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Fuzzy Monte Carlo Method

  • Chapter
Monte Carlo Methods in Fuzzy Optimization

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 222))

Introduction

This chapter introduces our fuzzy Monte Carlo method. We will be working with a very simple linear programming problem. The crisp linear program is presented in the next section. Then we fuzzify the linear program in the third section. We make some of the parameters in the problem triangular fuzzy numbers and allow all the variables to be triangular shaped fuzzy numbers. We will need to decide on a definition of ≤ between fuzzy numbers and we will use Kerre’s method (Section 2.6.2 of Chapter 2) first and then Chen’s method (Section 2.6.3 of Chapter 2) second. This chapter, and Chapters 7 and 8, are based on ([5],[6]), see also ([3],[4]).

Fuzzy linear programming has become a very large area of research. Put “fuzzy linear programming” into your search engine and obtain over 17, 000 web sites to visit. Obviously we can not search all of these sites. A few recent references to this topic are the papers ([10]-[16],[18],[20],[22]-[25],[27]) and books (or articles in these books) ([1],[2],[7]-[9],[17],[19],[21],[26]).

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Authors and Affiliations

  1. Mathematics Department University of Alabama at Birmingham Birmingham, AL 35294, USA

    James J. Buckley

  2. Department of Computer and Information Sciences University of Alabama at Birmingham Birmingham, AL 35294, USA

    Leonard J. Jowers

Authors
  1. James J. Buckley
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  2. Leonard J. Jowers
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© 2007 Springer-Verlag Berlin Heidelberg

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Buckley, J.J., Jowers, L.J. (2007). Fuzzy Monte Carlo Method. In: Monte Carlo Methods in Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76290-4_6

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  • DOI: https://doi.org/10.1007/978-3-540-76290-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76289-8

  • Online ISBN: 978-3-540-76290-4

  • eBook Packages: EngineeringEngineering (R0)

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