Paper Info
Title
Possibilistic linear regression with fuzzy data: Tolerance approach with prior information.
Abstract
We introduce the tolerance approach to the construction of fuzzy regression coefficients of a possibilistic linear regression model with fuzzy data (both input and output). The method is very general: the only assumption is that α-cuts of the fuzzy data are efficiently computable. We take into account possible prior restrictions of the parameters space: we assume that the restrictions are given by linear and quadratic constraints. The method for construction of the possibilistic regression coefficients is in a reduction of the fuzzy-valued model to an interval-valued model on a given α-cut, which is further reduced to a linear-time method (i.e., running in time O(np)) computing with endpoints of the intervals. (Here, n is the number of observations and p is the number of regression parameters.) The speed of computation makes the method applicable for huge datasets. Unlike various approaches based on mathematical programming formulations, the tolerance-based construction preserves central tendency of the resulting regression coefficients. In addition, we prove further properties: if inputs are crisp and outputs are fuzzy, then the construction preserves piecewise linearity and convex shape of fuzzy numbers. We derive an O(n2p)-algorithm for enumeration of breakpoints of the membership function of the estimated coefficients. Similar results are also derived for the fuzzy input-and-output model. We illustrate the theory for the case of triangular and asymmetric Gaussian fuzzy inputs and outputs of an inflation-consumption model.
Year
DOI
Venue
2018
10.1016/j.fss.2017.10.007
Fuzzy Sets and Systems
Keywords
Field
DocType
Possibilistic regression,Fuzzy regression,Linear regression,Constrained regression,Tolerance quotient
Defuzzification,Fuzzy classification,Linear model,Polynomial regression,Fuzzy logic,Proper linear model,Artificial intelligence,Fuzzy number,Membership function,Mathematics,Machine learning
Journal
Volume
ISSN
Citations 
340
0165-0114
0
PageRank 
References 
Authors
0.34
36
2
Name
Order
Citations
PageRank
Michal Cerný1142.02
Milan Hladík226836.33