Fuzzy modeling

Tong, R.M. (1978) Synthesis of fuzzy models for industrial processes, Int. J. General Systems, 4, pp. 143-162. 

In order to prepare the final multi-class predictor map, the input weighted layers are fused using various Fuzzy operators (Fig. 5). Figure 6 is a reclassified final Fuzzy map, predicting the high potential areas for further drilling at East-Kahang. To validate the accuracy of the Fuzzy model, the projected Cu values of the completed drill holes are overlain on the final predictive map. The results show... 

Fuzzy models may be slightly more difficult to program and develop than qualitative models, but they share all of the advantages. In addition, they provide smoother control. This may be a particular advantage in processes that require more rapid control decisions than autoclave curing. The cost of developing these controllers is relatively low and the data required to develop them is usually available from the development of the original process plan. Further, neural networks can be used to automate the development of control-process relationships. 

Source James C. Bezdek Fuzzy models - What are they and why IEEE Trans. Fuzzy Syst. 1993, 1. 1993 IEEE, Reprinted with permission. 

The architecture of an ANFIS model is shown in Figure 14.4. As can be seen, the proposed neuro-fuzzy model in ANFIS is a multilayer neural network-based fuzzy system, which has a total of five layers. The input (layer 1) and output (layer 5) nodes represent the descriptors and the response, respectively. Layer 2 is the fuzzification layer in which each node represents a membership. In the hidden layers, there are nodes functioning as membership functions (MFs) and rules. This eliminates the disadvantage of a normal NN, which is difficult for an observer to understand or to modify. The detailed description of ANFIS architecture is given elsewhere (31). 

Ibelings, B.W. et al.. Fuzzy modeling of cyanobacterial surface waterblooms validation with NOAA-AVHRR satellite images, Ecol. Appl, 13, 1456, 2003. 

Nelles, O. Nonlinear System Identification From Classical Approaches to Neural Networks and Fuzzy Models-, Springer Berlin, 2001. 

Fuzzy inference systems are also known as fuzzy associative memories, fuzzy models, fuzzy-rule-based systems, or fuzzy controllers. 

For fuzzy modeling or for comparison of fuzzy functions, the fundamentals of fuzzy arithmetics are needed (cf. Figure 8.25). These fundamentals are given, for example, in references [19] or [20]. Applications are known for calibration of analytical methods and for qualitative and quantitative comparison of chromatograms, spectra, or depth profiles. 

One of the biggest differences between conventional (crisp) and fuzzy sets is that every crisp set always has a unique membership function, whereas every fuzzy set has an infinite number of membership functions that may represent it. This is at once both a drawback and advantage uniqueness is sacrificed, but this gives a concomitant gain in terms of flexibility, enabling fuzzy models to be adjusted for maximum utility in a given situation. 

There are several kinds of fuzzy rules used to construct fuzzy models. These fuzzy rules can be classified into the following three types according to their consequent form [107] ... 

Lee, K.M., Kwak, D.K., and Lee-Kwang, H., Fuzzy inference neural network for fuzzy model tuning, IEEE Trans. Syst. Man Cybern. SMC-26 637-645,1996. 

Fuzzy models have been employed in robotics to establish the inverse dynamic model for a robot manipulator in its joint space (Qiao and Zhu 2000) or to avoid complex analytical formulation of isotropic target impedance and xmcertainty of parameters related to the robot and environment model through a new fuzzy impedance control law (Petrovic and Milacic 1998). Furthermore, fuzzy inference has been introduced into variable structure adaptive control for the nonlinear robot manipulator systems giving robusmess against system xmcertainties and external disturbances (Zhao and Zhu 1995). 

Fuzzy optimization covers the optimization of fuzzy models, involving non-probabdistic... 

T. Rauma, Fuzzy Modelling for Industrial Systems , Technical Research Centre of Finland. Espoo 1999. 

Konstandinidou, M., Nivolianitou, Z., Kyranoudis C. Markatos, N., 2006. A fuzzy modelling application of CREAM methodology for human reliability analysis. Reliability Engineering System Safety 91(6) 706—716. 

Babuska, R. 1988. Fuzzy Modeling for Control. Massachusetts Kluwer Academic Publishers. 

Braglia, M. Bevilacqua, M. 2000. Fuzzy modelling and analytical hierarchy processing as a means of quantifying risk levels associated with failure modes in production systems. Technology, Law and Insurance 5 125-134... 

Zio, E., Baraldi, P. 2003. Sensitivity analysis and fuzzy modelling for passive systems reliability assessment. Annals of Nuclear Energy 31(3) 277-301. 

The meaning of the application of fuzzy models in risk analysis is to provide mathematical formulations that could characterize the uncertain parameters involved in complex safety evaluation me ods. Fuzzy logic is a decisional system based on linguistic rules once the membership functions have been defined for all the fuzzy variable sets, each set has to be connect by... 

Amodel-based closed-loop controller was designed for maximization of polymer production under safe process condition in emulsion copolymerization processes, while keeping the copolymer composition constant [195]. The interesting feature of the proposed controller was the use of a fuzzy model for design of the optimum reference trajectories. 

Garibaldi JM, Ifeachor EC (1999) Application of simulated annealing fuzzy model tuning to umbilical cord acid-base interpretation. IEEE Trans Fuzzy Syst 7(l) 72-84... 

Dragan K (2002) Design of adaptive takagi-sugeno-kang fuzzy models. Appl Soft Comput 2(2) 89-103... 

Ji-Chang L, Chien-Hsing Y (1999) A heuristic error-feedback learning algorithm for fuzzy modeling. IEEE Trans Syst Man Cybernet Part A Syst Humans 29(6) 686-691... 

Deciu ER, Ostrosi E, Ferney M, Gheorghe M (2005) Configurable product design using multiple fuzzy models. J Eng Des 16(2-3) 209-235... 

Sezer,E.A., Pradhan, B.,Gokceoglu,C.2011. Manifestation of an adaptive neuro-fuzzy model on landslide susceptibility mapping Klang valley, Malaysia. Expert Systems with Applications 38(7) 8208-8219. 

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