IF–THEN rules generation based on fuzzy relational equations and genetic algorithm
Keywords:
нечіткі відношення, генерування нечітких правил, налаштування структури правил, розв’язання рівнянь нечітких відношеньAbstract
An approach to IF-THEN rules generation by solving fuzzy relational equations, which allows avoiding rules selection from the set of candidate rules, is suggested in this paper. The system of fuzzy rules can be rearranged as a collection of linguistic solutions of fuzzy relational equations using the composite system of fuzzy terms. Resolution of fuzzy relational equations using the genetic algorithm guarantees the optimal number of fuzzy rules for each output fuzzy term and the optimal geometry of input fuzzy terms for each linguistic solution.References
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Sarma R.D. (ed) Genetic diagnoses. — New York : Nova Science Publishers, 2011. — Pp. 53—97. — ISBN 978-1-61324-866-9
mining / H. Ishibuchi, T. Yamamoto // Fuzzy Sets and Systems. — 2004. — Vol. 141(1). — P. 59 — 88. — ISSN: 0165-0114.
2. Multiobjective genetic fuzzy rule selection of single granularity-based fuzzy classification rules and its interaction with the
lateral tuning of membership functions / [R. Alcala, Y. Nojima, F. Herrera, H. Ishibuchi] // Soft Computing. — 2011. — Vol. 15
(12). — pp. 2303-2318. — ISSN: 1432-7643.
3. Similarity measures in fuzzy rule base simplification / [M. Setnes, R. Babuska, U. Kaymak, H. R. van Nauta Lemke] //
IEEE Transactions on System, Man, Cybernetics. Part B. — 1998. — vol. 28 (3). — Pp. 376—386. — ISSN: 1083-4419.
4. Jin Y. Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement / Y. Jin //
IEEE Transactions on Fuzzy Systems. — 2000. — Vol. 8 (2). — Pp. 212—221. — ISSN 1063-6706.
5. Yager R. Essentials of fuzzy modeling and control / R. Yager, D. Filev. — New York : John Willey & Sons, 1994. —
408 p. — ISBN 0-471-01761-2.
6. Peeva K. Fuzzy relational calculus. Theory, applications and software / K. Peeva, Y. Kyosev. — New York : World Scientific,
2004. — 304 p. — ISBN: 978-981-256-076-6.
7. Rotshtein A. Fuzzy evidence in identification, forecasting and diagnosis / A. Rotshtein, H. Rakytyanska. — Heidelberg :
Springer, 2012. — 314 p. — ISBN 978-3-642-25785-8.
8. Zadeh L. A computational approach to fuzzy quantifiers in natural language / L. Zadeh // Computers and Mathematics with
Applications. — 1983. — Vol. 9. — P. 149—184. — ISSN 0898-1221.
9. Ракитянська Г. Б. Ідентифікація нелінійних залежностей нечіткими правилами і відношеннями / Г. Б. Ракитянська
// Контроль і управління в складних системах КУСС — 2012 : XI Міжн. наук. конф., 9 — 11 жовтня 2012 р.: тези доп. —
Вінниця : ВНТУ, 2012. — C. 255. — ISBN 966-641-187-3.
10. Rotshtein A. Expert rules refinement by solving fuzzy relational equations / A. Rotshtein, H. Rakytyanska // Human System
Interaction HSI — 2013 : VI IEEE Conference, 6 — 8 June, 2013 : Proceedings. — Sopot, Poland, 2013. — Pp. 257—264.
— ISBN 978-1-4673-5636-7.
11. Rotshtein A. Fuzzy logic and the least squares method in diagnosis problem solving / A. Rotshtein, H. Rakytyanska // In:
Sarma R.D. (ed) Genetic diagnoses. — New York : Nova Science Publishers, 2011. — Pp. 53—97. — ISBN 978-1-61324-866-9
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[1]
H. B. Rakytianska, “IF–THEN rules generation based on fuzzy relational equations and genetic algorithm”, Вісник ВПІ, no. 4, pp. 60–69, Aug. 2014.
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