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Inner Product over Fuzzy Matrices


Affiliations
1 P.G. and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli 620 020, India
2 Department of Mathematics and Statistics, University of Jaffna, Jaffna, Sri Lanka
3 Department of Mathematics, Sengunthar Arts and Science College, Neikkarapatti, Tiruchengode, Tamil Nadu 637205, India
 

The purpose of this study was to introduce the inner product over fuzzy matrices. By virtue of this definition, α-norm is defined and the parallelogram law is proved. Again the relative fuzzy norm with respect to the inner product over fuzzy matrices is defined. Moreover Cauchy Schwarz inequality, Pythagoras, and Fundamental Minimum Principle are established. Some equivalent conditions are also proved.
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  • Inner Product over Fuzzy Matrices

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Authors

A. Nagoor Gani
P.G. and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli 620 020, India
K. Kannan
Department of Mathematics and Statistics, University of Jaffna, Jaffna, Sri Lanka
A. R. Manikandan
Department of Mathematics, Sengunthar Arts and Science College, Neikkarapatti, Tiruchengode, Tamil Nadu 637205, India

Abstract


The purpose of this study was to introduce the inner product over fuzzy matrices. By virtue of this definition, α-norm is defined and the parallelogram law is proved. Again the relative fuzzy norm with respect to the inner product over fuzzy matrices is defined. Moreover Cauchy Schwarz inequality, Pythagoras, and Fundamental Minimum Principle are established. Some equivalent conditions are also proved.