Identification of structure and parameters of fuzzy cognitive models: expert and statistical methods

Aleksandr Podvesovskii, Ruslan Isaev

Abstract


The paper deals with the problems of structural and parametric identification of cognitive models by the example of Sylov’s fuzzy cognitive maps (FCM). It is demonstrated that the problem of parametric identification can be solved using two types of methods: expert and statistical ones. An approach to the FCM parametric identification is described based on the use of methods for constructing fuzzy set adjectives: T. Saaty’s pairwise comparison method and R. Yager’s method of level sets. Problems arising when applying these methods within the context of the specified task are considered. For both methods, modifications are proposed to solve the identified problems. Also issues of building FCMs based on statistical data are discussed. For the case when data are presented in the form of spatial sampling, a method for identifying FCM parameters is proposed based on the use of multiple regression analysis. For the case when data are presented in the form of time series, a modification of this technique is proposed, which also allows solving the problem of structural identification by applying Granger causality test. Besides, an approach to the construction of FCMs under conditions of processing heterogeneous information is described, based on coordinated application of the expert and statistical methods and techniques under study. The paper presents results of experimental validation of the modified methods and the proposed techniques confirming their efficiency. In the first part of the paper, modifications of methods for constructing fuzzy set adjectives used in FCM parametric identification are described. The second part of the work is devoted to the development and research of methods for constructing FCMs based on statistical information.

Full Text:

PDF (Russian)

References


Avdeeva Z.K., Kovriga S.V., Makarenko D.I. (2007) Kognitivnoe modelirovanie dlja reshenija zadach upravlenija slabostrukturirovannymi sistemami (situacijami) [Cognitive Modeling for Solving Problems of Managing Semi-Structured Systems (Situations)]. Large-scale Systems Control, vol. 16, pp. 26–39 (in Russian).

Borisov V.V., Kruglov V.V., Fedulov A.S. (2012) Nechetkie modeli i seti [Fuzzy Models and Networks]. M.: Gorjachaja linija – Telekom (in Russian).

Silov V.B. (1995) Prinjatie strategicheskih reshenij v nechetkoj obstanovke [Making Strategic Decisions in a Fuzzy Setting]. M.: INPRO-RES (in Russian).

Roberts F.S. (1976) Discrete Mathematical Models, with Applications to Social, Biological, and Environmental Problems. N.J.: Prentice-Hall.

Isaev R.A., Podvesovskii A.G. (2017) Generalized Model of Pulse Process for Dynamic Analysis of Sylov’s Fuzzy Cognitive Maps // CEUR Workshop Proceedings of the Mathematical Modeling Session at the International Conference Information Technology and Nanotechnology (MM-ITNT 2017), Vol. 1904. – pp. 57-63.

Podvesovskii A.G., Lagerev D.G., Korostelev D.A. (2009) Primenenie nechetkih kognitivnyh modelej dlja formirovanija mnozhestva al'ternativ v zadachah prinjatija reshenij [Application of Fuzzy Cognitive Models for Alternatives Set Generation in Decision Problems]. Bulletin of Bryansk state technical university, no 4 (24), pp. 77–84 (in Russian).

Litvak B.G. (2004) Jekspertnye tehnologii v upravlenii [Expert Technologies in Management]. M.: Delo (in Russian).

Podvesovskii A.G., Isaev R.A. (2016) Primenenie mnozhestvennogo regressionnogo analiza dlja parametricheskoj identifikacii nechetkih kognitivnyh modelej [Application of Multiple Regression Analysis for Parametric Identification of Fuzzy Cognitive Models]. Proceedings of the 4th International Conference on Information Technologies for Intelligent Decision Making Support, ITIDS’2016 (Ufa, Russia, May 17–19, 2016), ol. 2, pp. 28–33 (in Russian).

Isaev R.A., Podvesovskii A.G. (2018) Application of time series analysis for structural and parametric identification of fuzzy cognitive models // CEUR Workshop Proceedings of the International Conference Information Technology and Nanotechnology. Session Data Science (DS- ITNT 2018), Vol. 2212. – pp. 119-125.

Saaty T.L. (2001) Decision Making with Dependence and Feedback: The Analytic Network Process. RWS Publications.

