Resolution of fuzzy relational equations - Method, algorithm and software with applications

Analytical methods and algorithms for inverse problem resolution of fuzzy linear systems of equations in some BL-algebras (Godel algebra in case of max-min and min-max compositions, and Goguen algebra in case of max-product composition) are presented. Algorithms with software realization for solving fuzzy linear systems of equations are proposed. Applications include fuzzy optimization with fuzzy linear systems of equation constraint, fuzzy machines and covering problem.

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

[2]  K. Peeva.  Fuzzy linear systems , 1992 .

[3]  K. Peeva,et al.  Systems of linear equations over a bounded chain , 1986, Acta Cybernetica.

[4]  W. Issel,et al.  Aho, A. V. / Hopcroft, J. E. / Ullman, J. D., The Design and Analysis of Computer Algorithms. London‐Amsterdam‐Don Mills‐Sydney. Addison‐Wesley Publ. Comp. 1974 X, 470 S., $ 24,– , 1979 .

[5]  Yordan Kyosev,et al.  Algorithm for Solving Max-product Fuzzy Relational Equations , 2007, Soft Comput..

[6]  C. Pappis,et al.  A computer algorithm for the solution of the inverse problem of fuzzy systems , 1991 .

[7]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[8]  Eugene S. Santos,et al.  Max-product machines , 1972 .

[9]  Ada Lettieri,et al.  Relation equations in residuated lattices , 1989 .

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

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

[12]  Ketty Peeva,et al.  Resolution of Min-Max Fuzzy Relational Equations , 2004 .

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

[14]  Yan-Kuen Wu,et al.  An Efficient Procedure for Solving a Fuzzy Relational Equation With Max–Archimedean t-Norm Composition , 2008, IEEE Transactions on Fuzzy Systems.

[15]  Shu-Cherng Fang,et al.  On the resolution and optimization of a system of fuzzy relational equations with sup-T composition , 2008, Fuzzy Optim. Decis. Mak..

[16]  C. Pappis,et al.  Some results on the resolution of fuzzy relation equations , 1993 .

[17]  Paul P. Wang,et al.  Fuzzy relation equations (I): the general and specialized solving algorithms , 2002, Soft Comput..

[18]  Katarína Cechlárová,et al.  A note on unsolvable systems of max–min (fuzzy) equations , 2000 .

[19]  Yan-Kuen Wu,et al.  Minimizing a Linear Objective Function with Fuzzy Relation Equation Constraints , 2002, Fuzzy Optim. Decis. Mak..

[20]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[21]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[22]  M. Sugeno,et al.  Fuzzy relational equations and the inverse problem , 1985 .

[23]  Chi-Tsuen Yeh,et al.  On the minimal solutions of max-min fuzzy relational equations , 2008, Fuzzy Sets Syst..

[24]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[25]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

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

[27]  Vilém Novák,et al.  Algebraic analysis of fuzzy systems , 2007, Fuzzy Sets Syst..

[28]  Jun-Lin Lin,et al.  On fuzzy relational equations and the covering problem , 2011, Inf. Sci..

[29]  Jun-Lin Lin,et al.  On the relation between fuzzy max-Archimedean t-norm relational equations and the covering problem , 2009, Fuzzy Sets Syst..

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

[31]  Masoud Nikravesh,et al.  Fuzzy Partial Differential Equations and Relational Equations , 2004 .

[32]  Masaaki Miyakoshi,et al.  Lower solutions of systems of fuzzy equations , 1986 .

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

[34]  R. Tennant.  Algebra , 1941, Nature.

[35]  Jiranut Loetamonphong,et al.  An efficient solution procedure for fuzzy relation equations with max-product composition , 1999, IEEE Trans. Fuzzy Syst..

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

[37]  Ute St. Clair,et al.  Fuzzy Set Theory: Foundations and Applications , 1997 .

[38]  K. Peeva,et al.  Computing behavior of finite fuzzy machines - Algorithm and its application to reduction and minimization , 2008, Inf. Sci..

[39]  Eugene S. Santos,et al.  Maximin, minimax, and composite sequential machines , 1968 .

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

[41]  G. Grätzer.  General Lattice Theory , 1978 .

[42]  Shu-Cherng Fang,et al.  A survey on fuzzy relational equations, part I: classification and solvability , 2009, Fuzzy Optim. Decis. Mak..

[43]  Bih-Sheue Shieh,et al.  New Resolution of Finite Fuzzy Relation Equations with Max-Min Composition , 2008, Int. J. Uncertain. Fuzziness Knowl. Based Syst..