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Boolean and Fuzzy Relations

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Encyclopedia of Optimization

The conventional nonfuzzy relations using the classical two-valued Boolean logic connectives for defining their operations will be called crisp. The extensions that replace the 2-valued Boolean logic connectives by many-valued logic connectives will be called fuzzy. A unified approach of relations is provided here, so that the Boolean (crisp, nonfuzzy) relations and sets are just special cases of fuzzy relational structures. The first part of this entry on nonfuzzy relations can be used as reference independently, without any knowledge of fuzzy sets. The second part on fuzzy structures, however, refers frequently to the first part. This is so because most formulas in the matrix notation carry over to the many-valued logics based extensions.

In order to make this material useful not only theoretically but also in practical applications, we have paid special attention to the form in which the material is presented. There are seven distinguishing features of our approach that facilitate...

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Authors and Affiliations

  1. Dept. Computer Sci., Florida State Univ., Tallahassee, Florida, 32308-4530, USA

    Ladislav J. Kohout

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  1. Dept. Chemical Engin., Princeton Univ., Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optim. Dept. Industrial and Systems Engin., Univ. Florida, Gainesville, FL, 32611, USA

    Panos M. Pardalos

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Kohout, L.J. (2001). Boolean and Fuzzy Relations . In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-306-48332-7_42

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  • DOI: https://doi.org/10.1007/0-306-48332-7_42

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