relation constraints publication-title: Journal of Multi-Criteria Decision Analysis – volume: 8 start-page: 179 year: 2009 end-page: 229 ident: b24 article-title: A survey on fuzzy relational equations, Part I: Classification and solvability publication-title: Fuzzy Optimization and Decision Making – volume: 2 start-page: 41 year: 2003 end-page: 60 ident: b46 article-title: Solution sets of interval-valued fuzzy relational equations publication-title: Fuzzy Optimization and Decision Making – volume: 6 start-page: 73 year: 1981 end-page: 83 ident: b6 article-title: On identification in fuzzy systems and its applications in control problems publication-title: Fuzzy Sets and Systems – volume: 151 start-page: 393 year: 2005 end-page: 402 ident: b54 article-title: Some properties of sup–min fuzzy relational equations on infinite domains publication-title: Fuzzy Sets and Systems – year: 1991 ident: b57 article-title: Fuzzy Set Theory and its Applications – reference: W.B. Vasantha Kandasamy, F. Smarandache, Fuzzy relational maps and neutrosophic relational maps, hexis church rock (2004). (see Chapters one and two) at: – volume: 164 start-page: 189 year: 2004 end-page: 195 ident: b11 article-title: Some specific types of fuzzy relation equations publication-title: Information Sciences – volume: 118 start-page: 509 year: 2001 ident: 10.1016/j.cam.2009.09.042_b25 article-title: Optimization of fuzzy relation equations with max-product composition publication-title: Fuzzy Sets and Systems doi: 10.1016/S0165-0114(98)00417-5 – volume: 7 start-page: 169 year: 2008 ident: 10.1016/j.cam.2009.09.042_b23 article-title: On the resolution and optimization of a system of fuzzy relational equations with sup-T composition publication-title: Fuzzy optimization and Decision making doi: 10.1007/s10700-008-9029-y – volume: 50 start-page: 623 year: 2005 ident: 10.1016/j.cam.2009.09.042_b29 article-title: A new kind of fuzzy relation equations based on inner transformation publication-title: Computers and Mathematics with Applications doi: 10.1016/j.camwa.2004.10.049 – ident: 10.1016/j.cam.2009.09.042_b55 – volume: 81 start-page: 355 year: 1996 ident: 10.1016/j.cam.2009.09.042_b20 article-title: Solving fuzzy relational equations through logical filtering publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(95)00221-9 – year: 1983 ident: 10.1016/j.cam.2009.09.042_b48 – year: 1988 ident: 10.1016/j.cam.2009.09.042_b21 – volume: 8 start-page: 179 year: 2009 ident: 10.1016/j.cam.2009.09.042_b24 article-title: A survey on fuzzy relational equations, Part I: Classification and solvability publication-title: Fuzzy Optimization and Decision Making doi: 10.1007/s10700-009-9059-0 – volume: 120 start-page: 395 year: 2001 ident: 10.1016/j.cam.2009.09.042_b30 article-title: Resolution of composite fuzzy relation equations based on Archimedean triangular norms publication-title: Fuzzy Sets and Systems doi: 10.1016/S0165-0114(99)00117-7 – volume: 160 start-page: 2328 year: 2009 ident: 10.1016/j.cam.2009.09.042_b31 article-title: On the relation between fuzzy max-Archimedean t-norm relational equations and the covering problem publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2009.01.012 – volume: 30 start-page: 38 year: 1976 ident: 10.1016/j.cam.2009.09.042_b1 article-title: Resolution of composite fuzzy relation equations publication-title: Information and Control doi: 10.1016/S0019-9958(76)90446-0 – volume: 11 start-page: 100 issue: 1 year: 2003 ident: 10.1016/j.cam.2009.09.042_b35 article-title: Matrix-pattern-based computer algorithm for solving fuzzy relation equations publication-title: IEEE Transactions on Fuzzy Systems doi: 10.1109/TFUZZ.2002.806322 – volume: 164 start-page: 189 year: 2004 ident: 10.1016/j.cam.2009.09.042_b11 article-title: Some specific types of fuzzy relation equations publication-title: Information Sciences doi: 10.1016/j.ins.2003.05.007 – volume: 127 start-page: 141 year: 2002 ident: 10.1016/j.cam.2009.09.042_b26 article-title: Multi-objective optimization problems with fuzzy relation equation constraints