Method of Constructing Type-2 Fuzzy Models with Interval Membership Functions for Diagnostic Systems

Наталія Романівна Кондратенко


Background. Presently, the amounts of data accumulated by researchers in different areas of human activity are increasing dramatically due to rapid development of information technologies. The question of data analysis and knowledge presentation in decision support systems under uncertain conditions is important, namely detecting hidden rules and dependencies; extracting, presenting and processing of incomplete knowledge obtained with the help of experts, or knowledge, obtained as a result of experimental data processing. Since knowledge obtained from experts usually contains different kinds of uncertainty, it is important to look for methods that enable presentation and processing of incomplete or almost contradictory information. Methods of fuzzy set theory are the most suitable for processing of such data.

Objective. Improving the subject area reflection quality by implementing the method of generating type-2 fuzzy models with redundant knowledge bases.

Methods. The implementation method is directed at using redundancy of the fuzzy knowledge base. The knowledge base is built based on experimental data that is used to determine centers of the rules’ antecedents and consequents fuzzy sets. The given approach enables creating a fuzzy knowledge base in reasonable time. In order to build a fuzzy model with some of the values missing in the rules included into the knowledge base by an expert, and with partially missing experimental data, methods of generating fuzzy models based on type-2 fuzzy sets with partial experimental data are introduced. A fuzzy model is represented as an interval type-2 model with interval membership functions. Redundancy reduction and missing input data processing are implemented using optimization procedures. The quality of reflection of input values into output values is analyzed using a fuzzy models functioning quality criterion.

Results. A research of fuzzy type-2 models built using the given method is shown. On an example of a medical diagnostics problem the main parameters of the generated fuzzy models are given, and values of their performance criteria are calculated.

Conclusions. A method for generating type-2 fuzzy models with interval membership functions was developed, which includes rules built based on experimental data, and which provides the capabilities for taking an expert’s opinion into account. As part of the given method it is suggested to use the main and the secondary criteria to assess type-2 fuzzy models performance quality. These two criteria enable the developer of an expert system to make the right choice of the fuzzy model that describes the subject area in the most adequate way.


Type-2 fuzzy model; Interval membership function; Redundant knowledge bases; Expert; Quality criteria


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

Q. Liang and J. Mendel, “Interval Type-2 fuzzy logic systems: theory and design”, IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 535–550, 2000.

Y.P. Zaychenko, Fuzzy Models and Methods in the Intelligent Systems.Kyiv,Ukraine: Slovo, 2008, 344 p. (in Russian).

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

A.P. Rotshtein, Intellectual Technologies of identification: Fuzzy Sets, Genetic Algorithms and Neural Networks.Vinnytsya,Ukraine: UNIVERSUM-Vinnytsya, 1999, 320 p. (in Russian).

N.R. Kondratenko et al., “Diagnosis of hypothyroidism on the basis of fuzzy logic using interval membership function”, Naukovi Visti NTUU KPI, no. 4, pp. 52–57, 2003 (in Ukrainian).

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

GOST Style Citations

  1. Zadeh L.A. Fuzzy sets as a basis for theory of possibility // Fuzzy sets and systems 100 supplements. – 1999. – P. 9–34.

  2. Mendel J.M., John R.I., Liang Q. Interval Type-2 fuzzy logic systems: theory and design // IEEE Trans. Fuzzy Syst. – 2000. – 8. – P. 535–550.

  3. Зайченко Ю.П. Нечеткие модели и методы в интеллектуальных системах. – К.: ИД “Слово”, 2008. – 344 с.

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

  5. Ротштейн А.П. Интеллектуальные технологии идентификации: нечеткие множества, генетические алгоритмы, нейронные сети. – Винница: УНИВЕРСУМ-Вінниця, 1999. – 320 с.

  6. Кондратенко Н.Р., Зелінська Н.Б., Куземко С.М. Діагностика гіпотиреозу на основі нечіткої логіки з використанням інтервальних функцій належності // Наукові вісті НТУУ “КПІ”. – 2003. – № 4. – С. 52–58.

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



  • There are currently no refbacks.

Copyright (c) 2017 NTUU KPI