TARU PUBLICATIONS
Journal of Statistics and Management Systems cover

Journal of Statistics and Management Systems

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0014·ISSN (Print): 0972-0510

Indexed in ABDC Australia

Powered by:Powered by

Monthly Journal: Publishes peer-reviewed aticles on theoretical and applied statistics and management systems, expoloring industrial statistics, actuarial and decision sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Statistics and Management Systems
Open Access Research Article

Possibilistic linear and quadratic regression analysis for fuzzy random data and application

* ,

* Corresponding author · click or hover a name for details

pp. 1095–1115Vol. 27Issue 6September 2024DOI: 10.47974/JSMS-1031XML
Received:
07 Jun 2022
Accepted:
13 Sep 2022
Published Online:
19 Sep 2024
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1031
Pages:
1095–1115

Abstract

Regression is the study of how the distribution of response varies as the values of its predictors change. Regression models are employed in almost every area of science and engineering and are essential tools for analyzing data. Sometimes obtained data may be in the form of fuzzy uncertainty along with the associated probabilities. As such, it may be interesting and required to develop the corresponding regression models to figure out the process. Accordingly, in this work, the perception of fuzzy random variables (FRV) and associated expectations are discussed in the regression models. Linear and quadratic fuzzy random regression models have been investigated based on fuzzy random data to approximate the fuzzy coefficients. Trapezoidal fuzzy numbers have been considered to express both fuzzy input and fuzzy output variables. Finally, some problems have also been solved to illustrate the application of the current approach.

Keywords

Trapezoidal fuzzy numberFuzzy random variableExpectation valueFuzzy random linearQuadratic regression model

