Information Technology Reference
In-Depth Information
Chapter 6
Complete Orthogonal Semantic Spaces in
Problems of the Fuzzy Regression Analysis
6.1 The Analysis of Known Methods of Fuzzy Regression
Analysis
To analyze relations between qualitative characteristics and the prediction of their
values the methods of fuzzy regression analysis are used, which being actively
developed have already considerably expanded boundaries of application of
classical regression analysis methods, i.e. they allow to construct the regression
relations on the basis of fuzzy initial information. Besides, this information can be
of both quantitative and qualitative nature, thus, making possible application of
methods of fuzzy regression analysis in the theory of expert evaluations and
ensuring practical applications in various spheres of human activity [188, 189].
Methods of fuzzy regression analysis are used to study behavior of complex
engineering, ecological and other systems with output indexes depending on a
great many of parameters [188]. These methods are applied to construct regression
models not only within the limits of the fuzzy initial information, but also within
the limits of the definite information. In this case the predicted output values are
provided as fuzzy numbers. Such representation is explained by the fact that the
real system is always more complex than any of its model not capable of
combining all entering indexes on which the output index depends.
The first fuzzy linear regression model [190] excited interest in contributors,
thus resulting in occurrence of new fuzzy regression models based on outcomes
obtained in [191—193], and various optimizing criteria. Today, a number of linear
fuzzy regression models [194-210] is developed, and approaches to building of
nonlinear fuzzy regression models [210-212] are outlined. In [195, 196, 197, 199,
203, 209] optimizing criteria are constructed aimed at minimization of fuzziness
of output model fuzzy values and the subsequent application of linear
programming methods. In [206], based on [213, 214], interval regression model is
under construction using methods considered in [203, 208, 209].
There appears to be three different approaches under the heading of “Fuzzy
Regression”:
(a) Methods that were proposed by H. Tanaka [190] and further elaborated in
current literature [188, 189, 194, 196-212], where the coefficients of input
