Interval equations

My papers about interval equations can be found on the following web page:
Interval FEM on Wikipedia [link]

Intervals and Probability Distributions by Daniel Berleant (Ames, Iowa, USA)
Interesting web-pages which are related to the interval equations and imprecise probability

List of papers which are related to the interval equations

  1. M.V.Rama Rao, Andrzej Pownuk, Maarten DeMunck, David Moens,
    Fuzzy analysis of the moment of resistance of a doubly reinforced concrete beam with uncertain structural parameters.
    Life Cycle Reliability and Safety Engineering, Vol.2 Issue 1 (2013) 09-20

  2. Bernardini, Alberto, Tonon, Fulvio, Bounding Uncertainty in Civil Engineering, Springer 2010 [ Link ]

  3. M. V. Rama Rao, R. L. Mullen, and R. L. Muhanna, Primary and Derived Variables with the Same Accuracy in Interval Finite Elements.
    4th International Workshop on Reliable Engineering Computing (REC2010)
    March 3-5, 2010 | Singapore [
    Download ]

  4. Zhiping Qiu, · Xiaojun Wang, Structural anti-optimization with interval design parameters
    Structural and Multidisciplinary Optimization, Vol. 41, Issue 3 [ Download ]

  5. REC 2010 Abstracts [ Download ]

  6. Juan Ma, Wei Gao, Peter Wriggers, Tao Wu and Shahab Sahraee, The analyses of dynamic response and reliability of fuzzy-random truss under stationary stochastic excitation,
    Computational Mechanics, Volume 45, Number 5, 2010 [ Download ]

  7. D. Degrauwe, G. Lombaerta and G. De Roecka, Improving interval analysis in finite element calculations by means of affine arithmetic
    Computers & Structures, Volume 88, Issues 3-4, February 2010, Pages 247-254 [ Download ]

  8. A. Stenti, D. Moens, P. Sas, and W. Desmet, A three-level non-deterministic modeling methodology for the NVH behavior of rubber connections
    Journal of Sound and Vibration, Volume 329, Issue 7, 29 March 2010, Pages 912-930 [ Download ]

  9. Optimization with PDE Constraints Series: Mathematical Modelling: Theory and Applications , Vol. 23 Hinze, M., Pinnau, R., Ulbrich, M., Ulbrich, S. 2009, XI, 270 p. 26 illus., 19 in color., Hardcover ISBN: 978-1-4020-8838-4 Online version available [ Download ]

  10. I.A. Nikas , T.N. Grapsa, Bounding the zeros of an interval equation, Applied Mathematics and Computation Volume 213, Issue 2, 15 July 2009, Pages 466-478 [ Download ]

  11. N.F. Wang, Y.W. Yang, Structural design optimization subjected to uncertainty using fat Bezier curve Pages 210-219 Computer Methods in Applied Mechanics and Engineering Volume 199, Issues 1-4, Pages 1-222 (1 December 2009) [ Download ]

  12. M.V. Rama Rao, S. Vandewalle, M. de Munk, D. Moens, "Dynamic analysis of a cable-stayed bridge with uncertain structural parameters", Safety, Reliability and Risk of Structures, Infrastructures and Engineering Systems – Furuta, Frangopol & Shinozuka (eds), Taylor & Francis Group, London, ISBN 978-0-415-47557-0 , Proceedings of Tenth International Conference for Structural Reliability and Safety (ICOSSAR-2009), Kansai University, Osaka, Japan,12-17 September,2009 [ Download ]

  13. Yoshihiro Kanno, Izuru Takewaki, Semidefinite programming for dynamic steady-state analysis of structures under uncertain harmonic loads
    Computer Methods in Applied Mechanics and Engineering, Volume 198, Issues 41-44, 1 September 2009, Pages 3239-3261 [ Download ]

  14. Zhan Kang, Yangjun Luo, Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models
    Computer Methods in Applied Mechanics and Engineering, Volume 198, Issues 41-44, 1 September 2009, Pages 3228-3238 [ Download ]

    IMPERIAL COLLEGE PRESS; 2009, ISBN: 978-1-84816-477-2 [ Abstract ]

  16. D. Degrauwe, G. De Roeck, G. Lombaert, Uncertainty quantification in the damage assessment of a cable-stayed bridge by means of fuzzy numbers Computers & Structures, Vol. 87, Iss. 17-18, 2009, Pages 1077-1084 [ Download ]

  17. Small Workshop on Interval Methods, Ecole Polytechnique Fédérale de Lausanne, June 10-11, 2009 [ Download ]

  18. T. Allahviranloo, N. Mikaeilvand and M. Barkhordary, Fuzzy linear matrix equation, Fuzzy Optimization and Decision Making, Volume 8, Number 2 / June, 2009 [ Download ]

  19. Vasile Lupulescu, On a class of fuzzy functional differential equations, Fuzzy Sets and Systems, Volume 160, Issue 11, 1 June 2009, Pages 1547-1562 [ Download ]

  20. Y.Chalco-Canoa, H.Román-Floresb, Comparation between some approaches to solve fuzzy differential equations. Fuzzy Sets and Systems, 160(2009), 1517-1527 [ Download ]

  21. Su Huan Chen, Liang Ma, Guang Wei Meng, Rui Guo, An efficient method for evaluating the natural frequencies of structures with uncertain-but-bounded parameters, Computers and Structures 87 (2009) 582–590 [ Download ]

  22. M.V.Rama Rao and Stefan Vandewalle, Proceedings of the Sixth Structural Engineering Convention, SEC- 2008, Structural Engineering Research Centre, December 18 – 20, 2008, Chennai, India. pp.257-267 [ Download ]

  23. Shao-Qing Xua, Qiang-Yi Luob, Guang-Hui Xua and Lei Zhanga, Asymmetrical interval regression using extended ε-SVM with robust algorithm
    Fuzzy Sets and SystemsVolume 160, Issue 7, 1 April 2009, Pages 988-1002 [ Download ]

  24. I. Hlaváček , A. A. Novotny , J. Sokołowski and A. Żochowski, On Topological Derivatives for Elastic Solids with Uncertain Input Data
    Journal of Optimization Theory and Applications, DOI 10.1007/s10957-008-9490-3 [ Download ]

  25. Bart F. Zalewski, Robert L. Mullen and Rafi L. Muhanna, Interval boundary element method in the presence of uncertain boundary conditions, integration errors, and truncation errors,
    Engineering Analysis with Boundary Elements, Volume 33, Issue 4, April 2009, Pages 508-513 [ Download ]

  26. Xu Guo, Wei Bai, Weisheng Zhang, Confidence extremal structural response analysis
    of truss structures under static load uncertainty via SDP relaxation
    Computers & Structures, Volume 87, Issues 3-4, February 2009, Pages 246-253 [ Download ]

  27. Luna Majumder, S.S. Rao, Interval-based optimization of aircraft wings under landing loads,
    Computers & Structures, Volume 87, Issues 3-4, February 2009, Pages 225-235 [ Download ]


  29. A. Neumaier, Certified error bounds for uncertain elliptic equations, J. Comput. Appl. Math. 218 (2008), 125-136. [ Download ]

  30. Luciano Stefanini, Barnabas Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis: Theory, Methods & Applications [ Download ]

  31. Alicja Piasecka Belkhayat, Interval boundary element method for 2D transient diffusion problem,
    Engineering Analysis with Boundary Elements, Volume 32, Issue 5, May 2008, Pages 424-430 [ Download ]

