An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process

Nenad Stojanovic

doi:doi:10.11648/j.ijmfs.20200602.12

| Peer-Reviewed

An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process

Nenad Stojanovic

Published in International Journal of Management and Fuzzy Systems (Volume 6, Issue 2)

Received: 18 September 2020 Accepted: 6 October 2020 Published: 13 October 2020

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The input and output variables in fuzzy systems are linguistic variables. The base of the fuzzy rule represents the central part of a fuzzy controller, and the fuzzy rule represents its basic part, and it has the following form: "if R then P", where R and P represent the fuzzy relation, i.e. the proposition. Complex systems described by fuzzy relations generate a large number of inference rules. Grouping the states into clusters on the basis of which we make conclusions about the value of the output variable is performed by an expert based on his or her experience and knowledge. Ideally, the number of clusters should correspond to the number of attributes by which the value of the output variable is classified, which, in reality is not the case. In the absence of experts, we perform grouping on the basis of some of the criteria. One way of grouping descriptive states into clusters is presented in this paper. It presents a construction of the method of grouping descriptive states of fuzzy models, with the aim of drawing conclusions about the value of the output variable described by a given state. The presented method of grouping descriptive states is based on defined characteristic values associated with fuzzy numbers by which the input variables of the model are evaluated. They represent the basis for defining the characteristic value of the descriptive state of the output variable of a fuzzy model. For the presented method, a mathematical logical argumentation of the application is given, as an algorithm for the application of the constructed method. The application of the algorithm is demonstrated in measuring the economic dimension of the sustainability of tourism development, measured by comparative evaluation indicators.

Published in	International Journal of Management and Fuzzy Systems (Volume 6, Issue 2)
DOI	10.11648/j.ijmfs.20200602.12
Page(s)	29-46
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Data Clustering, Reduction of Inference Rules, Algorithms, Mathematical Modeling, FLC Processes

References

[1]	Jovicic, D., Turizam i zivotna sredina-koncepcija odrzivog turizma, Zaduzbina Andrijevic, Beograd. (2000).
[2]	Pap, E., Fazi mjere i njihova primjena, Univerzitet u Novom Sadu, PMF, Novi Sad. (1999).
[3]	Teodorovic, D., Kikuchi, S.: Uvod u teoriju fuzzy skupova i primjene u saobracaju, Saobracajni fakultet u Beogradu. (1994).
[4]	Ma, Z.; Zhang, F.; Yan, L.; Cheng, J., Fuzzy Knowledge Management for the Semantic Web, XI, 275 p. 67 illus, Hardcover, Springer-Verlag Berlin Heidelberg, (2014).
[5]	Zadeh, L. A., The concept of a lingustic variable and its application to aproximate reasoning, American Elsevire Publishing Company, (1973).
[6]	Mamdani, H. E., Application of fuzzy logic to approximative reasoning using linguistic systems, IEEE Transc Computer,(26) pp. 1189-1191. (1987).
[7]	Kovacic, Z., Bogdan, S. Inteligentno upravljanje sustavima, Fakultet elektrotehnike i racunarstva, Univerzitet u Zagrebu, Zagreb, (2000).
[8]	Hans, M.; Applied fuzzy aritmetic-an intraduction with engineering applications, Springer, (2005).
[9]	Stojanovic, N., Primjena teorije fazi skupova na odredjivanje inteziteta održivog razvoja turizma u zaštićenim područjima, PMF, Novi Sad, Disertacija. (2007).
[10]	Stojanovic, N., Mathematical modling with fuzzy sets of sustainable tourism development, Interdisciplinary Description of Complex Systems 9 (2), 134-160, (2011).
[11]	Stojanovic, N.: Application of Fuzzy Logic in Modeling Market Brand Value. American Journal of Mathematical and Computer Modelling. Vol. 4, No. 1. pp. 1-15.(2019). doi: 10.11648/j.ajmcm.20190401.11
[12]	Stojanovic, N.,: Measurung sustainability of touri sm development-Aplication of fuzzy logic, LAP Lambert, Academic Publishing, Saarbrucken, Germany, (2015).
[13]	Cupic, M., Basic,. D., B., Golub, M.: Neizrazito, evolucijsko i neuroracunarstvo. Zagreb. (2013).
[14]	Braee, M., Rutherford, A. D.: Theoretical and Linguistic Aspects of the Fuzzy Logic Controller, Automatica. Vol. 15. pp. 553-577. (1979).
[15]	N. S. Sivanandam, N. S., Sumathi, S. Deepa, S. N., Introducion to Fuzzy Logic using MATLAB, Springer, Verlag Berlin Heidelberg. (2007).

Cite This Article

Plain Text BibTeX RIS

APA Style

Nenad Stojanovic. (2020). An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process. International Journal of Management and Fuzzy Systems, 6(2), 29-46. https://doi.org/10.11648/j.ijmfs.20200602.12

Copy | Download

ACS Style

Nenad Stojanovic. An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process. Int. J. Manag. Fuzzy Syst. 2020, 6(2), 29-46. doi: 10.11648/j.ijmfs.20200602.12

Copy | Download

AMA Style

Nenad Stojanovic. An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process. Int J Manag Fuzzy Syst. 2020;6(2):29-46. doi: 10.11648/j.ijmfs.20200602.12

