By Asli Celikyilmaz
The aim of this publication is to provide an uncertainty modeling technique utilizing a brand new kind of fuzzy method version through "Fuzzy Functions". considering that so much researchers on fuzzy structures are extra acquainted with the traditional fuzzy rule bases and their inference approach buildings, many average instruments of fuzzy approach modeling ways are reviewed to illustrate the newness of the structurally assorted fuzzy features, sooner than we brought the recent methodologies. To make the discussions extra available, no targeted fuzzy common sense and process modeling wisdom is believed. consequently, the booklet itself could be a reference for a few comparable methodologies to such a lot researchers on fuzzy structures analyses. For these readers, who've wisdom of crucial fuzzy theories, bankruptcy 1, 2 can be handled as a assessment fabric. complex readers needs to be in a position to learn chapters three, four and five at once, the place proposed tools are provided. bankruptcy 6 demonstrates experiments carried out on quite a few datasets.
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Extra info for Modeling Uncertainty with Fuzzy Logic: With Recent Theory and Applications
Fig. 26 Actual and Predicted Stock Prices of an artificial Dataset of Stock Prices for a 10 days period. Predicted stocks from Hypothetical Model 1, Hypothetical Model2 and Actual Prices are shown. … Fig. 27 The effect of broker commission on profit for different values of investments………………………………………… Fig. …… Fig. 0}…………………. Fig. 30 The Elapsed times (min) of structure identification (learning) and reasoning algorithms of optimum methodologies using different samples of training and testing datasets, respectively.
Th input matrix structure in feature space comprised of original input variables (x) membership values and their transformations to be used in type-2 fuzzy functions strategies. Φψi =c*} (p)th embedded T1IFF model identifies different local fuzzy function structures, ψ=1,…,nf, in each of its clusters, i=1…c*. Φi(x,μi), Φi(x,τi) the training input matrix of ith cluster in feature space to identify “fuzzy functions” Φi′ Sample input matrix of cluster i in feature space Φ-Col The collection table that holds the optimum parameters and structures of the local fuzzy functions identified for each training data vector α, α-cut alpha:the threshold for membership values (α * ik lagrange multiplier of kth data vector in ith cluster used in support vector machines algorithm.
3 Outline of the Book In chapter 2, the basic concepts of fuzzy set and logic theory, which are required to explain the introduced algorithms, are presented. In this book, a new fuzzy functions approach is introduced; therefore, details of the introduced fuzzy functions are given. Reviews of some of the well-known fuzzy rule base structures and their extensions that are used in the chapter of experiments for benchmarking purposes (Chapter 6) are presented. In chapter 3, a detailed literature review on fuzzy cluster algorithms are given, since fuzzy clustering is the core of the structure identification method of the new fuzzy functions method of this book.