  32. Rosana Rodríguez-López, Monotone method for fuzzy differential equations
    Fuzzy Sets and Systems, Volume 159, Issue 16, 16 August 2008, Pages 2047-2076 [ Download ]

  33. Rostislav Horèík, Solution of a system of linear equations with fuzzy numbers
    Fuzzy Sets and Systems, Volume 159, Issue 14, 16 July 2008, Pages 1788-1810 [ Download ]

  34. Zhiping Qiua, Di Yanga and Isaac Elishakoff, Probabilistic interval reliability of structural systems
    International Journal of Solids and Structures Volume 45, Issue 10, 15 May 2008, Pages 2850-2860 [ Download ]

  35. Mehdi Modares and Robert L. Mullen, Static Analysis of Uncertain Structures Using Interval Eigenvalue Decomposition,
    NSF workshop on Reliable Engineering Computing, February 20-22, 2008, Savannah, Georgia, USA. [ Download ]

  36. F. Massa, K. Ruffin, T. Tison and B. Lallemand, A complete method for efficient fuzzy modal analysis,
    Journal of Sound and Vibration, Volume 309, Issues 1-2, , 8 January 2008, Pages 63-85. [ Download ]

  37. Youdong Lin and Mark A. Stadtherr, Validated solutions of initial value problems for parametric ODEs, Applied Numerical Mathematics archive, Volume 57 , Issue 10 (October 2007) Pages 1145-1162,2007 [ Download ]

  38. M. V. Rama Rao, R. Ramesh Reddy, Analysis of a cable-stayed bridge with uncertainties
    in Young’s modulus and load - A fuzzy finite element approach
    Structural Engineering and Mechanics, Vol. 27, No. 3 (2007) 263-276
    [ Download ]

  39. M. V. Rama Rao, R. Ramesh Reddy, Analysis of a cable-stayed bridge with uncertainties
    in Young’s modulus and load - A fuzzy finite element approach
    Structural Engineering and Mechanics, Vol. 27, No. 3 (2007) 263-276
    [ Download ]

  40. C. Jianga, X. Hana, , and G.R. Liub, Optimization of structures with uncertain constraints
    based on convex model and satisfaction degree of interval
    Computer Methods in Applied Mechanics and Engineering
    Volume 196, Issues 49-52, 1 November 2007, Pages 4791-4800
    [ Download ]

  41. David Moens and Dirk Vandepittea, Interval sensitivity theory and its application
    to frequency response envelope analysis of uncertain structures.
    Computer Methods in Applied Mechanics and Engineering
    Volume 196, Issues 21-24 , 1 April 2007, Pages 2486-2496
    [ Download ]

  42. Popova, E.: Solving Linear Systems whose Input Data are Rational Functions of Interval Parameters.
    In: T. Boyanov et al. (Eds.) Numerical Methods and Applications, LNCS 4310, 2007, Springer Berlin/Heidelberg, 345-352. Expanded version in: Preprint No. 3/2005, Institute of Mathematics and Informatics, BAS, Sofia, December 2005. (Full Text - PDF 550K)
    [ Download ]

  43. Popova, E. and W. Kraemer: Inner and Outer Bounds for Parametric Linear Systems.
    J. Computational and Applied Mathematics 199(2), 2007, 310-316.
    [ Download ]

  44. M.V. Rama Rao and R. Ramesh Reddy
    "Analysis of a cable-stayed bridge with multiple uncertainties - A fuzzy finite element approach",
    Journal of Structural Engineering,
    Vol. 33, No.6, February – March 2007 pp. 523–525
    [ Download ]

  45. Bulent Tutmeza, Erhan Tercan, Spatial estimation of some mechanical properties of rocks by fuzzy modelling.
    Computers and Geotechnics, Volume 34, Issue 1 , January 2007, Pages 10-18
    [ Download ]

  46. Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: The Single Step
    K. Makino, M. Berz, International Journal of Pure and Applied Mathematics, 36(2) (2006) 175-197

  47. Eldon R. Hansen: Sharpening Interval Computations. Reliable Computing 12(1): 21-34 (2006)

  48. Eldon R. Hansen: A Multidimensional Interval Newton Method. Reliable Computing 12(4): 253-272 (2006)

  49. Eldon R. Hansen, G. William Walster: Solving Overdetermined Systems of Interval Linear Equations. Reliable Computing 12(3): 239-243 (2006)

  50. Rafi L. Muhanna, Ayše Erdolen, and Robert Mullen, Geometric Uncertainty in Truss Systems: An Interval Approach, NSF Workshop on Modeling Errors and Uncertainty in Engineering Computations, February 22-24, 2006, Savanah Georgia, USA [ download ]

  51. Jiri Rohn, "A Handbook of Results on Interval Linear Problems", 2006
    [ Download ] [ Local copy ]

  52. Jiri Rohn: Regularity of Interval Matrices and Theorems of the Alternatives. Reliable Computing 12(2): 99-105 (2006)

  53. D. Moens and D. Vandepitte. Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis.
    Archives of Computational Methods in Engineering, 13(3):389-464, 2006.

    Rafi Muhanna, Vladik Kreinovich, Pavel Solin, Jack Chessa, Roberto Araiza, and Gang Xiang
    UTEP-CS-06-03 in pdf and in Compressed Postscript,2006 [ Download ] [ Local copy ]

  55. Popova, E., R. Iankov, Z. Bonev:
    Bounding the Response of Mechanical Structures with Uncertainties in all the Parameters.
    In R.L.Muhannah, R.L.Mullen (Eds): Proceedings of the NSF Workshop on Reliable Engineering Computing (REC),
    Svannah, Georgia USA, Feb. 22-24, 2006, 245-265. [ Download ]

  56. Youdong Lin and Mark A. Stadtherr, 2006, Validated Solution of Initial Value Problems for ODEs with Interval Parameters, [ Download ]

  57. I. Skalna, A Method for Outer Interval Solution of Systems of Linear Equations Depending Linearly on Interval Parameters,
    Reliable Computing, Volume 12, Number 2, April, 2006, Pages 107-120 [ Download ]

  58. Rama Rao,M.V.,Ramesh Reddy R.
    "Fuzzy finite element analysis of structures with uncertainty in load and material properties",
    Journal of Structural Engineering,
    Vol. 33, No.2, June–July 2006 pp. 129–137
    [ Download ]

  59. Götz Alefeld, Günter Mayer: Enclosing Solutions of Singular Interval Systems Iteratively. Reliable Computing 11(3): 165-190 (2005)

  60. I. Babuska, F. Nobile, and R. Tempone. Worst case scenario analysis for elliptic problems with uncertainty. Numer. Math., 101:185–219, 2005
    [ Download ]

  61. High-Order Verified Solutions of the 3D Laplace Equation
    S. Manikonda, M. Berz, K. Makino, Transactions on Computers 11,4 (2005) 1604-1610

  62. Suppression of the Wrapping Effect by Taylor Model-based Verified
    Integrators: Long-term Stabilization by Preconditioning K. Makino, M. Berz,
    International Journal of Differential Equations and Applications 10(4) (2005) 353-384

  63. Suppression of the Wrapping Effect by Taylor Model-based Verified
    Integrators: Long-term Stabilization by Shrink Wrapping M. Berz, K. Makino,
    International Journal of Differential Equations and Applications 10(4) (2005) 385-403

  64. An Accurate High-Order Method to Solve the Helmholtz Boundary Value Problem for the 3D Laplace Equation
    S. Manikonda, M. Berz, International Journal of Pure and Applied Mathematics, 23,3 (2005) 365-378

  65. D. Moens and D. Vandepitte. A survey of non-probabilistic uncertainty treatment in finite element analysis.
    Computer Methods in Applied Mechanics and Engineering, 194(14-16):1527-1555, 2005.

