Fuzzy data analysis by possibilistic linear models
Fuzzy Sets and Systems - Fuzzy Numbers
Possibilistic linear systems and their application to the linear regression model
Fuzzy Sets and Systems
Approaches to sensitivity analysis in linear programming
Annals of Operations Research
Recursive robust regression computational aspects and comparison
Computational Statistics & Data Analysis - Special issue dedicated to Toma´sˇ Havra´nek
Applying fuzzy linear regression to VDT legibility
Fuzzy Sets and Systems
Robust interval regression analysis using neural networks
Fuzzy Sets and Systems
Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data
Computational Statistics & Data Analysis
Support vector interval regression networks for interval regression analysis
Fuzzy Sets and Systems - Theme: Learning and modeling
Extended support vector interval regression networks for interval input-output data
Information Sciences: an International Journal
Interval regression analysis using support vector networks
Fuzzy Sets and Systems
Interval Regression Analysis with Soft-Margin Reduced Support Vector Machine
IEA/AIE '09 Proceedings of the 22nd International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems: Next-Generation Applied Intelligence
Support vector interval regression machine for crisp input and output data
Fuzzy Sets and Systems
Fuzzy regression by fuzzy number neural networks
Fuzzy Sets and Systems
Interval regression analysis by quadratic programming approach
IEEE Transactions on Fuzzy Systems
Interval regression analysis using quadratic loss support vector machine
IEEE Transactions on Fuzzy Systems
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In interval linear regression analysis, we are given crisp or interval data and we are to determine appropriate interval regression parameters. There are various methods for interval regression; many of them possess the property that while some of the resulting interval regression parameters are very wide, the other parameters are crisp. This drawback is the main limiting factor for such methods and much effort has been devoted to overcoming it. We propose a method motivated by tolerance analysis in linear systems. Our method yields intervals for regression parameters the widths of which are proportional to an in-advance given vector of parameters. Moreover, the method is computationally very cheap, and provides a natural measure of quality of a model. First we formulate the method for the basic model of crisp input-crisp output data and then extend it to crisp input-interval output and interval input-interval output models. For the interval-valued cases we study several formulations of the solution concept: possibility, strong possibility, weak possibility, necessity. Here, strong possibility is a new concept proposed as a natural counterpart to the remaining ones. We prove that the method provides optimal interval parameters meeting centrality and proportionality requirements. We also show that the method provides interval regression parameters satisfying various versions of Tanaka-Lee's inclusion property. We also derive a form of a complementarity theorem for the weak possibility and necessity solution concepts. Since practical problems may be affected by outlying observations we show that our approach is easily adapted to deal with them. We illustrate the theory by examples.