Infinite fuzzy relation equations with continuous t-norms

  • Authors:

  • Bih-Sheue Shieh

  • Affiliations:

  • Department of Mathematics Education, National University of Tainan 33, Sec. 2, Shu-Lin St., Tainan 700, Taiwan

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

This study develops a concept of infinite fuzzy relation equations with a continuous t-norm. It extends the work by Xiong and Wang [Q.Q. Xiong, X.P. Wang, Some properties of sup-min fuzzy relational equations on infinite domains, Fuzzy Sets and Systems 151 (2005) 393-402]. We describe attainable (respectively, unattainable) solutions, which are closely related to minimal solutions to the equations. It is shown that a solution set comprises both attainable and unattainable solutions. The study offers a characterization of these solutions. Under some assumptions, the solution set is presented and discussed. Two applications are also given.