메뉴 건너뛰기




Volumn 20, Issue 1, 2012, Pages 96-108

Zadehs extension principle for continuous functions of non-interactive variables: A parallel optimization approach

Author keywords

Extension principle; interval calculus; nonmonotone function; parallel computing; particle swarm optimization (PSO)

Indexed keywords

BENCHMARK FUNCTIONS; CONTINUOUS FUNCTIONS; ENGINEERING APPLICATIONS; EXTENSION PRINCIPLES; FUZZY INTERVAL; GRADIENT DESCENT; INTERVAL CALCULUS; NON-INTERACTIVE; NON-TRIVIAL; NONMONOTONE; OPTIMIZATION ALGORITHMS; OPTIMIZATION PROBLEMS; PARALLEL IMPLEMENTATIONS; PARALLEL OPTIMIZATION; PARALLEL VERSION; SEQUENTIAL QUADRATIC PROGRAMMING;

EID: 84856812699     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2011.2168406     Document Type: Article
Times cited : (17)

References (41)
  • 1
    • 34247199459 scopus 로고    scopus 로고
    • Joint propagation of probability and possibility in risk analysis: Towards a formal framework
    • DOI 10.1016/j.ijar.2006.07.001, PII S0888613X06000570
    • C. Baudrit, I. Couso, and D. Dubois, "Joint propagation of probability and possibility in risk analysis: Towards a formal framework," Int. J. Approx. Reason., vol. 45, pp. 82-105, 2007. (Pubitemid 46617875)
    • (2007) International Journal of Approximate Reasoning , vol.45 , Issue.1 , pp. 82-105
    • Baudrit, C.1    Couso, I.2    Dubois, D.3
  • 3
    • 33750318839 scopus 로고    scopus 로고
    • A fuzzy-probabilistic earthquake risk assessment system
    • DOI 10.1007/s00500-006-0063-9, Fuzzy-Neural Computation and Robitics
    • I. Karimi, E. Hüllermeier, and K. Meskouris, "A fuzzy-probabilistic earthquake risk assessment system," Soft Comput., vol. 11, pp. 229-238, 2007. (Pubitemid 44613751)
    • (2007) Soft Computing , vol.11 , Issue.3 , pp. 229-238
    • Karimi, I.1    Hullermeier, E.2    Meskouris, K.3
  • 4
    • 34247470855 scopus 로고    scopus 로고
    • A Takagi-Sugeno fuzzy rule-based model for soil moisture retrieval from SAR under soil roughness uncertainty
    • DOI 10.1109/TGRS.2007.894930
    • N. Verhoest, B. De Baets, and H. Vernieuwe, "A Takagi-Sugeno fuzzy rule-based model for soil moisture retrieval from SAR under soil roughness uncertainty," IEEE Trans. Geosci. Remote Sens., vol. 45, no. 5, pp. 1351-1360, May 2007. (Pubitemid 46652336)
    • (2007) IEEE Transactions on Geoscience and Remote Sensing , vol.45 , Issue.5 , pp. 1351-1360
    • Verhoest, N.E.C.1    De Baets, B.2    Vernieuwe, H.3
  • 5
    • 36649025275 scopus 로고    scopus 로고
    • A possibilistic approach to soil moisture retrieval from ERS synthetic aperture radar backscattering under soil roughness uncertainty
    • DOI 10.1029/2006WR005295
    • N. Verhoest, B. De Baets, G. Satalino, C. Lucau, and P. Defourny, "A pos-sibilistic approach to soil moisture retrieval from SAR synthetic aperture radar backscattering under soil roughness uncertainty," Water Resources Res., vol. 43, 2007, W07435, doi: 10.1029/2006WR005295. (Pubitemid 350194487)
    • (2007) Water Resources Research , vol.43 , Issue.7
    • Verhoest, N.E.C.1    De Baets, B.2    Mattia, F.3    Satalino, G.4    Lucau, C.5    Defourny, P.6
  • 6
    • 0016458950 scopus 로고
    • The concept of a linguistic variable and its application to approximate reasoning
    • L. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning," Inf. Sci., vol. 8, pp. 199-249, 1975.
