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International Journal of Fuzzy Logic and Intelligent Systems 2014; 14(1): 1-7
Published online March 1, 2014
https://doi.org/10.5391/IJFIS.2014.14.1.1
© The Korean Institute of Intelligent Systems
On a Novel Way of Processing Data that Uses Fuzzy Sets for Later Use in Rule-Based Regression and Pattern Classification
Jerry M. Mendel
Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA
Correspondence to :
Jerry M. Mendel (jmmprof@me.com)
This paper presents a novel method for simultaneously and automatically choosing the nonlinear structures of regressors or discriminant functions, as well as the number of terms to include in a rule-based regression model or pattern classifier. Variables are first partitioned into subsets each of which has a linguistic term (called a causal condition) associated with it; fuzzy sets are used to model the terms. Candidate interconnections (causal combinations) of either a term or its complement are formed, where the connecting word is AND which is modeled using the minimum operation. The data establishes which of the candidate causal combinations survive. A novel theoretical result leads to an exponential speedup in establishing this.
Keywords: Rule based regression,Pattern recognition,Fuzzy set
Jerry M. Mendel received the Ph.D. degree in electrical engineering from the Polytechnic Institute of Brooklyn, Brooklyn, NY. Currently he is Professor of Electrical Engineering and Systems Architecting Engineering at the University of Southern California in Los Angeles, where he has been since 1974. He has published over 550 technical papers and is author and/or editor of ten books, including Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions (Prentice-Hall, 2001), Perceptual Computing: Aiding People in Making Subjective Judgments (Wiley & IEEE Press, 2010), and Advances in Type-2 Fuzzy Sets and Systems (Springer 2013). His present research interests include: type-2 fuzzy logic systems and their applications to a wide range of problems, including smart oil field technology, computing with words, and fuzzy set qualitative comparative analysis. He is a Life Fellow of the IEEE, a Distinguished Member of the IEEE Control Systems Society, and a Fellow of the International Fuzzy Systems Association. He was President of the IEEE Control Systems Society in 1986. He was a member of the Administrative Committee of the IEEE Computational Intelligence Society for nine years, and was Chairman of its Fuzzy Systems Technical Committee and the Computing With Words Task Force of that TC. Among his awards are the 1983 Best Transactions Paper Award of the IEEE Geoscience and Remote Sensing Society, the 1992 Signal Processing Society Paper Award, the 2002 and 2014 Transactions on Fuzzy Systems Outstanding Paper Awards, a 1984 IEEE Centennial Medal, an IEEE Third Millenium Medal, and a Fuzzy Systems Pioneer Award (2008) from the IEEE Computational Intelligence Society.
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Original Article
International Journal of Fuzzy Logic and Intelligent Systems 2014; 14(1): 1-7
Published online March 1, 2014 https://doi.org/10.5391/IJFIS.2014.14.1.1
Copyright © The Korean Institute of Intelligent Systems.
On a Novel Way of Processing Data that Uses Fuzzy Sets for Later Use in Rule-Based Regression and Pattern Classification
Jerry M. Mendel
Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA
Correspondence to:Jerry M. Mendel (jmmprof@me.com)
Abstract
This paper presents a novel method for simultaneously and automatically choosing the nonlinear structures of regressors or discriminant functions, as well as the number of terms to include in a rule-based regression model or pattern classifier. Variables are first partitioned into subsets each of which has a linguistic term (called a causal condition) associated with it; fuzzy sets are used to model the terms. Candidate interconnections (causal combinations) of either a term or its complement are formed, where the connecting word is AND which is modeled using the minimum operation. The data establishes which of the candidate causal combinations survive. A novel theoretical result leads to an exponential speedup in establishing this.
Keywords: Rule based regression,Pattern recognition,Fuzzy set
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Table 1 . Number of surviving causal combinations for eight problems.
Problem Cases Variables ( p )Two terms per variablesa Candidate causal combinations (2 p )Surviving causal combinations ( R s )Abalone [14] 4,177 7 128 55 Concrete compressive strength [14] 1,030 8 256 73 Concrete slump test [14] 103 9 512 71 Wave force [16] 317 3 8 8 Chemical process concentration reading [17] 194 3 8 8 Chemical process temperature readings [17] 223 3 8 6 Gas furnace [17] 293 6 64 25 Mackey-Glass chaotic time series [18] 1,000 4 16 8 aThe two terms are low and high, and their fuzzy c-mean membership functions are the complements of one another..
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