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An Approach for Solving Fully Interval Production Planning Problems

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Fuzzy Information Processing 2020 (NAFIPS 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1337))

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Abstract

This paper shows a method for solving production planning problems involving interval-valued costs, standard times and constraints. An iterative method is used to solve the fully production planning problem using a global satisfaction degree and it is applied to an inventory/shortage example.

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References

  1. G. Alefeld, V. Kreinovich, G. Mayer, On the solution sets of particular classes of linear interval systems. J. Comput. Appl. Math. 152(1), 1–15 (2003)

    Article  MathSciNet  Google Scholar 

  2. M. Černý, M. Hladík, Optimization with uncertain, inexact or unstable data: linear programming and the interval approach, in Proceedings of the 10th International Conference on Strategic Management and its Support by Information Systems, ed. by R. Němec, F. Zapletal, VŠB - Technical University of Ostrava (2013), pp. 35–43

    Google Scholar 

  3. M. Delgado, J.L. Verdegay, M. Vila, A general model for fuzzy linear programming. Fuzzy Sets Syst. 29(1), 21–29 (1989)

    Article  MathSciNet  Google Scholar 

  4. J.C. Figueroa-García, An iterative procedure for fuzzy linear programming problems, in 2011 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS) (IEEE, 2011), pp. 1–6

    Google Scholar 

  5. J.C. Figueroa-García, An approximation method for type reduction of an interval Type-2 fuzzy set based on \(\alpha \)-cuts, in IEEE Proceedings of FEDCSIS 2012. IEEE (2012), pp. 1–6

    Google Scholar 

  6. J.C. Figueroa-García, Solving linear programming problems with interval type-2 fuzzy constraints using interval optimization, in Proceeedings of NAFIPS 2013. IEEE (2013), pp. 1–6

    Google Scholar 

  7. J.C. Figueroa-García, E.R. Lopez, C. Franco-Franco, A note about the \((x,y)\) coordinates of the centroid of a fuzzy set, in Proceeedings of WEA 2018. Springer (2018), pp. 78–88

    Google Scholar 

  8. J.C. Figueroa-García, Y. Olarte, F. Camargo, Linear programming with fuzzy joint parameters: an iterative method (2010), pp 1–6

    Google Scholar 

  9. E. Garajová, M. Hladík, M. Rada, Interval linear programming under transformations: optimal solutions and optimal value range. Cent. Eur. J. Oper. Res. 27(1), 601–614 (2019)

    Article  MathSciNet  Google Scholar 

  10. G. Heindl, V. Kreinovich, A.V. Lakeyev, Solving linear interval systems is NP-Hard even if we exclude Overflow and Underflow. Rel. Comput. 4(4), 383–388 (1998)

    Article  MathSciNet  Google Scholar 

  11. M. Hladík, Optimal value range in interval linear programming. Fuzzy Opt. Dec. Making 8(3), 283–294 (2009)

    Article  MathSciNet  Google Scholar 

  12. M. Hladík, Weak and strong solvability of interval linear systems of equations and inequalities. Linear Algebra Appl. 438(11), 4156–4165 (2013)

    Article  MathSciNet  Google Scholar 

  13. R.B. Kearfott, V. Kreinovich, Beyond convex? Global optimization is feasible only for convex objective functions: a theorem. J. Global Opt. 33(4), 617–624 (2005)

    Article  MathSciNet  Google Scholar 

  14. V. Kreinovich, J.C. Figueroa-Garcia, Optimization under fuzzy constraints: from a heuristic algorithm to an algorithm that always converges, in Proceeedings of WEA 2018. Springer (2018), pp. 3–16

    Google Scholar 

  15. V. Kreinovich, O. Kosheleva, The range of a continuous functional under set-valued uncertainty is always an interval. Rel. Comput. 24, 27–30 (2017)

    MathSciNet  Google Scholar 

  16. V. Kreinovich, C.W. Tao, Checking identities is computationally intractable (NP-Hard), so human provers will be always needed. Int. J. Intell. Syst. 19(1), 39–49 (2004)

    Article  Google Scholar 

  17. W.A. Lodwick, K.D. Jamison, Interval methods and fuzzy optimization. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5(3), 239–249 (1997)

    Article  MathSciNet  Google Scholar 

  18. R.E. Moore, R.B. Kearfott, M.J. Cloud, Introduction to Interval Analysis (SIAM, 2009)

    Google Scholar 

  19. F. Mráz, Calculating the exact bounds of optimal values in lp with interval coefficients. Ann. Oper. Res. 81, 51–62 (1998)

    Article  MathSciNet  Google Scholar 

  20. H.T. Nguyen, V. Kreinovich, Computing degrees of subsethood and similarity for interval-valued fuzzy sets: fast algorithms, in 9th International Conference on Intelligent Technologies InTec’08. IEEE (2008), pp. 47–55

    Google Scholar 

  21. T.A. Tuan, V. Kreinovich, T.N. Nguyen, Decision making under interval uncertainty: beyond hurwicz pessimism-optimism criterion, in Beyond Traditional Probabilistic Methods in Economics. IEEE (2019), pp. 176–184

    Google Scholar 

  22. A. Welteand, L. Jaulin, M. Ceberio, V. Kreinovich, Avoiding fake boundaries in set interval computing. J. Uncertain Syst. 11(2), 137–148 (2017)

    Google Scholar 

  23. H.J. Zimmermann, Fuzzy programming and Linear Programming with several objective functions. Fuzzy Sets Syst. 1(1), 45–55 (1978)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank to Prof. Vladik Kreinovich for his interest and invaluable support, and a special thanks is given to all members of LAMIC research group of Universidad Distrital Francisco José de Caldas - Bogotá, Colombia.

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Authors and Affiliations

  1. Universidad Distrital Francisco José de Caldas, Bogotá, Colombia

    Juan Carlos Figueroa García

  2. Universidad del Rosario, Bogotá, Colombia

    Carlos Franco

Authors
  1. Juan Carlos Figueroa García
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  2. Carlos Franco
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Corresponding author

Correspondence to Juan Carlos Figueroa García .

Editor information

Editors and Affiliations

  1. Department of Mathematics, DigiPen Institute of Technology, Redmond, WA, USA

    Barnabás Bede

  2. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  3. School of Engineering and Technology, University of Washington, Tacoma, WA, USA

    Martine De Cock

  4. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Figueroa García, J.C., Franco, C. (2022). An Approach for Solving Fully Interval Production Planning Problems. In: Bede, B., Ceberio, M., De Cock, M., Kreinovich, V. (eds) Fuzzy Information Processing 2020. NAFIPS 2020. Advances in Intelligent Systems and Computing, vol 1337. Springer, Cham. https://doi.org/10.1007/978-3-030-81561-5_22

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