  66. D. Moens and D. Vandepitte. A fuzzy finite element procedure for the calculation of uncertain frequency response functions of damped structures: Part 1 - procedure.
    Journal of Sound and Vibration, 288(3):431-462, 2005.

  67. H. De Gersem, D. Moens, and D. Vandepitte. A fuzzy finite element procedure for the calculation of uncertain frequency response functions of damped structures: Part 2 - numerical case studies.
    Journal of Sound and Vibration, 288(3):463-486, 2005.

  68. Eldon R. Hansen: A Theorem on Regularity of Interval Matrices. Reliable Computing 11(6): 495-497 (2005)

  69. Analyzing Uncertainty in Civil Engineering, by W. Fellin, H. Lessmann, M. Oberguggenberger, and R. Vieider (eds.), Springer-Verlag, Berlin, 2005 [ Table of contents ]

  70. Jiri Rohn: How Strong Is Strong Regularity? Reliable Computing 11(6): 491-493 (2005)

  71. Jiri Rohn: Linear Interval Equations: Midpoint Preconditioning May Produce a 100% Overestimation for Arbitrarily Narrow Data Even in Case n = 4. Reliable Computing 11(2): 129-135 (2005)

  72. Jiri Rohn: A Normal Form Supplement to the Oettli-Prager Theorem. Reliable Computing 11(1): 35-39 (2005)

  73. Dynamic Analysis of Structures with Interval Uncertainty , Ph. D. thesis, Mehdi Modares Zadeh, 2005. [ Download ]

  74. Hao Zhang, Nondeterministic Linear Static Finite Element Analysis: An Interval Approach, Ph.D. Dissertation, School of Civil and Environmental Engineering Georgia Institute of Technology, December 2005 [ Download ]

  75. Götz Alefeld, Zhengyu Wang, Shen Zuhe: Enclosing Solutions of Linear Complementarity Problems for H-Matrices. Reliable Computing 10(6): 423-435 (2004)

  76. Hlavácek, I., Chleboun, J., Babuška, I.: Uncertain Input Data Problems and the Worst Scenario Method. Elsevier, Amsterdam (2004) [ info ]

  77. Hong-Zhong Huanga, Hai-Bin Li, Perturbation finite element method of structural analysis under fuzzy environments, Engineering Applications of Artificial Intelligence Volume 18, Issue 1, February 2005, Pages 83-91 [ Download ]

  78. D. Moens and D. Vandepitte. An interval finite element approach for the calculation of envelope frequency response functions.
    International Journal for Numerical Methods in Engineering, 61(14):2480-2507, 2004.

  79. Popova, E.: Generalizing the Parametric Fixed-Point Iteration. Proceedings in Applied Mathematics & Mechanics (PAMM) 4, issue 1, 2004, pp. 680-681. [Download]

  80. Popova, E.: Strong Regularity of Parametric Interval Matrices. Mathematics & Education in Mathematics, 2004, (Eds. I. Dimovski et al.), BAS, pp. 446-451. [Download]

  81. J. Rohn, A Method for Handling Dependent Data. in Interval Linear Systems. Jir Rohn. Technical report No. 911. July 7, 2004 [Download]

  82. Rama Rao,M.V. (2004),
    "Analysis of Cable-stayed bridges by fuzzy finite element modelling",
    Unpublished Ph.D. thesis, Osmania University, India
    [ Download ]

  83. A. AYDEMIR, D. GUNAY, The Fuzzy Finite Element Stress Analysis of Adhesive-Bonded Single Lap Joints.
    Turkish J. Eng. Env. Sci. 28 (2004) , 121-127.
    [ Download ]

  84. AMAS Workshop on Smart Materials and Structures SMART’03 – (pp.15–23) – Jadwisin, September 2-5, 2003 Interval Finite Element Method applied to modelling of structures O. GARCÍA, J. VEHÍ, and J. RODELLAR
    [ Download ]

  85. Götz Alefeld, Uwe Schäfer: Iterative Methods for Linear Complementarity Problems with Interval Data. Computing 70(3): 235-259 (2003)

  86. Sensitivity and Uncertainty Analysis: Theory By D. G. Cacuci, Mihaela Ionescu-Bujor, Ionel Michael Navon, Published by CRC Press, 2003 [ Preview ]

  87. Götz Alefeld, Günter Mayer: On Singular Interval Systems. Numerical Software with Result Verification 2003: 191-197

  88. Makino, K. and M. Berz: 2003, `Taylor Models and Other Validated Functional Inclusion Methods'. Int. J. Pure Appl. Math. 4, 379-456.

  89. M. Janssen, P. Van Hentenryck, and Y. Deville.
    A Constraint Satisfaction Approach for Enclosing Solutions
    to Parametric Ordinary Differential Equations.
    SIAM Journal on Numerical Analysis, 40(5): 1896-1939, 2002.
    [ Download ]

  90. Popova, E.; Datcheva, M.; Iankov, R.; Schanz, T.: Mechanical Models with Interval Parameters. In: K. Guerlebeck, L. Hempel, C. Koenke (Eds.) IKM2003: Digital Proceedings of 16th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering, ISSN 1611-4086, Bauhaus University Weimar, 2003. [ Download ]

  91. Popova, E.; Datcheva, M.; Iankov, R.; Schanz, T.: Sharp Bounds for Strains and Stresses in Uncertain Mechanical Models. I. Lirkov et al. (Eds): LSSC 2003, Lecture Notes in Computer Science 2907, pp. 262-269, 2004. [ Download ]

  92. Interval Finite Element Analysis for Load Pattern and Load Combination , MS thesis, Veshal Saxena, 2003 [ Download ]

  93. Eldon R. Hansen, G. William Walster: Sharp Bounds on Interval Polynomial Roots. Reliable Computing 8(2): 115-122 (2002)

  94. M. Kleiber, J. Rojek, R. Stocki
    Reliability assessment for sheet metal forming operations
    Computer Methods in Applied Mechanics and Engineering, Volume 191, Issues 39-40, 30 August 2002, Pages 4511-4532
    [ Download ]

  95. D. Moens and D. Vandepitte. Fuzzy finite element method for frequency response function analysis of uncertain structures.
    AIAA Journal, 40(1):126-136, 2002.

