|
1. |
Novel Fuzzy Inference System (FIS) Analysis and Design Based on Lattice Theory
Kaburlasos, V.G.; Kehagias, A.;
Fuzzy Systems, IEEE Transactions on
Volume 15,
Issue 2,
April 2007
Page(s):243
-
260
Abstract:
We introduce novel (set- and lattice-theoretic) perspectives and tools for the analysis and design of fuzzy inference systems (FISs). We present an FIS, including both fuzzification and defuzzification, as a device for implementing a function f: RNrarr RM. The family of FIS functions has cardinality aleph2=2aleph1, where aleph1 is the cardinality of the set R of real numbers. Hence the FIS family is much larger than polynomials, neural networks, etc.; furthermore a FIS has a capacity for local generalization. A formulation in the context of lattice theory allows us to define the set F* of fuzzy interval numbers (FINs), which includes both (fuzzy) numbers and intervals. We present a metric dK on F*, which can introduce tunable nonlinearities. FIS design based on dK has advantages such as: an alleviation of the curse of dimensionality problem and a potential for improved computer memory utilization. We present a new FIS classifier, namely granular self-organizing map (grSOM), which we apply to an industrial fertilizer modeling application
|
Cart
