Similarity relations, eigenvalues and eigenvectors of bipolar fuzzy matrix

Eigenvalues and eigenvectors are one of the important topics over bipolar fuzzy linear algebra. In order to develop the bipolar fuzzy linear space we introduce in this article, the similarity relations, eigenvalues and eigenvectors of bipolar fuzzy matrices (BFMs). Idempotent, diagonally dominant and spectral radius of BFMs are considered here. Also, some properties and results of eigenvalues and eigenvectors for BFMs are investigated.

[1]  Wen-Ran Zhang Equilibrium relations and bipolar fuzzy clustering , 1999, 18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397).

[2]  J. Cacioppo,et al.  Beyond Bipolar Conceptualizations and Measures: The Case of Attitudes and Evaluative Space , 1997, Personality and social psychology review : an official journal of the Society for Personality and Social Psychology, Inc.

[3]  Wen-Ran Zhang,et al.  Bipolar Fuzzy Sets , 1997 .

[4]  Didier Dubois,et al.  Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions , 2006, Inf. Fusion.

[5]  M. Pal,et al.  Rank of interval-valued fuzzy matrices , 2016 .

[6]  H. Hashimoto,et al.  Transitivity of generalized fuzzy matrices , 1985 .

[7]  Madhumangal Pal,et al.  Intuitionistic Fuzzy Block Matrix and its Some Properties , 2012 .

[8]  Madhumangal Pal,et al.  Two new operators on fuzzy matrices , 2004 .

[9]  Fred W. Roush,et al.  Generalized fuzzy matrices , 1980 .

[10]  Madhumangal Pal,et al.  Intuitionistic Neutrosophic Set Relations and Some of Its Properties , 2010 .

[11]  Yung-Yih Lur,et al.  On nilpotent fuzzy matrices , 2004, Fuzzy Sets Syst..

[12]  Madhumangal Pal,et al.  Some properties of generalized intuitionistic fuzzy nilpotent matrices over distributive lattice , 2012 .

[13]  M. Thomason Convergence of powers of a fuzzy matrix , 1977 .

[14]  Madhumangal Pal,et al.  Some Results on Generalized Interval-Valued Intuitionistic Fuzzy Sets , 2012 .

[15]  Yong Beom Park,et al.  Generalized Intuitionistic Fuzzy Matrices , 2004 .

[16]  Li Jian-Xin,et al.  Controllable fuzzy matrices , 1992 .

[17]  H. Hashimoto Canonical form of a transitive fuzzy matrix , 1983 .

[18]  Madhumangal Pal,et al.  Interval-Valued Intuitionistic Fuzzy Matrices , 2014, ArXiv.

[19]  A. Katsaras,et al.  Fuzzy vector spaces and fuzzy topological vector spaces , 1977 .

[20]  Wen-Ran Zhang,et al.  Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis , 1994, NAFIPS/IFIS/NASA '94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige.

[21]  Wen-Ran Zhang Bipolar logic and bipolar fuzzy logic - a unification of truth, fuzziness, and bipolarity , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[22]  Madhumangal Pal,et al.  Intuitionistic Fuzzy Linear Transformations , 2014, ArXiv.

[23]  Madhumangal Pal,et al.  INTUITIONISTIC FUZZY DETERMINANT , 2001 .

[24]  M. Pal,et al.  Similarity relations, invertibility and eigenvalues of intuitoinistic fuzzy matrix , 2013 .

[25]  Sanjib Mondal Interval-valued Fuzzy Vector Space , 2012 .

[26]  H. Hashimoto,et al.  Convergence of powers of a fuzzy transitive matrix , 1983 .

[27]  Martin Gavalec,et al.  Computing Matrix Period in Max-min Algebra , 1997, Discret. Appl. Math..

[28]  M. Pal,et al.  Generalized Inverse of Block Intuitionistic Fuzzy Matrices , 2013 .

[29]  Madhumangal Pal,et al.  Intuitionistic Neutrosophic Set , 2009 .

[30]  D. Dubois,et al.  An introduction to bipolar representations of information and preference , 2008 .

[31]  Lulu Zhang,et al.  YinYang bipolar logic and bipolar fuzzy logic , 2004, Inf. Sci..

[32]  Jun-Sheng Duan,et al.  The transitive closure, convergence of powers and adjoint of generalized fuzzy matrices , 2004, Fuzzy Sets Syst..

[33]  Kwai-Sang Chin,et al.  An eigenvector method for generating normalized interval and fuzzy weights , 2006, Appl. Math. Comput..

[34]  Barbara Pekala,et al.  Equivalent bipolar fuzzy relations , 2010, Fuzzy Sets Syst..

[35]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[36]  C. Drossos,et al.  Correspondence analysis with fuzzy data: The fuzzy eigenvalue problem , 2007, Fuzzy Sets Syst..

[37]  M. Pal,et al.  Circulant Triangular Fuzzy Number Matrices , 2008 .