publication-title: Fuzzy Sets and Systems doi: 10.1016/S0165-0114(01)00052-5 – volume: 107 start-page: 520 year: 1985 ident: 10.1016/j.cam.2009.09.042_b39 article-title: On generalized fuzzy relational equations and their applications publication-title: Journal of Mathematical Analysis and Applications doi: 10.1016/0022-247X(85)90329-4 – year: 2006 ident: 10.1016/j.cam.2009.09.042_b5 article-title: Fuzzy relation equations (II): The branch-point-solutions and the categorized minimal solutions publication-title: Soft Computing – ident: 10.1016/j.cam.2009.09.042_b16 doi: 10.1016/j.fss.2009.03.007 – volume: 146 start-page: 198 year: 1998 ident: 10.1016/j.cam.2009.09.042_b19 article-title: Generalized variational inequalities with fuzzy relation publication-title: Journal of Computational and Applied Mathematics – volume: 6 start-page: 73 year: 1981 ident: 10.1016/j.cam.2009.09.042_b6 article-title: On identification in fuzzy systems and its applications in control problems publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(81)90081-6 – volume: 7 start-page: 441 issue: 4 year: 1998 ident: 10.1016/j.cam.2009.09.042_b27 article-title: An efficient solution procedure for fuzzy relational equations with max-product composition publication-title: IEEE Transactions on Fuzzy Systems doi: 10.1109/91.784204 – volume: 150 start-page: 147 year: 2005 ident: 10.1016/j.cam.2009.09.042_b52 article-title: Minimizing a linear function under a fuzzy max–min relational equation constraint publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2004.09.010 – volume: 3 start-page: 231 year: 2003 ident: 10.1016/j.cam.2009.09.042_b56 article-title: Programming problem with fuzzy relation inequality constraints publication-title: Journal of Liaoning Normal University – start-page: 271 year: 1989 ident: 10.1016/j.cam.2009.09.042_b34 article-title: Fuzzy relation equalities (Chapter 6) – year: 1991 ident: 10.1016/j.cam.2009.09.042_b57 – volume: 10 start-page: 552 issue: 4 year: 2002 ident: 10.1016/j.cam.2009.09.042_b51 article-title: An accelerated approach for solving fuzzy relation equations with a linear objective function publication-title: IEEE Transactions on Fuzzy Systems doi: 10.1109/TFUZZ.2002.800657 – volume: 8 start-page: 99 year: 1984 ident: 10.1016/j.cam.2009.09.042_b7 article-title: Fuzzy relation equations under a class of triangular norms: A survey and new results publication-title: Stochastica – volume: 103 start-page: 524 year: 1984 ident: 10.1016/j.cam.2009.09.042_b33 article-title: Reachable equation of a fuzzy relation equation publication-title: Journal of Mathematical Analysis and Applications doi: 10.1016/0022-247X(84)90144-6 – volume: 103 start-page: 107 year: 1999 ident: 10.1016/j.cam.2009.09.042_b10 article-title: Solving fuzzy relation equations with a linear objective function publication-title: Fuzzy Sets and Systems doi: 10.1016/S0165-0114(97)00184-X – volume: 2 start-page: 41 issue: 1 year: 2003 ident: 10.1016/j.cam.2009.09.042_b46 article-title: Solution sets of interval-valued fuzzy relational equations publication-title: Fuzzy Optimization and Decision Making doi: 10.1023/A:1022800330844 – ident: 10.1016/j.cam.2009.09.042_b18 doi: 10.1109/FUZZY.1995.409860 – volume: 4 start-page: 67 year: 1984 ident: 10.1016/j.cam.2009.09.042_b44 article-title: How many lower solutions of finite fuzzy relation equations publication-title: Fuzzy Mathematics – volume: 18 start-page: 67 year: 1984 ident: 10.1016/j.cam.2009.09.042_b49 article-title: How many lower solutions does a fuzzy relation equation have? publication-title: BUSEFAL – ident: 10.1016/j.cam.2009.09.042_b53 – year: 1993 ident: 10.1016/j.cam.2009.09.042_b12 – volume: 151 start-page: 393 year: 2005 ident: 10.1016/j.cam.2009.09.042_b54 article-title: Some properties of sup–min fuzzy relational equations on infinite domains publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2004.10.002 – volume: vol. 1 start-page: 291 year: 2000 ident: 10.1016/j.cam.2009.09.042_b3 article-title: Analytical solution methods for fuzzy relational equations – volume: 94 