On the minimal solutions of max-min fuzzy relational equations

In this paper, the minimal solutions of max-min fuzzy relational equations are investigated. A sufficient and necessary condition, for discriminating whether a given solution is minimal or not, is shown. Furthermore, we propose a new algorithm for computing all minimal solutions less than or equal to a given one.

[1]  Salvatore Sessa,et al.  Fuzzy relation equations for coding/decoding processes of images and videos , 2005, Inf. Sci..

[2]  Antonio di Nola,et al.  Lukasiewicz transform and its application to compression and reconstruction of digital images , 2007, Inf. Sci..

[3]  S. Kagei Fuzzy relational equation with defuzzification - algorithm for the largest solution , 2001, Fuzzy Sets Syst..

[4]  B. Baets Analytical solution methods for fuzzy relational equations. , 2000 .

[5]  Cheng Lichun,et al.  The fuzzy relation equation with union or intersection preserving operator , 1988 .

[6]  Wang Xue-ping Infinite fuzzy relational equations on a complete Brouwerian lattice , 2003 .

[7]  Shu-Cherng Fang,et al.  Solving nonlinear optimization problems with fuzzy relation equation constraints , 2001, Fuzzy Sets Syst..

[8]  Hideyuki Imai,et al.  Unattainable solutions of a fuzzy relation equation , 1998, Fuzzy Sets Syst..

[9]  Yordan Kyosev,et al.  Fuzzy Relational Calculus - Theory, Applications and Software , 2004, Advances in Fuzzy Systems - Applications and Theory.

[10]  Bih-Sheue Shieh,et al.  Solutions of fuzzy relation equations based on continuous t-norms , 2007, Inf. Sci..

[11]  Amin Ghodousian,et al.  Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition , 2006, Appl. Math. Comput..

[12]  Song-Chol Han,et al.  A new kind of fuzzy relation equations based on inner transformation , 2005 .

[13]  Katarína Cechlárová Unique solvability of max-min fuzzy equations and strong regularity of matrices over fuzzy algebra , 1995, Fuzzy Sets Syst..

[14]  Martin Gavalec Solvability and unique solvability of max-min fuzzy equations , 2001, Fuzzy Sets Syst..

[15]  Witold Pedrycz,et al.  A motion compression/reconstruction method based on max t-norm composite fuzzy relational equations , 2006, Inf. Sci..

[16]  Xue-ping Wang Method of solution to fuzzy relation equations in a complete Brouwerian lattice , 2001, Fuzzy Sets Syst..

[17]  E. Babolian,et al.  Numerical solution of fuzzy max-min systems , 2006, Appl. Math. Comput..

[18]  Masoud Allame,et al.  Iteration algorithm for solving Ax , 2006, Appl. Math. Comput..

[19]  Amin Ghodousian,et al.  An algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition , 2006, Appl. Math. Comput..

[20]  Yan-Kuen Wu,et al.  Minimizing a linear function under a fuzzy max-min relational equation constraint , 2005, Fuzzy Sets Syst..

[21]  W. Pedrycz,et al.  Fuzzy Relation Equations and Their Applications to Knowledge Engineering , 1989, Theory and Decision Library.

[22]  Hideyuki Imai,et al.  Some properties of minimal solutions for a fuzzy relation equation , 1997, Fuzzy Sets Syst..

[23]  G. Klir,et al.  Resolution of finite fuzzy relation equations , 1984 .

[24]  Elie Sanchez,et al.  Resolution of Composite Fuzzy Relation Equations , 1976, Inf. Control..

[25]  Spyros G. Tzafestas,et al.  Resolution of composite fuzzy relation equations based on Archimedean triangular norms , 2001, Fuzzy Sets Syst..

[26]  Amin Ghodousian,et al.  Solving linear optimization problems with max-star composition equation constraints , 2006, Appl. Math. Comput..

[27]  Kaoru Hirota,et al.  On various eigen fuzzy sets and their application to image reconstruction , 2006, Inf. Sci..

[28]  A. V. Markovskii,et al.  On the relation between equations with max-product composition and the covering problem , 2005, Fuzzy Sets Syst..

[29]  Wen-June Wang,et al.  New algorithms for solving fuzzy relation equations , 2002, Math. Comput. Simul..

[30]  Shu-Cherng Fang,et al.  Solving fuzzy relation equations with a linear objective function , 1999, Fuzzy Sets Syst..

[31]  Amin Ghodousian,et al.  Solving a linear programming problem with the convex combination of the max-min and the max-average fuzzy relation equations , 2006, Appl. Math. Comput..

[32]  Xue-ping Wang,et al.  Some properties of sup-min fuzzy relational equations on infinite domains , 2005, Fuzzy Sets Syst..

[33]  D. Grant Fisher,et al.  Solution algorithms for fuzzy relational equations with max-product composition , 1998, Fuzzy Sets Syst..

[34]  Jiranut Loetamonphong,et al.  Multi-objective optimization problems with fuzzy relation equation constraints , 2002, Fuzzy Sets Syst..

[35]  Jiranut Loetamonphong,et al.  Optimization of fuzzy relation equations with max-product composition , 2001, Fuzzy Sets Syst..

[36]  W. Pedrycz,et al.  Fuzzy relation equations on a finite set , 1982 .