Korostelev D.A., Lagerev D.G., Podvesovskii A.G. (2008) Sistema podderzhki prinjatija reshenij na osnove nechetkih kognitivnyh modelej «IGLA» [Decision Support System Based on Fuzzy Cognitive Models «IGLA»]. Proceedings of the 11th Russian Conference on Artificial Intelligence, RCAI-2008 (Dubna, Russia, September 29 – October 3, 2008), vol. 3, pp. 329-336 (in Russian).

Isaev R.A. (2016) Modificirovannyj metod parnyh sravnenij dlja jekspertnoj ocenki parametrov nechetkoj kognitivnoj modeli [Modified Pairwise Comparison Method for Expert Estimation of a Fuzzy Cognitive Model Parameters]. Modern Information Technology and IT-education, vol. 12, no 2, pp. 35–42 (in Russian).

Yager R.R. (1982) Level sets for membership evaluation of fuzzy subset / R.R. Yager // Fuzzy Sets and Possibility Theory: Recent Developments (R.R. Yager, ed.), – Pergamon, NewYork. – pp. 90-97.

Isaev R.A., Podvesovskii A.G. (2017) Ocenka soglasovannosti suzhdenij jeksperta pri postroenii funkcii prinadlezhnosti nechetkogo mnozhestva metodom mnozhestv urovnja [Evaluation of Expert Judgements Consistency When Constructing a Membership Function of Fuzzy Set Using the Method of Level Sets]. Modern Information Technology and IT-education, vol. 13, no 3, pp. 9-15 (in Russian).

Averchenkov V.I., Kozhuhar V.M., Podvesovskii A.G., Sazonova A.S. (2010) Monitoring i prognozirovanie regional'noj potrebnosti v specialistah vysshej nauchnoj kvalifikacii: monografija [Monitoring and Forecasting of Regional Need for Specialists of Higher Scientific Qualification]. Bryansk: BSTU (in Russian).

Makarova E.A., Gabdullina E.R., Zakieva E.Sh., Valiullina K.M. (2016) Algoritmy intellektual'nogo analiza pokazatelej kachestva zhizni v sfere zdravoohranenija na regional'nom urovne [Algorithms for intelligent analysis of life quality in the domain of public health on a regional level]. Proceedings of the 4th International Conference on Information Technologies for Intelligent Decision Making Support, ITIDS’2016 (Ufa, Russia, May 17–19, 2016), vol. 2, pp. 222-228 (in Russian).

Makarova E.A., Gabdullina E.R., Zakieva E.Sh., Makhmutova A.E. (2016) Algoritmy formirovanija znanij dlja postroenija kognitivnoj modeli kachestva zhizni v sfere vysshego obrazovanija na regional'nom urovne [Knowledge generation algorithms for construction of cognitive model of life quality in the domain of high Identification of structure and parameters of fuzzy cognitive models: expert and statistical methods Aleksandr Podvesovskii, Ruslan Isaev education on a regional level]. Proceedings of the 4th International Conference on Information Technologies for Intelligent Decision Making Support, ITIDS’2016 (Ufa,Russia, May 17–19, 2016), vol. 2, pp. 54-59 (in Russian).

Rogachyov A.F., Melikhova E.V. (2014) Problemy statisticheskogo ocenivanija parametrov kognitivnoj karty na osnove korreljacionnogo analiza [Problems of statistical estimation of cognitive map characteristics on the basis of correlation analysis]. Proceedings of the International Conferennce “Physico- Mathematical Sciences: Theory and Practice”, pp.55-62 (in Russian).

Kremer N.Sh., Putko B.A. (2010) Jekonometrika: ucheb. dlja vuzov [Econometrics: a Textbook for High Schools]. Moscow: JuNITIDANA (in Russian).

Isaev R.A., Podvesovskii A.G. Application of time series analysis for structural and parametric identification of fuzzy cognitive models // CEUR Workshop Proceedings of the International Conference Information Technology and Nanotechnology. Session Data Science (DS-ITNT 2018), Vol. 2212. – P. 119-125.

Magnus Ya.R., Katyshev P.K., Persetskii A.A. (2004) Jekonometrika. Nachal'nyj kurs [Econometrics: Basic Course]. – Мoscow: Delo (in Russian).


Refbacks

  • There are currently no refbacks.


Abava  Кибербезопасность IT Congress 2024

ISSN: 2307-8162