    • (1975) Inf. Sci. , vol.8 , pp. 199-249
    • Zadeh, L.1
  • 7
    • 49349119632 scopus 로고
    • A note on the extension principle for fuzzy sets
    • H. Nguyen, "A note on the extension principle for fuzzy sets," Math. Anal. Appl., vol. 64, pp. 369-380, 1978.
    • (1978) Math. Anal. Appl. , vol.64 , pp. 369-380
    • Nguyen, H.1
  • 10
    • 0001590853 scopus 로고    scopus 로고
    • Analytical expressions for the addition of fuzzy intervals
    • PII S0165011497001413
    • B. De Baets and A. Marková-Stupnanová, "Analytical expressions for the addition of fuzzy intervals," Fuzzy Sets Syst., vol. 91, pp. 203-213, 1997. (Pubitemid 127683714)
    • (1997) Fuzzy Sets and Systems , vol.91 , Issue.2 , pp. 203-213
    • De Baets, B.1    Markova-Stupnanova, A.2
  • 11
    • 0023435695 scopus 로고
    • Vertex method for computing functions of fuzzy variables
    • DOI 10.1016/0165-0114(87)90114-X
    • W. Dong and H. Shah, "Vertex method for computing functions of fuzzy variables," Fuzzy Sets Syst., vol. 24, pp. 65-78, 1987. (Pubitemid 18544508)
    • (1987) Fuzzy Sets and Systems , vol.24 , Issue.1 , pp. 65-78
    • Dong, W.1    Shah, H.2
  • 12
    • 16444375607 scopus 로고
    • Fuzzy weighted averages and implementation of the extension principle
    • W. Dong and F. Wong, "Fuzzy weighted averages and implementation of the extension principle," Fuzzy Sets Syst., vol. 21, pp. 183-199, 1987.
    • (1987) Fuzzy Sets Syst. , vol.21 , pp. 183-199
    • Dong, W.1    Wong, F.2
  • 13
    • 38249003320 scopus 로고
    • Approximating α-cuts with the vertex method
    • K. Otto, A. Lewis, and E. Antonsson, "Approximating α-cuts with the vertex method," Fuzzy Sets Syst., vol. 55, pp. 43-50, 1993.
    • (1993) Fuzzy Sets Syst. , vol.55 , pp. 43-50
    • Otto, K.1    Lewis, A.2    Antonsson, E.3
  • 14
    • 0037119860 scopus 로고    scopus 로고
    • The transformation method for the simulation and analysis of systems with uncertain parameters
    • DOI 10.1016/S0165-0114(02)00045-3, PII S0165011402000453
    • M. Hanss, "The transformation method for the simulation and analysis of systems with uncertain parameters," Fuzzy Sets Syst., vol. 130, pp. 277-289, 2002. (Pubitemid 34862873)
    • (2002) Fuzzy Sets and Systems , vol.130 , Issue.3 , pp. 277-289
    • Hanss, M.1
  • 15
    • 42549099494 scopus 로고    scopus 로고
    • Gradual numbers and their application to fuzzy interval analysis
    • DOI 10.1109/TFUZZ.2006.890680
    • J. Fortin, D. Dubois, and H. Fargier, "Gradual numbers and their application to fuzzy interval analysis," IEEE Trans. Fuzzy Syst., vol. 16, no. 2, pp. 388-402, Apr. 2008. (Pubitemid 351586039)
    • (2008) IEEE Transactions on Fuzzy Systems , vol.16 , Issue.2 , pp. 388-402
    • Fortin, J.1    Dubois, D.2    Fargier, H.3
  • 16
    • 34548683006 scopus 로고    scopus 로고
    • Gradual elements in a fuzzy set
    • DOI 10.1007/s00500-007-0187-6
    • D. Dubois and H. Prade, "Gradual elements in a fuzzy set," Soft Comput., vol. 12, pp. 165-175, 2008. (Pubitemid 47412748)
    • (2008) Soft Computing , vol.12 , Issue.2 , pp. 165-175
    • Dubois, D.1    Prade, H.2
  • 17
    • 7244247371 scopus 로고    scopus 로고
    • Treatment of precipitation uncertainty in rainfall-runoff modelling: A fuzzy set approach
    • DOI 10.1016/j.advwatres.2004.07.001, PII S0309170804001010
