ISSN 2456-0235

INDEXED IN 

International Journal of Modern Science and Technology

International Journal of Modern Science and Technology, 1(2), 2016, Pages 47-51. 

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Interval-valued intuitionistic fuzzy transition matrices

​​S. Vijayabalaji1, G. Shyamsundar2
1Department of Mathematics, University College of Engineering, Panruti
(A Constituent College of Anna University, Chennai), Panruti-607106, Tamilnadu, India.
2Department 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. Interval-valued 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-alued fuzzy matrix; Interval-valued intuitionistic fuzzy matrix; Fuzzy transition matrix; Interval-valued intuitionistic fuzzy transition matrix.


References

  1. Khan SK and Pal M. Some operations on intuitionistic fuzzy matrices, Presented in International Conference on Analysis and Discrete Structures, Indian Institute of Technology, Kharagpur, India. (2002) Dec.22-24
  2. Kim JB. Idempotent and inverses in fuzzy matrices, Malaysian Math, 6(2) (1983) 57-61.
  3. Meenakshi AR. Fuzzy Matrix Theory and Applications, MJP Publishers, 2008.
  4. Oliver CI. Fundamentals of applied probability and random processes, Elsevier Academic Press ( 2005).
  5. Pal M and Khan SK. Interval-Valued Intuitionistic Fuzzy Matrices, NIFS 11 (2005) 1, 16-27.
  6. Pal M, Khan SK and Shyamal AK. Intuitionistic fuzzy matrices, Notes on Intuitionistic Fuzzy Sets, 8(2) (2002) 51-62.
  7. Rudin W. Functional Analysis, McGraw Hill Science ( 1991).
  8. Tuckwell HC. Elementary Applications of Probability Theory, 2nd Ed., Chapman and Hall, London (1995).
  9. Vijayabalaji S, Shyamsundar G, Parthiban J and Narayanan T, Fuzzy operations on transition matrices, Global Journal of Pure and Applied Mathematics, (Accepted), 2016.