Subject Classifications

62J8662M1003E72

References

[1] Zadeh, L. A. Fuzzy sets. Information and control, 8(3), 338-353 (1965).
[2] Zadeh, L. A. Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 1(1), 3-28 (1978).
[3] Nahmias, S. Fuzzy variables. Fuzzy sets and systems, 1(2), 97-110 (1978).
[4] Sugeno, M. Fuzzy theory IV (Lecture note). J. of SICE, 22, 554-559 (1983).
[5] Asai, H. T. S. U. K., Tanaka, S., & Uegima, K. Linear regression analysis with fuzzy model. IEEE Trans. Systems Man Cybern, 12, 903-907 (1982).
[6] Tanaka, H., & Watada, J. Possibilistic linear systems and their application to the linear regression model. Fuzzy sets and systems, 27(3), 275-289 (1988).
[7] Tanaka, H., Hayashi, I., & Watada, J. Possibilistic linear regression analysis for fuzzy data. European Journal of Operational Research, 40(3), 389-396 (1989).
[8] Bisserier, A., Boukezzoula, R., & Galichet, S. A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals. Information Sciences, 180(19), 3653-3673 (2010).
[9] Chan, K. Y., Kwong, C. K., & Fogarty, T. C. Modeling manufacturing processes using a genetic programming-based fuzzy regression with detection of outliers. Information Sciences, 180(4), 506-518 (2010).
[10] Pourahmad, S., Taghi Ayatollahi, S. M., & Taheri, S. M. Fuzzy logistic regression: a new possibilistic model and its application in clinical vague status. Iranian Journal of Fuzzy Systems, 8(1), 1-17 (2011).
[11] Aliev, R. A., Fazlollahi, B., & Vahidov, R. Genetic algorithms-based fuzzy regression analysis. Soft Computing, 6, 470-475 (2002).
[12] Wang, N., Reformat, M., Yao, W., Zhao, Y., & Chen, X. Fuzzy Linear regression based on approximate Bayesian computation. Applied Soft Computing, 97, 106763 (2020).
[13] Diamond, P. Fuzzy least squares. Information sciences, 46(3), 141-157 (1988).
[14] Celmiņš, A. Least squares model fitting to fuzzy vector data. Fuzzy sets and systems, 22(3), 245-269 (1987).
[15] Papadopoulos, C., Spiliotis, M., Gkiougkis, I., Pliakas, F., & Papadopoulos, B. Relating hydro-meteorological variables to water table in an unconfined aquifer via fuzzy linear regression. Environments, 8(2), 9 (2021).
[16] Khammar, A. H., Arefi, M., & Akbari, M. G. A robust least squares fuzzy regression model based on kernel function. Iranian Journal of Fuzzy Systems, 17(4), 105-119 (2020).
[17] Watada, J. Fuzzy quantification theory type I. The Japanese Journal of Behaviormetrics (The Behaviormetric Society of Japan), 11(1), 66-73 (1983).
[18] Yabuuchi, Y. Fuzzy switching regression model based on genetic algorithm. In Proceedings of the 7th International Fuzzy Systems Association World Congress,  113-118 (1997).
[19] Yabuuchi, Y., & Watada, J. Formulation of fuzzy switching regression model. Official Journal of Japan Association of Intteligent Information and Fuzzy Systems, 16(1), 53-59 (2004).
[20] Tanaka, H., & Lee, H. Interval regression analysis by quadratic programming approach. IEEE Transactions on Fuzzy Systems, 6(4), 473-481 (1998).
[21] Kwakernaak, Huibert. “Fuzzy random variables—I. Definitions and theorems.” Information sciences 15.1 : 1-29 (1978).
[22] Kruse, R., Meyer, K. D., Kruse, R., & Meyer, K. D. On a software tool for statistics with vague data. Statistics with Vague Data, 231-245 (1987).
[23] Liu, Y. K., & Liu, B. Fuzzy random variables: A scalar expected value operator. Fuzzy Optimization and decision making, 2, 143-160 (2003).
[24] Puri, M. L., Ralescu, D. A., & Zadeh, L. Fuzzy random variables. In Readings in fuzzy sets for intelligent systems,  265-271 (1993).
[25] Hesamian, G., & Akbari, M. G. A robust multiple regression model based on fuzzy random variables. Journal of Computational and Applied Mathematics, 388, 113270 (2021).
[26] Yoon, J. H., & Grzegorzewski, P. On Optimal and Asymptotic Properties of a Fuzzy L 2 Estimator. Mathematics, 8(11), 1956 (2020).
[27] Yu, H., Lu, J., Zhang, G., & Wu, D. (2018, July). A dual neural network based on confidence intervals for fuzzy random regression problems. In 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (pp. 1-8). IEEE.
[28] Appadoo, S. S., Kumar, A., & Gajpal, Y. Generalized exponential trapezoidal fuzzy numbers based on variance. Journal of Information and Optimization Sciences, 42(7), 1409-1424 (2021).
[29] Rezvani, S. Ranking generalized exponential trapezoidal fuzzy numbers based on variance. Applied Mathematics and Computation, 262, 191-198 (2015).
[30] Watada, J., & Wang, S. Regression model based on fuzzy random variables. Views on Fuzzy Sets and Systems from Different Perspectives: Philosophy and Logic, Criticisms and Applications, 533-545 (2009).
[31] Chakraverty, S., Sahoo, D. M., Mahato, N. R., Chakraverty, S., Sahoo, D. M., & Mahato, N. R. Fuzzy numbers. Concepts of soft computing: Fuzzy and ANN with programming, 53-69 (2019).
[32] Chakraverty, S., Sahoo, D. M., Mahato, N. R., Chakraverty, S., Sahoo, D. M., & Mahato, N. R. Fuzzy Sets. Concepts of Soft Computing: Fuzzy and ANN with Programming, 25-51 (2019).
[33] Kaufmann, A. Introduction to the theory of fuzzy subsets. Academic press (1975).
[34] Wang, P. Z. Fuzzy contactibility and fuzzy variables. Fuzzy Sets and Systems, 8(1), 81-92 (1982).
[35] Liu, B., & Liu, Y. K. Expected value of fuzzy variable and fuzzy expected value models. IEEE transactions on Fuzzy Systems, 10(4), 445-450 (2002).
[36] Koissi, M. C., & Shapiro, A. F. Credibility theory in a fuzzy environment. In The 47th Actuarial Research conference Proc., University of Manitoba, Canada (2012).
[37] Sanchez, E. Solution of fuzzy equations with extended operations. Fuzzy sets and Systems, 12(3), 237-248 (1984).
[38] Tanaka, H., Shimomura, T., Watada, J., & Asai, K. Fuzzy Linear Regression Analysis Of The Number Of Staff In Local Government (1987).
[39] Watada, J. Applications in business, multiattribute decision—making. Applied fuzzy system, 244-252 (1994).
[40] Mateos, A., & Jiménez, A. A trapezoidal fuzzy numbers-based approach for aggregating group preferences and ranking decision alternatives in MCDM. In Evolutionary Multi-Criterion Optimization: 5th International Conference, EMO 2009, Nantes, France, Proceedings 5 (pp. 365-379). Springer Berlin Heidelberg (2009).

Views: 244Downloads: 75Citations: 0