On fuzzy relational equations and the covering problem

  • Authors:

  • Jun-Lin Lin;Yan-Kuen Wu;Sy-Ming Guu

  • Affiliations:

  • Department of Information Management, Yuan Ze University, Taoyuan 320, Taiwan;Department of Industrial Management, Vanung University, Taoyuan 320, Taiwan;Department of Business Administration, Yuan Ze University, Taoyuan 320, Taiwan

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

Previous studies have shown that fuzzy relational equations (FREs) based on either the max-continuous Archimedean t-norm or the max-arithmetic mean composition can be transformed into the covering problem, which is an NP-hard problem. Exploiting the properties common to the continuous Archimedean t-norm and the arithmetic mean, this study proposes a generalization of them as the ''u-norm'', enabling FREs that are based on the max-continuous u-norm composition also to be transformed into the covering problem. This study also proposes a procedure for transforming the covering problem into max-product FREs. Consequently, max-continuous u-norm FREs can be solved by extending any procedure for solving either the covering problem or max-product FREs.