  96. D. Moens. A Non-Probabilistic Finite Element Approach for Structural Dynamic Analysis with Uncertain Parameters, PhD thesis. K.U.Leuven, Leuven, 2002.
    [ Download ]

  97. E. Popova, Quality of the solution sets of parameter-dependeent interval linear systems. ZAMM, 82, 2002, pp.723-727

  98. G. William Walster, Eldon R. Hansen: Computing Interval Parameter Bounds from Fallible Measurements Using Overdetermined (Tall) Systems of Nonlinear Equations. COCOS 2002: 171-177

  99. Götz Alefeld, Vladik Kreinovich, Günter Mayer, Michael Huth: A Comment on the Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients. Reliable Computing 7(3): 275-277 (2001)

  100. Götz Alefeld, Vladik Kreinovich, Günter Mayer: Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem. Symbolic Algebraic Methods and Verification Methods 2001: 11-20

  101. McWilliam, Stewart, 2001
    Anti-optimisation of uncertain structures using interval analysis
    Computers and Structures Volume: 79, Issue: 4, February, 2001, pp. 421-430
    [ Download(ICM) ] [ Download(Science Direct) ]

  102. Muhanna in the paper Muhanna R.L., Mullen R.L., Uncertainty in Mechanics Problems - Interval - Based Approach. Journal of Engineering Mechanics, Vol.127, No.6, 2001, 557-556 [ Download ]

  103. E.Popova, On the Solution of Parametrised Linear Systems. W. Kraemer, J. Wolff von Gudenberg (Eds.): Scientific Computing,Validated Numerics, Interval Methods. Kluwer Acad. Publishers, 2001, pp. 127-138.

  104. Qiu, Zhiping; Müller, Peter C.; Frommer, Andreas, 2001
    Ellipsoidal set-theoretic approach for stability of linear state-space models with interval uncertainty
    Mathematics and Computers in Simulation Volume: 57, Issue: 1-2, August 15, 2001, pp. 45-59
    [ Download(ICM) ] [ Download ]

  105. I. Hlavá£ek: Reliable solution of problems in the deformation theory of plasticity with respect to uncertain material function. Appl. Math. 41 (1996), 447-466.

  106. I. Hlavacek: Reliable solutions of elliptic boundary value problems with respect to uncertain data. Proceedings of the WCNA-96. Nonlin. Anal., Theory Methods Appl. 30 (1997), 3879-3890.

  107. I. Hlavacek: Reliable solution of a quasilinear nonponential elliptic problem of a nonmonotone type with respect to the uncertainty in coeffcients. J. Math. Anal. Appl. 212 (1997), 452-466.

  108. I. Hlavacek: Reliable solution of linear parabolic problems with respect to uncertain coeffients. ZAMM, Z. Angew. Math. Mech. 79 (1999), 291-301.

  109. I. Hlavacek: Reliable solution of an elasto-plastic Reissner-Mindlin beam for the Hencky's model with uncertain yield function. Appl. Math. 43 (1998), 223-237.

  110. I. Hlavacek: Reliable solution of a Signorini contact problem with friction, considering uncertain data. Numer. Linear Algebra Appl. 6 (1999), 411-434.

  111. I. Hlavacek: Reliable solution of a torsion problem in Hencky plasticity with uncertain yield function. Math. Models Methods Appl. Sci. 11 (2001), 855-865.

  112. I. Hlavacek: Reliable solution of a perfect plastic problem with uncertain stress-strain law and yield function. SIAM J. Numer. Anal. 39 (2001), 1539-1555.

  113. I. Hlavacek: Worst scenario approach for elastoplasticity with hardening and uncertain input data. ZAMM, Z. Angew. Math. Mech. 82 (2002), 671-684.

  114. I. Hlavacek: Reliable solution in strain space of elastoplastic problems with isotropic hardening and uncertain input data. Math. Models Methods Appl. Sci. 12 (2002), 1337-1357.

  115. I. Hlavacek: Post-buckling range of plates in axial compression with uncertain initial imperfections. Appl. Math. 47 (2002), 25-44.

  116. I. Hlavacek: Buckling of a Timoshenko beam on elastic foundation with uncertain input data. IMA J. Appl. Math. 68 (2003), 185-204.

  117. I. Hlavacek: Plate bending problems with uncertain input data. I. Classical problems.

  118. I. Hlavacek, J. Chleboun: Reliable analysis of transverse vibrations of Timoshenko-Mindlin beams with respect to uncertain shear correction factor. Comput. Methods Appl. Mech. Eng. 190 (2000), 903-918.

  119. I. Hlavacek, J. Chleboun, and I. Babu²ka: Uncertain Input Data Problems and the Worst Scenario Method. Elsevier, Amsterdam, 2004.

  120. I. Hlavacek, J. Lovíek: Control in obstacle-pseudoplate problems with friction on the boundary. Optimal design and problems with uncertain data. Appl. Math. (Warsaw) 28 (2001), 407{426 ; zbAlpproximate optimal design and worst scenario problems. Appl. Math. (Warsaw) 29 (2002), 75-95.

  121. I. Hlavacek, M. Kiek, and J. Maly: On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type. J. Math. Anal. Appl. 184 (1994), 168-189.

  122. I. Hlavacek, J. Loví²ek: Semi-coercive variational inequalities with uncertain input data. Applications to shallow shells. Math. Models Methods Appl. Sci. 15 (2005), 273-299. zbl

  123. I. Hlavacek, J. Nedoma: Reliable solution of a unilateral contact problem with friction and uncertain input data in thermoelasticity. Math. Comput. Simul. 67 (2005), 559-580.

  124. I. Hlavacek: Unilateral contact with Coulomb friction and uncertain input data. Numer. Funct. Anal. Optimization 24 (2003), 509-530.

  125. I. Hlavacek, J. Ple²ek, and D. Gabriel: Validation and sensitivity study of an elastoplastic problem using the worst scenario method. Comput. Methods Appl. Mech. Eng. 195 (2006), 763-774.

  126. G. Alefeld, V. Kreinovich, G. Mayer, Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem, 2000. [ Download ]

  127. Akpan U.O., Koko T.S., Orisamolu I.R., Gallant B.K., Practical fuzzy finite element analysis of structures,
    Finite Elements in Analysis and Design, 38 (2000) 93-111 [ Download ]

  128. Elishakoff I., 2000, Possible limitations of probabilistic methods in engineering. Applied Mechanics Reviews, Vol.53, No.2,pp.19-25

  129. Floudas Ch.A., 2000, Deterministic Global Optimization. Theory, Methods and Applications. Kluwer Academic Publisher, London

  130. Ganzerli S., Pantelides Ch.P., 2000, Optimum structural design via convex model superposition. Computers and Structures, Vol. 74,pp.639-647

  131. Eldon R. Hansen: The Hull of Preconditioned Interval Linear Equations. Reliable Computing 6(2): 95-103 (2000)

  132. Jaulin L., 2000, Interval constraint propagation with application to bounded-error estimation. Automatica, Vol.36, No.10,pp.1547-1552

  133. McWilliam S., Anti-optimization of uncertain structures using interval analysis, Computers and Structures, 79 (2000) 421-430

  134. Möller B., Graf W., Beer M., 2000, Fuzzy structural analysis using a-level optimization. Computational Mechanics, Vol.26,pp.547-565

  135. Pownuk A., 2000, Applications of sensitivity analysis for modelling of structures with uncertain parameters. International Conference on Interval Methods in Science and Engineering Interval'2000, Karlsruhe, Germany,pp.116

  136. Pownuk A., 2000, Calculation of reliability of structures by using interval probability. Proc. AI-MECH 2000. Symposium on Methods of Artificial Intelligence in Mechanics and Mechanical Engineering, Gliwice,pp.273-276

  137. Pownuk A., 2000, Calculation of reliability of structures using fuzzy sets theory. The 32nd Symposium on Mathematical Physics with special session "Symmetries in Nonlinear Systems", June 6-10, 2000, Toruñ (referat wyg³oszony na konferencji)

