Rank of interval-valued fuzzy matrices

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• 作者：Sanjib Mondal ; Madhumangal Pal
• 关键词：Interval ; valued fuzzy matrix ; Row rank ; Column rank ; Fuzzy rank ; Schein rank ; Cross vector ; 15B15
• 刊名：Afrika Matematika
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：27
• 期：1-2
• 页码：97-114
• 全文大小：518 KB
• 参考文献：1.Abdukhalikov, K.S., Tulenbaev, M.S., Umirbarv, U.U.: On fuzzy bases of vector spaces. Fuzzy Sets Syst. 63, 201–206 (1994)CrossRef MATH
  2.Abdukhalikov, K.S.: The dual of a fuzzy subspace. Fuzzy Sets Syst. 82, 375–381 (1996)CrossRef MathSciNet MATH
  3.Adak, A.K., Bhowmik, M., Pal, M.: Some properties of generalized intuitionistic fuzzy nilpotent matrices over distributive lattice. Fuzzy Inf. Eng. 4(4), 371–387 (2012)CrossRef MathSciNet MATH
  4.Adak, A.K., Bhowmik, M., Pal, M.: Intuitionistic fuzzy block matrix and its some properties. Ann. Pure Appl. Math. 1(1), 13–31 (2012)MathSciNet
  5.Adak, A.K., Pal, M., Bhowmik, M.: Distributive lattice over intuitionistic fuzzy matrices. J. Fuzzy Math. 21(2), 401–416 (2013)MathSciNet MATH
  6.Atanassov, K.T.: Intuitionistic Fuzzy Sets. VII ITKR’s Session, Sofia (1983)
  7.Biswas, R.: Rosenfeld’s fuzzy subgroups with interval-valued membership functions. Fuzzy Sets Syst. 63, 87–90 (1994)CrossRef MATH
  8.Bhowmik, M., Pal, M.: Generalized intuitionistic fuzzy matrices. Far-East J. Math. Sci. 29(3), 533–554 (2008)MathSciNet MATH
  9.Bhowmik, M., Pal, M.: Some results on intuitionistic fuzzy matrices and intuitionistic circulant fuzzy matrices. Int. J. Math. Sci. 7, 81–96 (2008)
  10.Bhowmik, M., Pal, M., Pal, A.: Circulant triangular fuzzy number matrices. J. Phys. Sci. 12, 141–154 (2008)
  11.Bhowmik, M., Pal, M.: Intuitionistic neutrosophic set. J. Inf. Comput. Sci. 4(2), 142–152 (2009)
  12.Bhowmik, M., Pal, M.: Intuitionistic neutrosophic set relations and some of its properties. J. Inf. Comput. Sci. 5(3), 183–192 (2010)
  13.Bhowmik, M., Pal, M.: Generalized interval-valued intuitionistic fuzzy sets. J. Fuzzy Math. 18(2), 357–371 (2010)MathSciNet MATH
  14.Bhowmik, M., Pal, M.: Some results on generalized interval-valued intuitionistic fuzzy sets. Int. J. Fuzzy Syst. 14(2), 193–203 (2012)MathSciNet
  15.Deschrijver, G., Kerre, E.E.: On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst. 133, 227–235 (2003)CrossRef MathSciNet MATH
  16.Deschrijver, G.: Arithmetic operations in interval-valued fuzzy set theory. Inf. Sci. 177, 2906–2924 (2007)CrossRef MathSciNet MATH
  17.Duan, J.-S.: The transitive closure, convergence of powers and adjoint of generalized fuzzy matrices. Fuzzy Sets Syst. 145, 301–311 (2004)CrossRef MATH
  18.Hedayati, H.: On properties of fuzzy subspaces of vectorspaces. Ratio Math. 19, 1–10 (2009)
  19.Kang, D., Koh, H., Cho, I.G.: On the Mazur–Ulam theorem in non-Archimedean fuzzy normed spaces. Appl. Math. Lett. 25, 301–304 (2012)CrossRef MathSciNet MATH
  20.Karakus, S., Demirci, K., Duman, O.: Statistical convergence on intuitionistic fuzzy normed spaces. Chaos Solitons Fractals 35, 763–769 (2008)CrossRef MathSciNet MATH
  21.Katsaras, A.K., Liu, D.B.: Fuzzy vector spaces and fuzzy topological vector spaces. J. Math. Anal. Appl. 58, 135–146 (1977)CrossRef MathSciNet MATH
  22.Kim, K.H., Roush, F.W.: Generalized fuzzy matrices. Fuzzy Sets Syst. 4, 293–315 (1980)CrossRef MathSciNet MATH
  23.Khan, S.K., Pal, M.: Interval-valued intuitionistic fuzzy matrices. Notes Intuit. Fuzzy Sets 11(1), 16–27 (2005)
  24.Khan, S.K., Pal, M.: Some operations on intuitionistic fuzzy matrices. Acta Ciencia Indica XXXII M(2), 515–524 (2006)
  25.Khan, S.K., Pal, A.: The generalized inverse of intuitionistic fuzzy matrix. J. Phys. Sci. 11, 62–67 (2007)
  26.Li, X.P., Wang, G.J.: The \(S_H\) -interval-valued fuzzy subgroup. Fuzzy Sets Syst. 112, 319–325 (2000)CrossRef MATH
  27.Lubczonok, P.: Fuzzy vector spaces. Fuzzy Sets Syst. 38, 329–343 (1990)CrossRef MathSciNet MATH
  28.Lur, Y.-Y., Pang, C.-T., Guu, S.-M.: On nilpotent fuzzy matrices. Fuzzy Sets Syst. 145, 287–299 (2004)CrossRef MathSciNet MATH
