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On regularity of block triangular fuzzy matrices

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Abstract

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idempotency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.

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Author information

Correspondence to AR. Meenakshi.

Additional information

AR. Meenakshi received her M. Math. from University of Waterloo (Canada) and Ph. D at Annamalai University. Since 1973, she has been at Annamalai University as Teaching Faculty, and she is the Dean, Faculty of Science from 2002. She was the receipient of Tamil Nadu State Council for Science and Technology, Scientist award for the year 1999. Her research interests focus on Generalized inverses of matrices, structure theory of Fuzzy Matrices and operators with applications.

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Meenakshi, A. On regularity of block triangular fuzzy matrices. JAMC 16, 207–220 (2004). https://doi.org/10.1007/BF02936162

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AMS Mathematics Subject Classification

  • 15A26
  • 15A09

Key words and phrases

  • Fuzzy matrix
  • fuzzy relational equation
  • block triangular matrix
  • triangular Toeplitz matrix