Application of Type-2 Membership Functions in Fuzzy Logic Systems

Наталія Романівна Кондратенко

Abstract


Background. Developing decision making models for problems, that are not easily formalized, and which operate the expert information, became possible by utilizing the capabilities of fuzzy sets theory and building fuzzy logic systems. Use of fuzzy sets theory techniques for knowledge formalization automatically results in the researcher having to select the type of fuzzy sets used for constructing membership functions, as well as the fuzzy model, that would fit the selected fuzzy set type. Therefore, the task of investigating the capabilities of type-2 membership functions in fuzzy logic systems is one of great interest.

Objective. Expanding the capabilities of fuzzy logic systems by using type-2 membership functions.

Methods. Research methods are directed towards utilizing interval and three-dimensional type-2 fuzzy sets in forecasting problems and medical diagnostics. The matter of investigating the capabilities of interval membership functions built on experimental data will be considered in two aspects: the first one – of how well interval membership functions reflect the uncertainties present in the source data, and the second one – of the advantages and disadvantages of an interval output of a fuzzy model with interval membership functions.

Results. A research of interval type-2 membership functions in fuzzy logic systems was conducted in the areas of forecasting problem and medical diagnostics. Applicability of three-dimensional type-2 membership functions built from experimental data was shown.

Conclusions. This paper shows the advantages of using interval membership functions in fuzzy logic systems, when developing fuzzy models using the multiple models principle. A research of three-dimensional type-2 membership functions’ applicability when modeling existing uncertainties is given. A technique for generating three-dimensional membership functions in fuzzy logic systems generated from experimental data is proposed.


Keywords


Experimental data; Type-2 membership functions; Interval fuzzy model; Three-dimensional membership function

References


А.C. Narinyani, “Underdetermination in the knowledge representation and processing system”, Technicheskaya Kibernetica, no. 5, pp. 3–28, 1986 (in Russian).

L.A. Zadeh, “Fuzzy sets as a basis for theory of possibility”, Fuzzy Sets and Systems 100 Suplements, pp. 9–34, 1999.

J.M. Mendel et al., “Interval type-2 fuzzy logic systems made simple”, IEEE Trans. Fuzzy Systems, vol. 14, no. 6, ­­pp. 808–821, 2006.

A.N. Borisov, Decisions-Making Based on Fuzzy Models. Examples of Use. Moscow, USSR: Mir, 1976, 167 p. (in Russian).

N.R. Kondratenko et al., “Fuzzy logic systems with allowance for the blank in experimental data taken”, Naukovi Visti NTUU KPI, no. 5, pp. 37–41, 2004 (in Ukrainian).

N.R. Kondratenko and O.V. Cheboraka, “Investigation of the capabilities of the aggregation interval type-2 fuzzy model for time series prediction”, Visnik Vinnitskogo Politehnichnogo Instituty, no. 5, pp. 22–27, 2008 (in Ukrainian).

N.R. Kondratenko et al., “Time series prediction using fuzzy models with different input number based on the interval belonging function”, Naukovi Visti NTUU KPI, no. 4, pp. 62–68, 2007 (in Ukrainian).

N.R. Kondratenko et al., “Interval type-2 fuzzy models concerning identification problems of multiple-input multiple output objects”, Sistemy Obrobky Informatsiyi, no. 3, pp. 48–52, 2011 (in Ukrainian).

N.R. Kondratenko and C.M. Kuzemko, “Fuzzy logic systems with the use of general type fuzzy sets”, Naukovi visti NTUU KPI, no. 1, pp. 16–21, 2004 (in Ukrainian).

J. Zeng and Z.Q. Liu, “Type-2 fuzzy sets for pattern classifications: A review”, in Proc. of IEEE Symposium FOCI, Honolulu, Hawaii, April 1–5, 2007, pp. 193–200.

A.G. Ivahnenko, Heuristic Self-Organization Systems in Technical Cybernetics. Kyiv, USSR: Technika, 1971, 372 p. (in Russian).


GOST Style Citations


  1. Нариньяни А.С. Недоопределенность в системе представления и обработки знаний // Техническая кибернетика. – 1986. – № 5. – С. 3–28.

  2. Zadeh L.A. Fuzzy sets as a basis for theory of possibility // Fuzzy Sets and Systems 100 Suplements. – 1999. – P. 9–34.

  3. Mendel J.M., John R.I., Liu F. Interval type-2 fuzzy logic systems made simple // IEEE Trans. Fuzzy Syst. – 2006. – 14,    № 6. – P. 808–821.

  4. Борисов А.Н. Принятие решений на основе нечетких моделей. Примеры использования. – М.: Мир, 1976. – 167 с.

  5. Кондратенко Н.Р., Зелінська Н.Б., Куземко С.М. Нечіткі логічні системи з врахуванням пропусків в експериментальних даних // Наукові вісті НТУУ “КПІ”. – 2004. – № 5. – С. 37–41.

  6. Кондратенко Н.Р., Чеборака О.В. Дослідження можливостей узагальнювальної інтервальної типу-2 нечіткої моделі для прогнозування часових послідовностей // Вісник Вінницького політехн. ін-ту. – 2008. – № 6. – С. 22–27.

  7. Кондратенко Н.Р., Чеборака О.В., Куземко С.М. Прогнозування часових послідовностей з використанням різно­вхо­дових нечітких моделей на основі інтервальних функцій належності // Наукові вісті НТУУ “КПІ”. – 2007. – № 4. – С. 62–68.

  8. Кондратенко Н.Р., Чеборака О.В., Ткачук О.А. Інтервальні нечіткі моделі типу-2 в задачах ідентифікації об’єктів з багатьма входами та виходами // Системи обробки інформації. – 2011. – Вип. 3 (93). – С. 48–52.

  9. Кондратенко Н.Р., Куземко С.М. Нечіткі логічні системи з використанням нечітких множин загального типу // Наукові вісті НТУУ “КПІ”. – 2004. – № 1. – С. 16–21.

  10. Zeng J., Liu Z.Q. Type-2 fuzzy sets for pattern classifications: A review // Proc. IEEE Symposium FOCI, April 1–5, 2007, Honolulu, Hawaii. – Hawaii, 2007. – P. 193–200.

  11. Ивахненко А.Г. Системы эвристической самоорганизации в технической кибернетике. – К.: Техніка, 1971. – 372 с.




DOI: https://doi.org/10.20535/1810-0546.2016.2.51636

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