  138. Pownuk A., 2000, Calculation of displacement in elastic and elastic-plastic structures with interval parameters. 33 rd SOLID MECHANICS CONFERENCE (SolMech2000), Zakopane,pp.135

  139. Noor, Ahmed K.; Starnes Jr, James H.; Peters, Jeanne M., Uncertainty analysis of composite structures Computer Methods in Applied Mechanics and Engineering Volume: 185, Issue: 2-4, May 12, 2000, pp. 413-432

  140. Pantelides C.P., Booth B.C., 2000, Computer-aided design of optimal structures with uncertainty. Computers and Structures, Vol. 74,pp.293-307

  141. Abdel-Tawab K., Noor A.K., 1999, Uncertainty analysis of welding residual stress fields.
    Computer methods in applied mechanics and engineering, Vol.179,pp.327-344 [ Download ]

  142. Ben-Haim Y., 1999, Design certification with information-gap uncertainty. Structural Safety, Vol.21,pp.269-289 [ Download ]

  143. Fritz F.M., 1999, Development of a finite element analysis program based on interval arithmetic. Praca dyplomowa, Markuette University, USA

  144. Ganzerli S., Pantelides C.P., 1999, Load and resistance convex models for optimum design. Structural Optimization, Vol.17,pp.259-268

  145. Makino, K. and M. Berz: 1999, `Ecient Control of the Dependency Problem Based on Taylor Model Methods'. Reliable Computing 5, 3-12.

  146. David Ira Schwartz , Deterministic Interval Uncertainty Methods for Structural Analysis, A dissertation submitted to the Faculty of the Graduate School of State University of New York at Buffalo, New York, 1999

  147. Ma M., Friedman M., Kandel A., 1999, Numerical solution of fuzzy differential equations. Fuzzy Sets and Systems, Vol.105,pp.133-138

  148. Mullen R.L., Muhanna L., 1999, Bounds of Structural Response for all Possible Loading Combinations. Journal of Structural Engineering, Vol.125, No.1,pp.98-106 [ Download ]

  149. Nakagiri S., Suzuki K., 1999, Finite element interval analysis of external loads identified by displacement input with uncertainty. Computer methods in applied mechanics and engineering, Vol.168,pp.63-72

  150. Nedialkov, N. S., K. R. Jackson, and G. F. Corliss: 1999, `Validated Solutions of Initial Value Problems for Ordinary Di erential Equations'. Appl. Math. Comput. 105, 21-68. [ Download ]

  151. Nedialkov, N. S., K. R. Jackson, and J. D. Pryce: 2001, `An Effective High-Order Interval Method for Validating Existence and Uniqueness of The Solution of an IVP for an ODE'. Reliable Computing 7, 449-465.

  152. Pownuk A., 1999, Applications of Regular Interval Jacobian Matrices to Calculation Extreme Values of Mechanical Quantities. Reliable Computations and Interval Algebra, Bulgaria, Sozopol,pp.18

  153. Shieh Ch.S., Tsai J.S.H., Sun Y.Y., 1999, Digital modelling and hybrid control of sampled-data uncertain system with input time delay using the low of mean. Applied Mathematical Modelling, Vol.23, No.1 ,pp.131-152

  154. Ayyub B.M., 1998, Uncertainty Modelling and Analysis in Civil Engineering. CRC Press, New York

  155. Barberi E., Lombardi M., 1998, Minimum weight shape and size optimization of truss structures made of uncertain materials. Structural Optimization, Vol.16,pp.147-154 [ Download ]

  156. Ben-Haim Y., Laufer A., 1998, Robust Reliability of Projects with Activity-Duration Uncertainty. Journal on Construction Engineering and Management, Vol.124, No.2,pp.125-132 [ Download ]

  157. Title: Generalized convexity, generalized monotonicity: recent results Volume 27 of Nonconvex optimization and its applications Authors: Jean-Pierre Crouzeix, Juan-Enrique Martínez-Legaz, Michel Volle Editors: Jean-Pierre Crouzeix, Juan-Enrique Martínez-Legaz, Michel Volle Publisher Springer, 1998 [ Preview ]

  158. Zhiping Qiu and Isaac Elishakoff, Antioptimization of structures with large uncertain-but-non-random parameters
    via interval analysis Computer Methods in Applied Mechanics and Engineering,
    Volume 152, Issues 3-4, 24 January 1998, Pages 361-372 [ Download ]

  159. Elishakoff, I (1998). “Editorial: Three Facets of Uncertainty,” Computers & Structures, 67, 1–2.

  160. Elishakoff I., 1998, Three versions of the finite element method based on concepts of either stochasticity, fuzziness or anti-optimization. Applied Mechanics Review, Vol.51, No.3,pp.209-218

  161. Ferrari P., Savoia M., 1998, Fuzzy number theory to obtain conservative results with respect to probability. Computer methods in applied mechanics and engineering, Vol.160,pp.205-222

  162. Gau, Ch.-Y. Stadtherr M.A., 1998, Global Nonlinear Parameter Estimation Using Interval Analysis Parallel Computing Strategies. Department of Chemical Engineering University of Notre Dam

  163. Günter Mayer, Jiri Rohn: On the Applicability of the Interval Gaussian Algorithm. Reliable Computing 4(3): 205-222 (1998)

  164. Kay, Herbert, 1998
    SQSIM: a simulator for imprecise ODE models
    Computers & Chemical Engineering Volume: 23, Issue: 1, November 15, 1998, pp. 27-46
    [ Download(ICM) ] [ Download ]

  165. Kulpa Z., Pownuk A., Skalna I., 1998, Analysis of linear mechanical structures with uncertainties by means of interval methods, CAMES, Vol.5, No.4,pp.443-477

  166. Köylüoglu, H. Ugur; et. al., 1998
    A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties
    Computers & Structures Volume: 67, Issue: 1-3, April 1, 1998, pp. 91-98
    [ Download(ICM) ] [ Download ]

  167. Hu Ch.-F., Fang S.-Ch., 1998, Solving fuzzy inequalities with concave membership functions. Fuzzy Sets and Systems, Vol.99,pp.233-240

  168. Kaleva O., 1998, The Peano theorem for fuzzy differential equations revisited. Fuzzy Sets and Systems, Vol.98,pp.147-148

  169. Köylüoglu H.U., Elischakoff I., 1998, A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties. Computers and Structures, Vol.67, No.1/3,pp.91-98

  170. Lombardi, M. (1998). “Optimization of Uncertain Structures Using Non-probabilistic Models,” Computers & Structures, 67, 99–103

  171. Rao S.S., Asaithambi A., Agrawal S.K., 1998, Inverse Kinematics Solution of Robot Manipulators Using Interval Analysis. Journal of Mechanical Design, Vol.120, pp.147-153

  172. Rao S.S., Chen L., 1998, Numerical solution of fuzzy linear equations in engineering analysis, International Journal for Numerical Methods in Engineering, Vol.42, pp.829-846

  173. Rao S.S., Chen L., Mulkay E., 1998, Unified Finite Element Method for Engineering Systems with Hybrid Uncertainties, AIAA Journal, Vol.36, No.7,pp.1291-1299

  174. Sanchez L., 1998, A random sets-based method for identifying fuzzy models. Fuzzy Sets and System, Vol.98,pp.343-354

  175. Sarveswaran V., Smith J.W., Blockley D.I., 1998, Reliability of corrosion-damaged steel structures using interval probability theory. Structural Safety, Vol.20,pp.237-255

