Neuro-rough-fuzzy approach for regression modelling from missing data

Abstract

Real life data sets often suffer from missing data. The neuro-rough-fuzzy systems proposed hitherto often cannot handle such situations. The paper presents a neuro-fuzzy system for data sets with missing values. The proposed solution is a complete neuro-fuzzy system. The system creates a rough fuzzy model from presented data (both full and with missing values) and is able to elaborate the answer for full and missing data examples. The paper also describes the dedicated clustering algorithm. The paper is accompanied by results of numerical experiments.

Rough subspace neuro-fuzzy system

“…The system is an extension the neuro-rough-fuzzy system for data with missing values [56]. In the system each fuzzy rule exists in its own subspace.…”

“…The reasons are various [56]: errors in answer acquisition, failure of sensors, impossibility to get data (e.g. patient has died), the refusal to answer some questions in the questionnaire, inapplicability of questions, random noise, impossible values, retrospective usage of data i.e.…”

Center-based l1–clustering method

“…This means that the probability of a random choice of a good initial approximation is significantly larger in the case of the l 1 -clustering algorithm. In order to examine the sensitivity of l 1 and l 2 -clustering algorithms, we will consider the incomplete data set (see Hathaway and Bezdek, 2001;Simiński, 2012). Suppose that in the set A there are data in which there is no information about all attributes, i.e., components.…”

A comprehensive survey on formal concept analysis, its research trends and applications

“…In this section, we provide a discussion on handling incomplete data (Simiński, 2012). (Krajca et al, 2012;Li et al, 2013a;Simiński, 2012 Table 18. Second possible complete formal context for Table 16.…”