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Solving the Minimal Solutions of Max-Product Relation Equation by Graph Method and Branch Method

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Book cover Artificial Intelligence and Computational Intelligence (AICI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7002))

Abstract

Max-product fuzzy relation equations is one of the important classes of fuzzy relation equations. As max-min fuzzy relation equations, the main problem of solving max-product fuzzy relation equations is to find all its minimal solutions. Although some methods and algorithms have been proposed for finding them, they are still too complex in applications. In this paper, the properties of the equations’ minimal solutions are studied, and two methods, graph method and branch method, are presented based on reference [1] to find the minimal solution of max-min fuzzy relation equations. Lastly, an example is given to illustrate the two methods.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, China Jiliang University, Hangzhou, China, 310018

    Zhonglin Chai

Authors
  1. Zhonglin Chai
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Editor information

Editors and Affiliations

  1. School of Business Information Technology, RMIT University, City Campus, 124 La Trobe Street, 3000, Melbourne, VIC, Australia

    Hepu Deng

  2. School of Electronics and Information, Tongji University, 201804, Shanghai, China

    Duoqian Miao

  3. School of Computer and Information Engineering, Shanghai University of Electric Power, 200090, Shanghai, China

    Jingsheng Lei

  4. Department of Business Administration, Caritas Institute of Higher Education, 18 Chui Ling Road, Tseung Kwan O, Hong Kong, China

    Fu Lee Wang

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© 2011 Springer-Verlag Berlin Heidelberg

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Chai, Z. (2011). Solving the Minimal Solutions of Max-Product Relation Equation by Graph Method and Branch Method. In: Deng, H., Miao, D., Lei, J., Wang, F.L. (eds) Artificial Intelligence and Computational Intelligence. AICI 2011. Lecture Notes in Computer Science(), vol 7002. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23881-9_72

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  • DOI: https://doi.org/10.1007/978-3-642-23881-9_72

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23880-2

  • Online ISBN: 978-3-642-23881-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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