  176. Skrzypczyk J., 1998, A Note on Interval Fredholm Integral Equations. Zeszyty Naukowe Politechniki Œl¹skiej, Seria Budownictwo, Z.85,pp.75-83

  177. Skrzypczyk J., 1998, On Existence of Solutions of Interval Fredholm Integral Equations with Degenerate Kernels. Zeszyty Naukowe Politechniki Œl¹skiej, Seria Budownictwo, Z.85,pp.85-94

  178. Tonon F., Bernardini A., 1998, A random set approach to the optimization of uncertain structures. Computers and Structures, Vol.68,pp.583-600

  179. Yoshikawa N., Elischakoff I., Nakagiri S., 1998, Worst case estimation of homology design by convex analysis. Computers and Structures, Vol.67, No.1/3,pp.191-196

  180. Yue Z.Z., Qiao G.W., 1998, Solving process for a system of first-order fuzzy differential equations. Fuzzy Sets and Systems, Vol.95,pp.333-347

  181. Burczynski T., Skrzypczyk J., 1997, Fuzzy aspects of the boundary element method, Engineering Analysis with Boundary Elements, Vol.19, No.3,pp.209-216 [ Download ]

  182. Chen, R. and A. C. Ward (1997). “Generalizing Interval Matrix Operations for Design,” Journal of Mechanical Design, 119, 65–72.

  183. Chen L., Rao S.S., 1997, Fuzzy finite-element approach for the vibration analysis of imprecisly-defined systems. Finite Element in Analysis and Design, Vol.27,pp.69-83 [ Download ]

  184. Enling L., 1997, A New Solution to Structural Fuzzy Finite Element Equilibrium Equations. Applied Mathematics and Mechanics, Vol.18, No.4,pp.385-391

  185. Lakeyev, A.V. and V. Kreinovich (1997). “NP-Hard Classes of Linear Algebraic Systems with Uncertainties,” Reliable Computing, 3, 51–81

  186. M. Kleiber, H. Antúnez, T.D. Hien, P. Kowalczyk. Parameter Sensitivity in Nonlinear Mechanics. John Wiley & Sons, Chichester, 1997

  187. Eldon R. Hansen: Sharpness in Interval Computations. Reliable Computing 3(1): 17-29 (1997)

  188. Maglaras G., Nikolaidids E., Haftka R.T., Cudney H.H., 1997, Analytical-experimental comparison of probabilistic methods and fuzzy set based methods for designing under uncertainty. Structural Optimization, Vol.13,pp.69-80

  189. Rao S.S., Berke L., 1997, Analysis of Uncertain Structural Systems Using Interval Analysis, AIAA Journal, Vol.35, No. 4,pp.727-735

  190. Jiri Rohn: On Overestimations Produced by the Interval Gaussian Algorithm. Reliable Computing 3(4): 363-368 (1997)

  191. Skrzypczyk J., 1997, Fuzzy finite element methods – A new methodology. In: Computer Methods in Mechanics (Proc. XIII Polish Conference on Computer Methods in Mechanics, Poznañ, Poland, May 5-8, 1995), Vol. 4.pp.1187-1194. Poznañ University of Technology, Poznañ

  192. Shary, S. P. (1997). “Algebraic Approach in the ‘Outer Problem’ for Interval Linear Equations,” Reliable Computing, 2, 103–135

  193. G. Alefeld and G. Mayer, On the solution set of symmetric interval systems. ZAMM, Suplement 3, 76 (1996), pp.259-262.

  194. Benedetti A. Guglielmi N., 1996, Tracing Characteristic of Smooth Nonlinear Resistive Circuits by Interval Analysis.

  195. Kearfott, R. B. (1996). Applications of Interval Computations (editor), Kluwer Academic Publishers, Dordrecht, The Netherlands

  196. Nakagiri, S. and N. Yoshikawa (1996). “Finite Element Interval Estimation by Convex Model” in Probabilistic Mechanics and Structural and Geotechnical Reliability, Proceedings of the 1996 7th Specialty Conference, ASCE, New York, 278–281

  197. Pantelides C.P., 1996, Stability of elastic bars on uncertain foundations using a convex model. International Journal of Solids and Structures, Vol.33, No.9,pp.1257-1269

  198. Rao, S. S. and L. Berke (1996). “Analysis of Uncertain Structural Systems using Interval Analysis” in AIAA/ASME/ASCE/AHS/ASC 37th Structures, Structural Dynamics and Materials Conference, AIAA, Washington, D. C., 1273–1280

  199. Schwartz, D. I. and S. S. Chen (1996). “Interval Methods for Qualitatively Uncertain Models in Structural Design,” in International Conference on Information Technology in Civil and Structural Engineering Design – Taking Stock and Future Directions, B. Kumar and A. Retik (editors), Civil-Comp Press, Scotland, 63–68

  200. Shokin, Y. I. (1996). “On Interval Problems, Interval Algorithms, and their Computational Complexity” in Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN–95), G. Alefeld, A. Frommer, and B. Lang (editors), Akademie Verlag, Berlin, 314–328

  201. Tetreault, M. (1996). “Improving Qualitative Simulation with Interval Arithmetic and Additional Constraints,” International Journal of Intelligent Systems, 11, 1041–1057

  202. Walley P., Cooman G., 1996, The imprecise probabilities project,

  203. Zhiping, Qiu; Suhuan, Chen; Elishakoff, Isaac, 1996
    Bounds of Eigenvalues for Structures with an Interval Description of Uncertain-but-non-random Parameters
    Chaos, Solitons & Fractals Volume: 7, Issue: 3, March, 1996, pp. 425-434
    [ Download(ICM) ] [ Download ]

  204. Zhiping, Qiu; Elishakoff, Isaac; Starnes Jr, James H., 1996
    The Bound Set of Possible Eigenvalues of Structures with Uncertain But Non-random Parameters
    Chaos, Solitons & Fractals Volume: 7, Issue: 11, November, 1996, pp. 1845-1857
    [ Download(ICM) ] [ Download ]

  205. G. Alefeld and G. Mayer, On the symmetric and unsymmetric solution set of interval systems. SIAM Journal on Matrix Analysis and Applications, 16 (1995), pp. 1223-1240.

  206. Balaji G.V., Seader J.D., 1995, Application of interval Newton's method to chemical engineering problems. Reliable Computing, Vol.1, No.3,pp.215-223 [ Download ]

  207. Del Grosso, A. and A. Zucchini (1995). “Bounded-State Active Control of Structures: A Set-Theoretic Approach,” Smart Materials and Structures, 4, A15–A24.

  208. Dimarogonas A.D., 1995, Interval Analysis of Vibrating Systems, Journal of Sound and Vibration, Vol.183,pp.739-749

  209. Dobronets B.S., 1995, Numerical methods using defects, Reliable Computing, Vol.1, No.4,pp.383-391

  210. Elishakoff I., 1995, Essay on uncertainties in elastic and viscoelastic structures: from A.M.Freudenthal's criticisms to modern convex modelling. Computers and Structures, Vol.56, No.6,pp.871-895

  211. Köylüoglu H.U., A.S. Çakmak, and S. R. K. Nielsen (1995). “Interval Algebra to Deal with Pattern Loading of Structural Uncertainties,” ASCE Journal of Engineering Mechanics, 11, 1149–1157.