    • S. Maskey, V. Guinot, and R. Price, "Treatment of precipitation uncertainty in rainfall-runoff modelling: A fuzzy set approach," Adv. Water Resources., vol. 27, pp. 889-898, 2004. (Pubitemid 39437057)
    • (2004) Advances in Water Resources , vol.27 , Issue.9 , pp. 889-898
    • Maskey, S.1    Guinot, V.2    Price, R.K.3
  • 18
    • 34547803268 scopus 로고    scopus 로고
    • Analysis and propagation of uncertainties due to the stage-discharge relationship: A fuzzy set approach
    • DOI 10.1623/hysj.52.4.595
    • R. Shrestha, A. Bárdossy, and F. Nestmann, "Analysis and propagation of uncertainties due to the stage-discharge relationship: A fuzzy set approach," Hydrol. Sci., vol. 52, pp. 595-610, 2007. (Pubitemid 47241717)
    • (2007) Hydrological Sciences Journal , vol.52 , Issue.4 , pp. 595-610
    • Shrestha, R.R.1    Bardossy, A.2    Nestmann, F.3
  • 19
    • 34548733039 scopus 로고    scopus 로고
    • The extension principle and a decomposition of fuzzy sets
    • DOI 10.1016/j.ins.2007.07.007, PII S0020025507003623, Including: Mathematics of Uncertainty
    • Y. Chalco-Cano, H. Román-Flores, M. Rojas-Medar, O. Saavedra, and M. Jiménez-Gamero, "The extension principle and a decomposition of fuzzy sets," Inf. Sci., vol. 177, pp. 5394-5403, 2007. (Pubitemid 47422256)
    • (2007) Information Sciences , vol.177 , Issue.23 , pp. 5394-5403
    • Chalco-Cano, Y.1    Roman-Flores, H.2    Rojas-Medar, M.3    Saavedra, O.R.4    Jimenez-Gamero, M.D.5
  • 21
    • 17044434288 scopus 로고    scopus 로고
    • Uncertainty modeling using fuzzy arithmetic based on sparse grids: Applications to dynamic systems
    • DOI 10.1142/S0218488504003181, PII S0218488504003181, Reportnr 1206
    • A. Klimke, B. Wohlmuth, and K. Willner, "Uncertainty modeling using fuzzy arithmetics based on sparse grids: Application to dynamic systems," Int. J. Uncertainty, Fuzz. Knowl.-Based Syst., vol. 12, pp. 745-759, 2004. (Pubitemid 40493394)
    • (2004) International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems , vol.12 , Issue.6 , pp. 745-759
    • Klimke, A.1    Willner, K.2    Wohlmuth, B.3
  • 22
    • 21744460436 scopus 로고    scopus 로고
    • Computing expensive multivariate functions of fuzzy numbers using sparse grids
    • DOI 10.1016/j.fss.2005.02.017, PII S0165011405000904
    • A. Klimke and B. Wohlmuth, "Computing expensive multivariate functions of fuzzy numbers using sparse grids," Fuzzy Sets Syst., vol. 153, pp. 432-453, 2005. (Pubitemid 40940832)
    • (2005) Fuzzy Sets and Systems , vol.154 , Issue.3 , pp. 432-453
    • Klimke, A.1    Wohlmuth, B.2
  • 23
    • 0345373438 scopus 로고    scopus 로고
    • Surrey U.K.: Network Threory
    • J. Eaton., GNU Octave Manual. Surrey, U.K.: Network Threory, 2002.
    • (2002) GNU Octave Manual
    • Eaton, J.1
  • 25
    • 0030243170 scopus 로고    scopus 로고
    • The simplex-simulated annealing approach to continuous non-linear optimization
    • M. Cardoso,R.Salcedo, and S. F. deAzevedo, "The simplex-simulated annealing approach to continuous non-linear optimization," Comput. Chem. Eng., vol. 20, pp. 1065-1080, 1996.
    • (1996) Comput. Chem. Eng. , vol.20 , pp. 1065-1080
    • Cardoso, M.1    Salcedo, R.2    Deazevedo, S.F.3
  • 28
    • 0030704933 scopus 로고    scopus 로고
    • Possibility theory III: Possibilistic independence