Copy | Download

@article{10.11648/j.ijmfs.20200602.12,
  author = {Nenad Stojanovic},
  title = {An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {6},
  number = {2},
  pages = {29-46},
  doi = {10.11648/j.ijmfs.20200602.12},
  url = {https://doi.org/10.11648/j.ijmfs.20200602.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20200602.12},
  abstract = {The input and output variables in fuzzy systems are linguistic variables. The base of the fuzzy rule represents the central part of a fuzzy controller, and the fuzzy rule represents its basic part, and it has the following form: "if R then P", where R and P represent the fuzzy relation, i.e. the proposition. Complex systems described by fuzzy relations generate a large number of inference rules. Grouping the states into clusters on the basis of which we make conclusions about the value of the output variable is performed by an expert based on his or her experience and knowledge. Ideally, the number of clusters should correspond to the number of attributes by which the value of the output variable is classified, which, in reality is not the case. In the absence of experts, we perform grouping on the basis of some of the criteria. One way of grouping descriptive states into clusters is presented in this paper. It presents a construction of the method of grouping descriptive states of fuzzy models, with the aim of drawing conclusions about the value of the output variable described by a given state. The presented method of grouping descriptive states is based on defined characteristic values associated with fuzzy numbers by which the input variables of the model are evaluated. They represent the basis for defining the characteristic value of the descriptive state of the output variable of a fuzzy model. For the presented method, a mathematical logical argumentation of the application is given, as an algorithm for the application of the constructed method. The application of the algorithm is demonstrated in measuring the economic dimension of the sustainability of tourism development, measured by comparative evaluation indicators.},
 year = {2020}
}

Copy | Download

TY - JOUR
T1 - An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process
AU - Nenad Stojanovic
Y1 - 2020/10/13
PY - 2020
N1 - https://doi.org/10.11648/j.ijmfs.20200602.12
DO - 10.11648/j.ijmfs.20200602.12
T2 - International Journal of Management and Fuzzy Systems
JF - International Journal of Management and Fuzzy Systems
JO - International Journal of Management and Fuzzy Systems
SP - 29
EP - 46
PB - Science Publishing Group
SN - 2575-4947
UR - https://doi.org/10.11648/j.ijmfs.20200602.12
AB - The input and output variables in fuzzy systems are linguistic variables. The base of the fuzzy rule represents the central part of a fuzzy controller, and the fuzzy rule represents its basic part, and it has the following form: "if R then P", where R and P represent the fuzzy relation, i.e. the proposition. Complex systems described by fuzzy relations generate a large number of inference rules. Grouping the states into clusters on the basis of which we make conclusions about the value of the output variable is performed by an expert based on his or her experience and knowledge. Ideally, the number of clusters should correspond to the number of attributes by which the value of the output variable is classified, which, in reality is not the case. In the absence of experts, we perform grouping on the basis of some of the criteria. One way of grouping descriptive states into clusters is presented in this paper. It presents a construction of the method of grouping descriptive states of fuzzy models, with the aim of drawing conclusions about the value of the output variable described by a given state. The presented method of grouping descriptive states is based on defined characteristic values associated with fuzzy numbers by which the input variables of the model are evaluated. They represent the basis for defining the characteristic value of the descriptive state of the output variable of a fuzzy model. For the presented method, a mathematical logical argumentation of the application is given, as an algorithm for the application of the constructed method. The application of the algorithm is demonstrated in measuring the economic dimension of the sustainability of tourism development, measured by comparative evaluation indicators.
VL - 6
IS - 2
ER -

Copy | Download

Author Information

Nenad Stojanovic

Faculty of Agriculture, University of Banja Luka, Banja Luka, Bosnia and Herzegovina

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Nenad Stojanovic. (2020). An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process. International Journal of Management and Fuzzy Systems, 6(2), 29-46. https://doi.org/10.11648/j.ijmfs.20200602.12

Copy | Download

ACS Style

Nenad Stojanovic. An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process. Int. J. Manag. Fuzzy Syst. 2020, 6(2), 29-46. doi: 10.11648/j.ijmfs.20200602.12

Copy | Download

AMA Style

Nenad Stojanovic. An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process. Int J Manag Fuzzy Syst. 2020;6(2):29-46. doi: 10.11648/j.ijmfs.20200602.12

Copy | Download

@article{10.11648/j.ijmfs.20200602.12,
  author = {Nenad Stojanovic},
  title = {An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {6},
  number = {2},
  pages = {29-46},
  doi = {10.11648/j.ijmfs.20200602.12},
  url = {https://doi.org/10.11648/j.ijmfs.20200602.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20200602.12},
  abstract = {The input and output variables in fuzzy systems are linguistic variables. The base of the fuzzy rule represents the central part of a fuzzy controller, and the fuzzy rule represents its basic part, and it has the following form: "if R then P", where R and P represent the fuzzy relation, i.e. the proposition. Complex systems described by fuzzy relations generate a large number of inference rules. Grouping the states into clusters on the basis of which we make conclusions about the value of the output variable is performed by an expert based on his or her experience and knowledge. Ideally, the number of clusters should correspond to the number of attributes by which the value of the output variable is classified, which, in reality is not the case. In the absence of experts, we perform grouping on the basis of some of the criteria. One way of grouping descriptive states into clusters is presented in this paper. It presents a construction of the method of grouping descriptive states of fuzzy models, with the aim of drawing conclusions about the value of the output variable described by a given state. The presented method of grouping descriptive states is based on defined characteristic values associated with fuzzy numbers by which the input variables of the model are evaluated. They represent the basis for defining the characteristic value of the descriptive state of the output variable of a fuzzy model. For the presented method, a mathematical logical argumentation of the application is given, as an algorithm for the application of the constructed method. The application of the algorithm is demonstrated in measuring the economic dimension of the sustainability of tourism development, measured by comparative evaluation indicators.},
 year = {2020}
}

Copy | Download