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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
H. H. Cho,Regular fuzzy matrices and fuzzy equations, fuzzy sets and systems105 (1999), 445–451.
Cornelius T. Leondes,Fuzzy Theory Systems: Techniques and Applications, Vol. II. Academic Press, 1999.
K. H. Kim and F. W. Roush,Generalized Fuzzy Matrices, Fuzzy Sets and Systems4 (1980), 293–315.
C. D. Meyer,Generalized Inverses of Block triangular Matrices, SIAM. J. Appl. Math.19(4) (1970), 741–750.
Timothy J. Ross,Fuzzy Logic with Engineering Applications, McGraw Hill Inc. 1995.
Witold Pedrycz,Fuzzy Relational Calculus, Hand Book of Fuzzy Computations, IOP. Ltd., 1998.
C. K. Zhao,Inverses of L Fuzzy Matrices, Fuzzy Sets and Systems.34 (1990), 103–116.
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.
About this article
Cite this article
Meenakshi, A. On regularity of block triangular fuzzy matrices. JAMC 16, 207–220 (2004). https://doi.org/10.1007/BF02936162
AMS Mathematics Subject Classification
Key words and phrases
- Fuzzy matrix
- fuzzy relational equation
- block triangular matrix
- triangular Toeplitz matrix