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Solution Sets of Interval-Valued Min-S-Norm Fuzzy Relational Equations

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An Erratum to this article was published on 29 August 2007

Abstract

This paper introduces the concepts of tolerable solution set, united solution set, and controllable solution set for interval-valued fuzzy relational equations. Given a continuous s-norm, it is shown that each of the three types of the solution sets of interval-valued fuzzy relational equations with a min-s-norm composition, if nonempty, is composed of one minimum solution and a finite number of maximal solutions. Necessary and sufficient conditions for the existence of solutions are given. Computational procedures based on the constructive proofs are proposed to generate the complete solution sets. An example is given to illustrate the proposed procedures.

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Authors and Affiliations

  1. Operations Research Program, North Carolina State University, Raleigh, NC, 27695-7913, USA

    Shunmin Wang

  2. Department of Industrial Engineering, North Carolina State University, Raleigh, NC, 27695-7906, USA

    Shu-cherng Fang & Henry L. W. Nuttle

Authors
  1. Shunmin Wang
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  2. Shu-cherng Fang
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  3. Henry L. W. Nuttle
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Corresponding author

Correspondence to Shunmin Wang.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s10700-007-9013-y.

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Wang, S., Fang, Sc. & Nuttle, H.L.W. Solution Sets of Interval-Valued Min-S-Norm Fuzzy Relational Equations. Fuzzy Optim Decis Making 4, 331–349 (2005). https://doi.org/10.1007/s10700-005-3667-0

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