International Journal of Modern Science and Technology · ISSN 2456-0235

Research Article · Biotechnology & Bioeng. · Volume 1, Issue 2 · May 2016 · Pages 47–51

Interval-valued intuitionistic fuzzy transition matrices

S. Vijayabalaji, G. Shyamsundar

  • S. Vijayabalaji: Department of Mathematics, University College of Engineering, Panruti, (A Constituent College of Anna University, Chennai), Panruti-607106, Tamilnadu, India.
  • G. Shyamsundar: Department of Mathematics, Kongunadu College of Engineering and Technology, Tiruchirappalli – 621215, Tamilnadu, India.

Abstract

Matrix theory plays a vital role in linear algebra its applications to several areas is highly remarkable. A matrix over the fuzzy algebra is called a fuzzy matrix. Transition probability matrix plays a vital role in Markov process. Transition matrix defined in fuzzy setting called as fuzzy transition matrix. Intervalvalued fuzzy matrix is another generalization of fuzzy matrix. This Paper is an inspiration received from the theory of interval valed fuzzy matrices and fuzzy transition matrices. This structure namely interval valued intiutionistic fuzzy transition matrices (IVIFTM) generalizes the concept of fuzzy transition matrices. Various operations in this IVITFTMS are discussed in this paper. The complement and transpose of IVIFTM is defined and we provide some results on them. The union and intersection of two IVIFTMS are also fefoned and their commutative and associative properties are also discussed.

Keywords

Interval-valued fuzzy matrix; Interval-valued intuitionistic fuzzy matrix; Fuzzy transition

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