Building a Type-2 Fuzzy Qualitative Regression Model

Yicheng Wei; Junzo Watada

doi:10.20965/jaciii.2012.p0527

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JACIII Vol.16 No.4 pp. 527-532

doi: 10.20965/jaciii.2012.p0527

(2012)

Paper:

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Building a Type-2 Fuzzy Qualitative Regression Model

Yicheng Wei and Junzo Watada

Graduate School of Information, Production and Systems, Waseda University, 2-7 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan

Received:

December 29, 2011

Accepted:

April 15, 2012

Published:

June 20, 2012

Keywords:

type-2 fuzzy qualitative regression model, quantification, type-1 fuzzy set, type-2 fuzzy set, linear programming

Abstract

Type-1 fuzzy regression model is constructed with type-1 fuzzy coefficients dealing with real value inputs and outputs. From the fuzzy set-theoretical point of view, uncertainty also exists when associated with qualitative data (membership degrees). This paper intends to build a qualitative regression model to measure uncertainty by applying the type-2 fuzzy set as the model’s coefficients. We are thus able to quantitatively describe the relationship between qualitative object variables and qualitative values of multivariate attributes (membership degree or type-1 fuzzy set), which are given by subjective recognition and judgment. We will build a basic qualitative model first and then improve it capable of ranging inputs. We will also give a heuristic solution in the end.

Cite this article as:

Y. Wei and J. Watada, “Building a Type-2 Fuzzy Qualitative Regression Model,” J. Adv. Comput. Intell. Intell. Inform., Vol.16, No.4, pp. 527-532, 2012.

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References

[1] C. Hayashi, “On the Quantification of Qualitative Data from the Mathematico-Statistical Point of View,” Annals of the Institute of Statistical Mathematics, Vol.2, No.1, pp. 35-47, 1950.
[2] C. Hayashi, “On the Prediction of Phenomena from Qualitative Data and the Quantification of Qualitative Data from the Mathmatico-Statistical Point of View,” Annals of the Institute of Statistical Mathematics, Vol.3, pp. 69-98, 1952.
[3] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, No.3, pp. 338-353, 1965.
[4] J. Watada and H. Tanaka, “Fuzzy quantification methods,” In Proc. of the 2nd IFSA Congress, Tokyo, pp. 66-69, 1987.
[5] L. A. Zadeh, “The Concept of a Linguistic Variable and its Application to Approximate Reasoning-1,” Information Sciences, Vol.8, No.3, pp. 199-249, 1975.
[6] H. Tanaka and K. Asai, “Fuzzy linear programming problems with fuzzy number,” Fuzzy Sets and Systems, Vol.13, No.1, pp. 1-10, 1984.
[7] H. Tanaka, I. Hayashi, and J. Watada, “Possibilistic linear regression for fuzzy data,” European J. of Operational Research, Vol.40, No.3, pp. 389-396, 1989.
[8] H. Tanaka and J. Watada, “Possibilistic linear systems and their application,” Int. J. of Fuzzy Sets and Systems, Vol.27, No.3, pp. 275-289, 1988.
[9] J.Watada and W. Pedrycz, “A Possibilistic Regression Approach to Acquisition of Linguistic Rules,” In Handbook on Granular Commutation, W. Pedrycz, A. Skowron, and V. Kreinovich (Eds.), ch.32, John Wiley and Sons, Chichester, pp.719-740, 2008.
[10] J. Watada, S. Wang, and W. Pedrycz, “Building Confidence-Interval-Based Fuzzy Random Regression Models,” IEEE Trans. on Fuzzy Systems, Vol.17, Issue 6, pp. 1273-1283, 2009.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] C. Hayashi, “On the Quantification of Qualitative Data from the Mathematico-Statistical Point of View,” Annals of the Institute of Statistical Mathematics, Vol.2, No.1, pp. 35-47, 1950.

[2] [2] C. Hayashi, “On the Prediction of Phenomena from Qualitative Data and the Quantification of Qualitative Data from the Mathmatico-Statistical Point of View,” Annals of the Institute of Statistical Mathematics, Vol.3, pp. 69-98, 1952.

[3] [3] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, No.3, pp. 338-353, 1965.

[4] [4] J. Watada and H. Tanaka, “Fuzzy quantification methods,” In Proc. of the 2nd IFSA Congress, Tokyo, pp. 66-69, 1987.

[5] [5] L. A. Zadeh, “The Concept of a Linguistic Variable and its Application to Approximate Reasoning-1,” Information Sciences, Vol.8, No.3, pp. 199-249, 1975.

[6] [6] H. Tanaka and K. Asai, “Fuzzy linear programming problems with fuzzy number,” Fuzzy Sets and Systems, Vol.13, No.1, pp. 1-10, 1984.

[7] [7] H. Tanaka, I. Hayashi, and J. Watada, “Possibilistic linear regression for fuzzy data,” European J. of Operational Research, Vol.40, No.3, pp. 389-396, 1989.

[8] [8] H. Tanaka and J. Watada, “Possibilistic linear systems and their application,” Int. J. of Fuzzy Sets and Systems, Vol.27, No.3, pp. 275-289, 1988.

[9] [9] J.Watada and W. Pedrycz, “A Possibilistic Regression Approach to Acquisition of Linguistic Rules,” In Handbook on Granular Commutation, W. Pedrycz, A. Skowron, and V. Kreinovich (Eds.), ch.32, John Wiley and Sons, Chichester, pp.719-740, 2008.

[10] [10] J. Watada, S. Wang, and W. Pedrycz, “Building Confidence-Interval-Based Fuzzy Random Regression Models,” IEEE Trans. on Fuzzy Systems, Vol.17, Issue 6, pp. 1273-1283, 2009.