Fuzzy Semi-Parametric Partially Cluster-Wise Regression Analysis

Asadollahi, Masoumeh; Akbari, Mohammad Ghasem

doi:10.22055/jamm.2017.13103

Fuzzy Semi-Parametric Partially Cluster-Wise Regression Analysis

Authors

Masoumeh Asadollahi

Mohammad Ghasem Akbari

Department of Statistics, University of Birjand, Birjand, Iran

10.22055/jamm.2017.13103

Abstract

Cluster analysis is one of the most important methods in classification in which the observations of each cluster has maximum similarity in terms of some desirable variables. In general the clustering methods are divided into two parts, crisp and fuzzy. In usual clustering methods an observation is in only one cluster whereas in fuzzy clustering it may fall into two or more clusters simultaneously. Yang and Ko (1996) introduced a fuzzy clustering method. Their method is an extension of the usual k-means clustering method as they assumed that the observations are fuzzy. A fuzzy regression model is used for studying the relationship between the explanatory variables and dependent variable. In some situations when some observations are dispersed and are heterogeneous, the regression model may not have a goodness of fit for data. To solve this problem Yang and Ko classified data and then based on fuzzy observations fitted a regression model to each cluster. In this paper we first explain the semi-parametric regression model introduced by Hesamian et al. [2017] and then use their model to perform our clustering method for fuzzy observations. Finally, based on some suggested goodness of fit criterions. We compare our results with those of Yang and Ko.

Keywords

Fuzzy number

α-pessimistic

Fuzzy clustering

One-stage generalized regression

Semi-parametric regression

Subjects

Statistics

]1[ خالقی گزیک، سارا (1393). مدلهای رگرسیون خطی بر اساس خوشهبندی فازی، پایاننامه کارشناسی ارشد آمار، دانشکده علوم ریاضی و آمار، دانشگاه بیرجند.

]2[ طاهری، سید محمود (1375). آشنایی با نظریه مجموعههای فازی، انتشارات جهاد دانشگاهی دانشگاه فردوسی مشهد.

[3] Arefi, M. (2016). Clustering regression based on interval-valued fuzzy outputs and interval-valued fuzzy parameters. Journal of Intelligent and Fuzzy Systems, 30, 1339–1351.

[4] Bellman, R. Kalaba, R. and Zadeh, L.A. (1966). Abstraction and pattern classification, Journal of Mathematical Analysis and Applications, 13, 1-7.

[5] Bezdek, J.C. (1981). Pattern recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York.

[6] Cannon, R. Dave, J. and Bezdek, J.C. (1986). Efficient implementation of the fuzzy c-means clustering algorithms, IEEE Transactions on Pattern Analysis and Machine Intelligence, 8, 248-255.

[7] Dunn, J.C. (1974). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, Journal of Cybernetics, 3, 32-57.

[8] Hesamian, G. Akbari, M.G. and Asadollahi, M. (2017). Fuzzy semi-parametric partially linear model with fuzzy inputs and fuzzy outputs, Expert Systems with Applications, 71, 230-239.

[9] Liu, B. (2013). Uncertainty Theory, 4^th ed., Springer, Berlin.

[10] Robinson, P. (1988). Root-N-Consistent Semi-parametric Regression, Econometrics, 56, 931–954.

[11] Ruspini, E. (1969). A new approach to clustering, Information and Control, 15, 22-32.

[12] Schnatter, S.F. (1992). On statistical inference for fuzzy data with applications to descriptive statistics, Fuzzy Sets and Systems, 50, 143-165.

[13] Taheri, S.M. and Kelkinnama, M. (2012). Fuzzy linear regression based on least absolute deviations, Iranian Journal of Fuzzy Systems, 9, 121-140.

[14] Yang, M.S. (1993). A survey of fuzzy clustering, Math. Computer Modeling, 18, 1-16.

[15] Yang, M.S. (1993). On a class of fuzzy classification maximum likelihood procedures, Fuzzy Sets and Systems, 57, 365-375.

[16] Yang, M.S. and Ko, C.H. (1996). On a class if fuzzy c-numbers clustering procedures for fuzzy data, Fuzzy Sets and Systems, 84, 49-60.

[17] Yang M.S. and Ko C.H. (1997). On cluster-wise fuzzy regression analysis, IEEE Transactions onSystems, Man, and Cybernetics-Part B: Cybernetics, 27, 1-13.

[18] Zadeh, L.A. (1956). Fuzzy sets, Information and Control, 8, 338-353.