    • G. De Cooman, "Possibility theory-Part III: Possibilistic independence," Int. J. General Syst., vol. 25, pp. 353-371, 1997. (Pubitemid 127621278)
    • (1997) International Journal of General Systems , vol.25 , Issue.4 , pp. 353-371
    • De Cooman, G.1
  • 29
    • 1842475634 scopus 로고    scopus 로고
    • On interactive fuzzy numbers
    • F. Fullér and P. Majlender, "On interactive fuzzy numbers," Fuzzy Sets Syst., vol. 143, pp. 355-369, 2004.
    • (2004) Fuzzy Sets Syst. , vol.143 , pp. 355-369
    • Fullér, F.1    Majlender, P.2
  • 30
    • 79151482029 scopus 로고    scopus 로고
    • Possibilistic soil roughness identification for uncertainty reduction on SAR-retrieved soil moisture
    • Feb.
    • H. Vernieuwe, N. Verhoest, H. Lievens, and B. De Baets, "Possibilistic soil roughness identification for uncertainty reduction on SAR-retrieved soil moisture," IEEE Trans. Geosci. Remote Sens., vol. 49, no. 2, pp. 628-638, Feb. 2011.
    • (2011) IEEE Trans. Geosci. Remote Sens. , vol.49 , Issue.2 , pp. 628-638
    • Vernieuwe, H.1    Verhoest, N.2    Lievens, H.3    De Baets, B.4
  • 32
    • 0000238336 scopus 로고
    • A simplex method for function minimization
    • J. Nelder and R. Mead, "A simplex method for function minimization," Comput. J., vol. 7, pp. 308-313, 1965.
    • (1965) Comput. J. , vol.7 , pp. 308-313
    • Nelder, J.1    Mead, R.2
  • 33
    • 26444479778 scopus 로고
    • Optimization by simulated annealing
    • S. Kirkpatrick, C. Gelatt, and M. Vecchi, "Optimization by Simulated Annealing," Science, vol. 220, pp. 671-680, 1983.
    • (1983) Science , vol.220 , pp. 671-680
    • Kirkpatrick, S.1    Gelatt, C.2    Vecchi, M.3
  • 38
    • 69949173291 scopus 로고    scopus 로고
    • A kernel-based method to determine optimal sampling times for the simultaneous estimation of the parameters of rival mathematical models
    • B. Donckels, D. De Pauw, P. Vanrolleghem, and B. De Baets, "A kernel-based method to determine optimal sampling times for the simultaneous estimation of the parameters of rival mathematical models," J. Comput. Chem., vol. 30, pp. 2064-2077, 2009.
    • (2009) J. Comput. Chem. , vol.30 , pp. 2064-2077
    • Donckels, B.1    De Pauw, D.2    Vanrolleghem, P.3    De Baets, B.4
  • 39
    • 75849135622 scopus 로고    scopus 로고
    • An ideal point method for the design of compromise experiments to simultaneously estimate the parameters of several rival models
    • B. Donckels, D. De Pauw, P. Vanrolleghem, and B. De Baets, "An ideal point method for the design of compromise experiments to simultaneously estimate the parameters of several rival models," Chem. Eng. Sci., vol. 65, pp. 1705-1719, 2010.
    • (2010) Chem. Eng. Sci. , vol.65 , pp. 1705-1719
    • Donckels, B.1    De Pauw, D.2    Vanrolleghem, P.3    De Baets, B.4
  • 40
    • 72149092658 scopus 로고    scopus 로고
    • Calibration of a water and energy balance model: Recursive parameter estimation versus particle swarm optimization
    • doi: 10.1029/2009WR008051
    • K. Scheerlinck, V. Pauwels, H. Vernieuwe, and B. De Baets, "Calibration of a water and energy balance model: Recursive parameter estimation versus particle swarm optimization," Water Resources Res., vol. 45, p. W10422, 2009, doi: 10.1029/2009WR008051.
    • (2009) Water Resources Res. , vol.45
    • Scheerlinck, K.1    Pauwels, V.2    Vernieuwe, H.3    De Baets, B.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.