By Cornelius T. Leondes
This quantity covers the combination of fuzzy common sense and professional structures. an essential source within the box, it comprises strategies for employing fuzzy platforms to neural networks for modeling and keep an eye on, systematic layout methods for understanding fuzzy neural structures, concepts for the layout of rule-based professional structures utilizing the hugely parallel processing services of neural networks, the transformation of neural platforms into rule-based professional platforms, the features and relative advantages of integrating fuzzy units, neural networks, genetic algorithms, and tough units, and functions to approach id and keep watch over in addition to nonparametric, nonlinear estimation. Practitioners, researchers, and scholars in commercial, production, electric, and mechanical engineering, in addition to laptop scientists and engineers will enjoy this reference resource to assorted program methodologies. Key positive aspects* Fuzzy process options utilized to neural networks for modeling and regulate* Systematic layout techniques for understanding fuzzy neural structures* concepts for the layout of rule-based specialist platforms* features and relative advantages of integrating fuzzy units, neural networks, genetic algorithms, and tough units* process identity and regulate* Nonparametric, nonlinear estimationPractitioners, researchers, and scholars in business, production, electric, and mechanical engineering, in addition to laptop scientists and engineers will locate this quantity a special and complete connection with those assorted software methodologies
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Extra resources for Fuzzy Logic and Expert Systems Applications (Neural Network Systems Techniques and Applications)
Sample text
This is because the relative importance of Class 1 patterns was monotonically increased by the decreasing function CL>(U) attached to Class 2 patterns. From Fig. 10b, we can see that the output from the neural network can be viewed as the possibility grade of Class 1. For example, the output o(x) in Fig. 35 belongs to Class 2. We can define the possibility area using the output from the trained neural network. 5, X G Q], (18) where Q\^^ is the possibility area of Class 1 and o^^^(x) is the output from the neural network trained for the possibility analysis.
0 Figure 18 Three-class classification problem on the one-dimensional pattern space [0,1]. , Opc) from the neural network as follows: (28) = J2^P^^ k=i where epk is the cost function for the /:th output unit, which is defined as epk = (tpk Opkf/2, o)(u) • (tpk - Opk)^/2, ifxp e Class A;, otherwise. (29) From the comparison between (15) and (29), we can see that the cost function epk for the A;th output unit in (29) is for the possibility analysis of Class k. Let us consider a three-class classification problem on the one-dimensional pattern space [0,1] in Fig.
5, X € ^ } , Q A: = 1, 2 , . . , c. Nes r Input value ;c *••• • • — g • mmmi 1 10 Input valued 1st output unit 2nd output unit Figure 20 Input value :)C 3rd output unit Results of the necessity analysis. (32) 20 Hisao Ishibuchi and Manabu Nii The fuzzy boundary is defined from (25) as follows: ^PB = ^ - {^1 U ^ 2 U • • . U ^ c (33) The decision areas and the fuzzy boundary for the classification problem in Fig. 18 are shown in Fig. 21 together with the shape of /XjtCx). From this figure, we can see that intuitively acceptable results were obtained by our fuzzy classification method.