Fuzzy Calculus Core FC2ore

Software package for fuzzy relational calculus tasks with applications.

This package is created with the highly appreciated theoretical help and under the supervision of Prof. DSc. Ketty Peeva.
Theoretical results and methods can be found in:
1. B. De Baets, Analytical solution methods for fuzzy relational equations, in the series: Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, D. Dubois and H. Prade (eds.), Vol. 1, Kluwer Academic Publishers, pp. 291-340 (2000).
2. Di Nola, A., Lettieri, A.: Relation Equations in Residuated Lattices. Rendiconti del Circolo Matematico di Palermo, s. II, XXXVIII, pp.246-256 (1989).
3. A. Di Nola, S. Sessa, W. Pedrycz, E. Sanchez, Fuzzy Relation Equations and Their Applications to Knowledge Engineering, Kluwer Academic Press, Boston, 1989.
4. G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall PTR, NJ, 1995.
5. G. Klir, U. H. St. Clair, B. Yuan, Fuzzy Set Theory Foundations and Applications, Prentice Hall PRT, 1997.
6. K. Peeva, Finite L-Fuzzy Machines, Fuzzy Sets and Systems, Vol 141, No 3, 2004, pp. 415-437.
7. K. Peeva, Universal algorithm for solving fuzzy relational equations, Italian Journal of Pure and Applied Mathematics 19, 2006, pp. 9-20.
8. K. Peeva, Y. Kyosev, Fuzzy Relational Calculus-Theory, Applications and Software (with CD-ROM), In the series Advances in Fuzzy Systems - Applications and Theory, Vol. 22, World Scientific Publishing Company, 2004.
9. K. Peeva, Y. Kyosev, Algorithm for Solving Max-product Fuzzy Relational Equations, Soft Computing 11(7), 2007, pp. 593-605.
10. K. Peeva, Zl. Zahariev, Software for Testing Linear Dependence in Fuzzy Algebra, Second International Scientific Conference Computer Science, Chalkidiki, 30 Sept -2 Oct 2005, ISBN 954 438 526 6, part I, pp 294-299, 2005.
11. K. Peeva, Zl. Zahariev, Linear dependence in fuzzy algebra, Proceedings of 31th International Conference AMЕE, Sozopol June 2005 Softrade, Sofia 2006, ISBN 10: 954-334-032-3, pp. 71-83.
12. K. Peeva, Zl, Zahariev, Iv. Atanasov, Optimization of Linear Objective Function Under Max-product Fuzzy Relational Constraint, Proceedings of the 9th WSEAS International Conference on FUZZY SYSTEMS (FS’08) – Advanced Topics on Fuzzy Systems, Book Series: Artificial Intelligence Series- WSEAS, Sofia, Bulgaria, May 2-4, 2008, ISBN: 978-960-6766-56-5, ISSN: 1790-5109, 132-137.
13. K. Peeva, Zl. Zahariev, Computing behavior of finite fuzzy machines – Algorithm and its application to reduction and minimization, Information Sciences, Vol. 178 (2008) issue 21, 4152-4165.
14. K. Peeva, D. Petrov, Optimization of linear objective function under fuzzy equation constraint in BL-algebras – theory, algorithm and software, Springer Series "Studies in Computational Intelligence" V. Sgurev, M. Hadjiski. (eds), A post conference IEEE IS'08 volume in SCI-Springer Verlag. Topic: Intelligent Systems - from Theory to Practice, Scope: Advanced Intelligent Systems ISSN: 1860-949X, http://www.springer.com/series/7092 (in press).
15. K. Peeva, Zl. Zahariev, I. Atanasov, Software for optimization of linear objective function with fuzzy relational constraint, Fourth International IEEE Conference on Intelligent Systems, Sept. 2008, Varna, Vol. 3 (2008), pp. 18-14–18-19, ISBN 978-I-4244-1739.
16. I. Perfilieva, L. Noskova, System of fuzzy relation equations with inf-? composition: complete sets of solutions, Fuzzy Sets and Systems 150, 17, 2256-2271.
17. E. Sanchez, Resolution of composite fuzzy relation equations, Information and Control, 30 (1976) 38-48.
18. Z. Zahariev, Software Packages to Deal with Fuzzy Systems, in Proceedings of 33rd International Conference Application of Mathematics in Engineering and Economics’33, M. Todorov (ed.) American Institute of Physics, 978-0-7354-0460, 2007, 217-278.
19. Z. Zahariev, Solving Max-min Relational Equations. Software and Applications, in International conference on Applications of Mathematics in Engineering and Economics, June 2008, Sozopol, Bulgaria, December 2008, pp 516-523.
20. Z. Zahariev, Software package and API in MATLAB for working with fuzzy algebras, In International Conference "Applications of Mathematics in Engineering and Economics (AMEE'09)", AIP Conference Proceedings, vol. 1184, G. Venkov, R. Kovatcheva, V. Pasheva (eds.) American Institute of Physics, ISBN 978-0-7354-0750-9, 2009, 434-350.
Supported operations:
I. Fuzzy matrices compositions:
Max-Min
Min-Max
Max-Product
Max-Epsilon
Min-Godel
Min-Goguen
Min-Lukasiewicz
II. Linear combinations, checking linear independence.

III. Direct and inverse problems resolution for fuzzy linear systems of equations and inequalities with the following compositions:
Max-Min
Min-Max
Max-Product
Min-Godel
Min-Goguen
Min-Lukasiewicz

IV. Solving fuzzy optimization problems.

V. Fuzzy machines - find, minimize and reduce behavior and full behavior matrices.