  29.Malik, D.S., Mordeson, J.N.: Fuzzy vector spaces. Inf. Sci. 55, 271–281 (1991)CrossRef MathSciNet MATH
  30.Mondal, S.: Interval-valued fuzzy vector space. Ann. Pure Appl. Math. 2(1), 86–95 (2012)
  31.Mondal, S., Pal, M.: Similarity relations, invertibility and eigenvalues of intuitoinistic fuzzy matrix. Fuzzy Inf. Eng. 5(4), 431–443 (2013)CrossRef MathSciNet
  32.Mondal, S., Pal, M.: Intuitionistic fuzzy incline matrix and determinant. Ann. Fuzzy Math. Inf. 8(1), 19–32 (2014)MathSciNet MATH
  33.Mondal, S., Pal, M.: Bipolar fuzzy matrices (communicated)
  34.Mondal, S., Pal, M.: Bipolar fuzzy vector space and rank of bipolar fuzzy matrix (communicated)
  35.Mordeson, J.N.: Bases of fuzzy vector spaces. Inf. Sci. 67, 87–92 (1993)CrossRef MathSciNet MATH
  36.Pal, M.: Intuitionistic fuzzy determinant. V.U.J. Phys. Sci. 7, 87–93 (2001)
  37.Pal, M., Khan, S.K., Shyamal, A.K.: Intuitionistic fuzzy matrices. Notes Intuit. Fuzzy Sets 8(2), 51–62 (2002)MATH
  38.Pal, M., Khan, S.K.: Interval-valued intuitionistic fuzzy matrices. Notes Intuit. Fuzzy Sets 11(1), 16–27 (2005)
  39.Pal, A., Pal, M.: Some results on interval-valued fuzzy matrices. In: Proceedings of 2010 International Conference on E-Business Intelligence, Atlantis Press, pp. 554–559 (2010)
  40.Pal, M.: Fuzzy matrices with fuzzy rows and columns (communicated)
  41.Pal, M.: Interval-valued fuzzy matrices with interval-valued rows and columns. Fuzzy Inf. Eng. (2015, to appear)
  42.Pradhan, R., Pal, M.: Intuitionistic fuzzy linear transformations. Ann. Pure Appl. Math. 1(1), 57–68 (2012)
  43.Pradhan, R., Pal, M.: Generalized inverse of block intuitionistic fuzzy matrices. Int. J. Appl. Fuzzy Sets Artif. Intell. 3, 23–38 (2013)
  44.Pradhan, R., Pal, M.: Convergence of maxgeneralized mean-mingeneralized mean powers of intuitionistic fuzzy matrices. J. Fuzzy Math. 22(2), 477–492 (2013)
  45.Sambuc, R.: Fonctions ø-floues. Application laide au diagnostic en pathologiethyroidienne, Ph. D. Thesis. Univ. Marseille, France (1975)
  46.Shi, F.G., Huang, C.E.: Fuzzy bases and the fuzzy dimension of fuzzy vector space. Math. Commun. 15(2), 303–310 (2010)MathSciNet MATH
  47.Shyamal, A.K., Pal, M.: Distances between intuitionistic fuzzy matrices. V.U.J. Phys. Sci. 8, 81–91 (2002)
  48.Shyamal, A.K., Pal, M.: Two new operations on fuzzy matrices. J. Appl. Math. Comput. 15(1–2), 91–107 (2004)CrossRef MathSciNet MATH
  49.Shyamal, A.K., Pal, M.: Distance between intuitionistic fuzzy matrices and its applications. Nat. Phys. Sci. 19(1), 39–58 (2005)MathSciNet
  50.Shyamal, A.K., Pal, M.: Interval-valued fuzzy matrices. J. Fuzzy Math. 14(3), 583–604 (2006)MathSciNet MATH
  51.Thomason, M.G.: Convergence of powers of a fuzzy matrix. J. Math. Anal. Appl. 57, 476–480 (1977)CrossRef MathSciNet MATH
  52.Turksen, I.B.: Interval-valued fuzzy sets based on normal forms. Fuzzy Sets Syst. 20, 191–210 (1986)CrossRef MathSciNet MATH
  53.Yang, M.S., Liu, H.H.: Fuzzy clustering procedures for conical fuzzy vector data. Fuzzy Sets Syst. 106, 189–200 (1999)CrossRef MATH
  54.Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, Part 1. Inf. Sci. 8, 199–249 (1975a)
  55.Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, Part 2. Inf. Sci. 8, 301–357 (1975b)
  56.Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, Part 3. Inf. Sci. 9, 43–80 (1975c)
  57.Zeng, W., Shi, Y.: Note on interval-valued fuzzy set, FSKD 2005. LNAI 3613, 20–25 (2005)
  
• 作者单位：Sanjib Mondal (1)
  Madhumangal Pal (1)
  
  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

Like fuzzy matrix the interval-valued fuzzy matrix has also three types of ranks, viz, row rank, column rank and fuzzy rank. In this article, some methods are described to find these three type of ranks for interval-valued fuzzy matrices and investigated the relationship between them. Using the cross vector such ranks are investigated by very simple way. Many results are presented by using the definition of scalar multiplication of an interval-valued fuzzy matrix. Keywords Interval-valued fuzzy matrix Row rank Column rank Fuzzy rank Schein rank Cross vector