  212. Köylüoglu H.U., Cakmak A., Nielsen S.R.K., 1995, Interval mapping in structural mechanics. In: Spanos, ed. Computational Stochastic Mechanics. 125-133. Balkema, Rotterdam

  213. Kupriyanova, L. (1995). “Inner Estimation of the United Solution Set of Interval Linear Algebraic System,” Reliable Computing, 1, 15–31

  214. Muhanna, R. L. and R. L. Mullen (1995). “Development of Interval Based Methods for Fuzziness in Continuum Mechanics” in Proceedings of the 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society (ISUMA–NAFIPS’95),IEEE, 705–710

  215. Onisawa T., Kacprzyk J., 1995, Reliability and Safety Analyses under Fuzziness. Physica-Verlag, Heidelberg

  216. Qiu, Zhiping; Chen, Suhuan; Jia, Hongbo, 1995
    The rayleigh quotient iteration method for computing eigenvalue bounds of structures with bounded uncertain parameters
    Computers & Structures Volume: 55, Issue: 2, April, 1995, pp. 221-227
    [ Download(ICM) ] [ Download ]

  217. Rao S.S., Sawyer J.P., 1995, Fuzzy Finite Element Approach for the Analysis of Imprecisly Defined Systems. AIAA Journal, Vol.33, No.12,pp.2364-2370

  218. Saint-Pierre P., 1995, Newton and Other Continuation Methods for Multivalued Inclusions. Set-Valued Analysis, Vol.3,pp.143-156 [ Download ]

  219. Shary, Sergey P., 1995
    Solving the linear interval tolerance problem
    Mathematics and Computers in Simulation Volume: 39, Issue: 1-2, November 8, 1995, pp. 53-85
    [ Download(ICM) ] [ Download ]

  220. Valliappan S. Pham T.D., 1995, Elasto-Plastic Finite Element Analysis with Fuzzy Parameters. International Journal for Numerical Methods in Engineering, 38, s.531-548

  221. Boese F.G., 1994, Stability of a Special Class of Retarded Difference-Differential Equations with Interval-Valued Parameters. Journal of Mathematical Analysis and Applications, Vol.181,pp.227-247 [ Download ]

  222. Chen, S, Z. Qui, D. Song (1994). “A New Method for Computing the Upper and Lower Bounds on Frequencies of Structures with Interval Parameters,” Mechanics Research Communications, 21, 583–592.

  223. Elishakoff I., Elisseeff P., Glegg A.L., 1994, Nonprobablistic, Convex-Theoretic Modelling of Scatter in Material Properties, AIAA Journal, Vol.32, No.4,pp.843-849

  224. Elishakoff I., Li Y.W., Starnes J.H., 1994, A deterministic method to predict the effect of unknown-but-bounded elastic moduli on the buckling of composite structures. Computer methods in applied mechanics and engineering, Vol.111,pp.155-167

  225. Gutman P., Baril C., Neumann L., 1994, An Algorithm for Computing Value Sets of Uncertain Transfer Functions in Factored Real Form, IEEE Transactions on Automatic Controll, Vol.39, No.6,pp.1268-1273

  226. Madsen, K. and O. Toft (1994). “A Parallel Method for Linear Interval Equations,” Interval Computations, 3, 81–105

  227. Rump S.M., 1994, Verification methods for dense and sparse systems of equations. J. Herzberger, ed., Topics in Validated Computations. Elsevier Science B.V.,pp.63-135

  228. Shary, S. P. (1994). “Solving the Tolerance Problem for Interval Linear Systems,” Interval Computations, 2, 6–26

  229. Cheng C.H., Mon D.L., 1993, Fuzzy system reliability analysis by interval of confidence. Fuzzy Sets and Systems, 56,pp.29-35. [ Download ]

  230. Elishakoff I., Colombi P., 1993, Combination of probabilistic and convex models of uncertainty when scare knowledge is present on acoustic excitation parameters. Computer methods in applied mechanics and engineering, Vol.104,pp.187-209

  231. Kolev, L. V. (1993). Interval Methods for Circuit Analysis, World Scientific Publishing Company, River Edge, New Jersey

  232. Kristinsdottir B.P., Zabinsky Z.B., Csendes T., Tuttle M.E., 1993, Methodologies for Tolerance Intervals. Interval Computations, No.3,pp.133-147

  233. Kurzhanski A.B., Veliov V.M., 1993, Set-valued Analysis and Differential Inclusions. The International Institute for Applied Systems and Analysis, Boston

  234. Smith, I. F. C. and B. Faltings (1993). “Implementing Qualitative Reasoning for Structural Design Using Constraint Propagation,” in Proceedings of the Fifth International Conference on Computing in Civil Engineering, L. Cohn (editor), ASCE, New York, 1251–1258

  235. Valliappan S., Pham T.D., 1993, Fuzzy Finite Element Analysis of A Foundation on Elastic Soil Medium. International Journal for Numerical and Analytical Methods in Geomechanics, Vol.17,pp.771-789

  236. Buckley J.J., 1992, Solving fuzzy equations. Fuzzy Sets and Systems, Vol.50,pp.1-14 [ Download ]

  237. Chen, R. (1992). Generalizing Interval Matrix Operations for Design: Fusing the Labeled Interval Calculus and Interval Matrix Arithmetic, Ph.D. Dissertation, University of Michigan

  238. Hansen, E. (1992). “Bounding the Solutions of Interval Linear Equations,” SIAM Journal of Numerical Analysis, 29, 1493–1503

  239. Global Optimization Using Interval Analysis, by Elden R. Hansen, Marcel Dekker, New York, 1992, ISBN 0824786963.

  240. Hyvönen E., 1992, Constraint reasoning based on interval arithmetic: the tolerance propagation approach. Artificial Intelligence, Vol.58,pp.71-112

  241. Parsons, S. and M. Dohnal (1992). “Qualitative, Semiqualitative and Interval Algebras, and their Application to Engineering Problems,” Engineering Applications of Artificial Intelligence, 5, 553–560

  242. Shary, S. P. (1992). “On Controlled Solution Set of Interval Algebraic Systems,” Interval Computations, 4, 66–75

  243. Buckley J.J., Qy Y., 1991, Solving fuzzy equations: a new solution concept. Fuzzy Sets and Systems, Vol.39,pp.291-301 [ Download ]

  244. Deif, A. (1991). “The Interval Eigenvalue Problem,” ZAMM (Angewandte Analysis und Mathematische Physik), 71, 61–64.

  245. Dubois D., Prade H., 1991, Random sets and fuzzy interval analysis. Fuzzy Sets and Systems, Vol. 38,pp.309-312

  246. Buckley J.J., Qy Y., 1990, On using a-cuts to evaluate fuzzy equations. Fuzzy Sets and Systems, Vol.38,pp.309-312 [ Download ]

  247. Ben-Haim Y., Elishakoff I., 1990, Convex Models of Uncertainty in Applied Mechanics. Elsevier Science Publishers, New York

  248. C. Jansson. Interval linear systems with symmetric matrices. skew-symmetric matrices and dependencies in the right hand side. Computing, 46:265–274, 1991

  249. Kaleva O., 1990, The Cauchy Problem for Fuzzy Differential Equations. Fuzzy Sets and Systems, Vol.35,pp.389-396

  250. Neumaier A., 1990, Interval methods for systems of equations, Cambridge University Press, New York

  251. Struss, P. (1990). “Problems of Interval Based Qualitative Reasoning” in Readings In Qualitative Reasoning About Physical Systems, D. S. Weld and J. de Kleer (editors), Morgan Kaufmann Publishers, San Mateo, California, 288–305