start-page: 61 year: 1998 ident: 10.1016/j.cam.2009.09.042_b2 article-title: Solution algorithms for fuzzy relational equations with max-product composition publication-title: Fuzzy Sets and Systems doi: 10.1016/S0165-0114(96)00246-1 – volume: 119 start-page: 1 year: 2001 ident: 10.1016/j.cam.2009.09.042_b32 article-title: Solving nonlinear optimization problems with fuzzy relation equations constraints publication-title: Fuzzy Sets and Systems doi: 10.1016/S0165-0114(98)00471-0 – start-page: 221 year: 1977 ident: 10.1016/j.cam.2009.09.042_b43 article-title: Solutions in composite fuzzy relation equations – year: 1995 ident: 10.1016/j.cam.2009.09.042_b22 – volume: 159 start-page: 72 year: 1991 ident: 10.1016/j.cam.2009.09.042_b45 article-title: Lattecized linear programming and fuzzy relational inequalities publication-title: Journal of Mathematical Analysis and Applications doi: 10.1016/0022-247X(91)90222-L – volume: 1 start-page: 347 year: 2002 ident: 10.1016/j.cam.2009.09.042_b15 article-title: Minimizing a linear objective function with fuzzy relation equation constraints publication-title: Fuzzy Optimization and Decision Making doi: 10.1023/A:1020955112523 – year: 1989 ident: 10.1016/j.cam.2009.09.042_b41 – year: 2004 ident: 10.1016/j.cam.2009.09.042_b42 – volume: 40 start-page: 77 year: 1991 ident: 10.1016/j.cam.2009.09.042_b40 article-title: Processing in relational structures: Fuzzy relation equations publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(91)90047-T – volume: 28 start-page: 183 year: 1988 ident: 10.1016/j.cam.2009.09.042_b38 article-title: Approximate solutions of fuzzy relational equations publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(88)90199-6 – volume: 19 start-page: 752 year: 2006 ident: 10.1016/j.cam.2009.09.042_b17 article-title: Resolution of finite fuzzy relation equations based on strong pseudo-t-norms publication-title: Applied Mathematics Letters doi: 10.1016/j.aml.2005.11.001 – start-page: 401 year: 2000 ident: 10.1016/j.cam.2009.09.042_b13 article-title: Generalized solvability behaviour for systems of fuzzy equations – volume: 40 start-page: 415 year: 1991 ident: 10.1016/j.cam.2009.09.042_b9 article-title: Fuzzy relation equations theory as a basis of fuzzy modeling: An overview publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(91)90170-U – volume: 153 start-page: 261 year: 2005 ident: 10.1016/j.cam.2009.09.042_b36 article-title: On the relation between equations with max-product composition and the covering problem publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2005.02.010 – ident: 10.1016/j.cam.2009.09.042_b50 – volume: 5 start-page: 33 year: 2006 ident: 10.1016/j.cam.2009.09.042_b14 article-title: An algorithm for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities publication-title: Fuzzy Optimization and Decision Making doi: 10.1007/s10700-005-4914-0 – volume: 15 start-page: 79 year: 1985 ident: 10.1016/j.cam.2009.09.042_b37 article-title: Fuzzy relation equations and the inverse problem publication-title: Fuzzy Sets and Systems doi: 10.1016/0165-0114(85)90036-3 – year: 1989 ident: 10.1016/j.cam.2009.09.042_b8 – volume: 4 start-page: 23 year: 1995 ident: 10.1016/j.cam.2009.09.042_b47 article-title: A multi-objective mathematical programming problem with fuzzy relation constraints publication-title: Journal of Multi-Criteria Decision Analysis doi: 10.1002/mcda.4020040103 – volume: 6 start-page: 428 year: 2002 ident: 10.1016/j.cam.2009.09.042_b4 article-title: Fuzzy relation equations (I): The general and specialized solving algorithms publication-title: Soft Computing doi: 10.1007/s00500-001-0157-3 – volume: 171 start-page: 145 year: 2005 ident: 10.1016/j.cam.2009.09.042_b28 article-title: Fuzzy relation equations for coding/decoding processes of images and videos publication-title: Information Sciences doi: 10.1016/j.ins.2004.04.003 |
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| Title | Two new algorithms for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities |
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