  252. He Q., Yi W., 1989, On Fuzzy Differential Equations. Fuzzy Sets and Systems, Vol.32,pp.321-325

  253. Neumaier A., 1989, Rigorous Sensitivity Analysis for Parameter-Dependent Systems of equations. Journal of Mathematical Analysis and Applications, Vol. 144, 1989,pp.16-25

  254. Rohn, J. (1989). “Systems of Linear Equations,” Linear Algebra and its Applications, 156,39–78

  255. Wood, K. L., E. K. Antonsson, and J. L. Beck (1989). “Comparing Fuzzy and Probability Calculus for Representing Imprecision in Preliminary Engineering Design,” Design Theory and Methodology – DTM ‘89, ASME, New York, 99–105

  256. Lin, S., Y. T. Juang, I. K. Fong, C. F. Hsu, and T. S. Kuo (1988). “Dynamic Interval Systems Analysis and Design,” International Journal of Control, 48, 1807–1818

  257. Neumaier A., 1988, The enclosure of solutions for parameter-depedent system of equations, in Reliability in Computing, Academic Press, New York,pp.269-286

  258. Rohn, J. (1988). “Solving Systems of Linear Interval Equations” in Reliability in Computing, R. E. Moore (editor), Academic Press, New York, 171–181

  259. Shakel, J. (1988). “Asymptotic Estimation of Oscillating Functions Using an Interval Calculus” in Symbolic and Algebraic Computation, P. Giann (editor), Springer-Verlag, 481–489

  260. Dong W., Shah H.C., 1987, Vertex Method for Computing Functions of Fuzzy Variables. Fuzzy Sets and Systems, Vol.24,pp.65-78

  261. Kaleva O., 1987, Fuzzy Differential Equations. Fuzzy Sets and Systems, Vol.24, s.301-317

  262. Dubois D., Prade H., 1987, On Several Definition of the Differentiation of Fuzzy Mapping, Fuzzy Sets and Systems, Vol.24,pp.117-120

  263. Deif A., 1986, Sensitivity Analysis in Linear Systems. Springer-Verlag, New York

  264. Rohn, J. (1986). “Inner Solutions of Linear Interval Systems” in Interval Mathematics 1985: Proceedings of the International Symposium, K. Nickel (editor), Springer- Verlag, New York, 157–158

  265. Eldon R. Hansen: Global optimization with data perturbations. Computers & OR 11(2): 97-104 (1984)

  266. Ratschek H., Rokne J., 1984, Computer Method for the Range of Function. John Willey & Sons, New York

  267. Alefeld, G. and J. Herzberger (1983). Introduction to Interval Computations, Academic Press, New York.

  268. Gay D.M., 1983, Computing Preturbation Bounds for Nonlinear Algebraic Equations, SIAM Journal on Numerical Analysis, Vol.20, No.3,pp.638-651

  269. Asaithambi N.S., Zuhe S., Moore R.E., 1982, On Computing the Range of Values. Computing, Vol.28,pp.225-237 [ Download ]

  270. Dubois D., Prade H., 1982, Towards Fuzzy Differential Calculus. Part III: Differentiation. Fuzzy Sets and Systems, Vol.8,pp.225-233

  271. Hart, G. C. (1982). Uncertainty Analysis, Loads, and Safety in Structural Engineering, Prentice Hall, New Jersey

  272. Hartfiel, D. J. (1980). “Concerning the Solution Set of Ax=b where Q A P and a b q, Numerische Mathematik, 35, 355–359

  273. Ditlevsen, O. (1981). Uncertainty Modeling with Applications to Multidimensional Civil Engineering Systems, McGraw-Hill, New York

  274. Markov S., 1980, Interval Differential Equations. Interval Mathematics,pp.145-164

  275. Nickel, K. (1980). Interval Mathematics 1980: Proceedings of an International Symposium on Interval Mathematics (editor), Academic Press, New York

  276. Cope, J. E. and B. W. Rust (1979). “Bounds on Solutions of Linear Systems with Inaccurate Data,” SIAM Journal on Numerical Analysis, 16, 950–963.

  277. Moore, R. E. (1979). Methods and Applications of Interval Analysis, SIAM, Philadelphia

  278. Nickel, K. (1975). Interval Mathematics 1975 (editor), Springer, New York

  279. Nuding, V. E. and J. Wilhelm (1972). “Über Gleichungen und Über Lösungen [On Equations and On Solutions]” ZAMM (Angewandte Analysis und Mathematische Physik), 52, T 188–T 190

  280. Karl Nickel, On the Newton method in interval analysis, MRC Rechnical Summary Report #1136, University of Wisconsin, Madison, 1971 [ download ].

  281. Kuperman, I. B. (1971). Approximate Linear Algebraic Equations, Van Nostrand Reinhold Ltd., New York

  282. Götz Alefeld, Jürgen Herzberger: Über die Berechnung der inversen Matrix mit Hilfe der Intervallrechnung. Elektronische Rechenanlagen 12(5): 259-261 (1970)

  283. R. Krawczyk: Newton - Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing 4, 187-201 (1969).

  284. E. R. Hansen: On solving systems of equations using interval arithmetic. Math. of Comp. 22, 374-384 (1968).

  285. Dempster, A. P. (1967). "Upper and lower probabilities induced by a multivalued mapping". The Annals of Mathematical Statistics 38 (2): 325-339. Retrieved 2009-09-23 [Download]

  286. R. E. Moore. Interval Analysis. Prentice-Hall, Englewood Cliffs N. J., 1966.

  287. Oettli, W. (1965). “On the Solution Set of a Linear System with Inaccurate Coefficients,” SIAM Journal of Numerical Analysis, Series B: Volume 2, 1, 115–118.

  288. Oettli, W., Prager, W. (1964): Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides. Numer. Math. 6: 405-409

  289. Sunaga, T. (1958). “Theory of an Interval Algebra and its Application to Numerical Analysis,” in RAAG Memoirs, K. Kondo (editor), Gaukutsu Bunkwen Fukeyu-kai, Tokyo, 29–46 [ download ]

  290. M. Warmus, "Calculus of Approximations", Bulletin de l'Academie Polonaise de Sciences, 1956, Vol. 4, No. 5, pp. 253-257 [ download ]

  291. M. Warmus, "Approximations and Inequalities in the Calculus of Approximations. Classification of Approximate Numbers", Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 1961, Vol. 9, pp. 241-245. [ download ]

  292. P. S. Dwyer, Linear Computations, J. Wiley, N.Y., 1951.

  293. Young, R.C. (1931). “The Algebra of Many-Valued Quantities,” Mathematische Annalen, 104, 260–290.

  294. V. M. Bradis, "An experience of the verification of practically useful operations with approximate numbers", Proceedings of Tver Pedagogical Institute, 1927, No. 3, in Russian.

  295. W. H. Young, "Sull due funzioni a piu valori constituite dai limiti d'una funzione di variable reale a destra ed a sinistra di ciascun punto", Rendiconti Academia di Lincei, Classes di Scienza Fiziche, 1908, Vol. 17, No. 5, pp. 582-587

  296. Archimedes, "On the measurement of the circle", In: Thomas L. Heath (ed.), The Works of Archimedes, Cambridge University Press, Cambridge, 1897; Dover edition, 1953, pp. 91-98

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