Fuzzy applications

Neural and fuzzy applications have been successfully applied to the chemical engineering processes [1], and several control strategies have been reported in literature for the distillation plant modeling and control tasks [2]. Recent years have seen a rapidly growing number of neurofuzzy control applications [3]. Beside this, several software products are currently available to help with neurofuzzy problems. 

Mure S., Demichela M. Fuzzy Application Procedure (FAP) for risk assessment of occupational accidents , Journal of Loss Prevention in the Process Industry, 2009, 22, 593-599. 

All the three techniques mentioned above may make use of fuzzy sets and fuzzy logic (for fuzzy classification, fuzzy rules or fuzzy matching) but this does not effect the discussion of the applicability to NDT problems in the next section. 

Fuzzy logic and fuzzy set theory are applied to various problems in chemistry. The applications range from component identification and spectral Hbrary search to fuzzy pattern recognition or calibrations of analytical methods. 

An overview over different applications of fuzzy set theory and fuzzy logic is given in [15] (see also Chapter IX, Section 1.5 in the Handbook). 

Here, the application of fuzzy logic for multicomponent spectral analysis is described. 

APPLICATION OF FUZZY SETS THEORY TO SOLVING TASKS OF MULTICOMPONENT QUALITATIVE ANALYSIS... 

In this work, the crisp numerical data for the analyte and reference samples were transformed into the fuzzy form with the application of the L/ -representation. The procedure of fuzzyfication is illustrated roughly by the figure, where a and b are the nominal (crisp) measured values ... 

Chen et al. [24] provide a good review of Al techniques used for modeling environmental systems. Pongracz et al. [25] presents the application of a fuzzy-rule based modeling technique to predict regional drought. Artificial neural networks model have been applied for mountainous water-resources management in Cyprus [26] and to forecast raw-water quality parameters for the North Saskatchewan River [27]. 

Pongracz R, Bogardi I, Duckstein L (1999) Application of fuzzy rule-based modelling technique to regional drought. J Hydrol 224 100-114... 

Y. Chtioui, D. Bertrand, D. Barba and Y. Dattee, Application of fuzzy C-means clustering for seed discrimination by artificial vision. Chemom. Intell. Lab. Syst., 38 (1997) 75-87. 

Whereas the first applications of the AFDF approach were based on a numerical combination of fuzzy fragment electron densities, each stored numerically as a set density values specified at a family of points in a three-dimensional grid, a more powerful approach is the generation of approximate macromolecular density matrices within the framework of the ADMA method [142-146]. A brief summary of the main steps in the ADMA method is given below. 

Zadeh [1975] extended the classical set theory to the so-called fuzzy set theory, introducing membership functions that can take on any value between 0 and 1. As illustrated by the intersection of the (hard) reference data set (A) and the fuzzed test data set (C), the intersection (E) shows an agreement of about 80%. Details on application of fuzzy set theory in analytical chemistry can be found in Blaffert [1984], Otto and Bandemer [ 1986a,b] and Otto et al. [1992],... 

Zadeh LA (1975) Fuzzy sets and their applications to cognitive and decision processes. Academic Press, New York... 

The application of both of these hedges concentrates the region to which the hedge applies. Nonzero membership of the fuzzy set "very low pH" covers the same overall range of pH as membership of the group "low pH," even with the hedge in place, but the effect of the hedge is to reduce membership in the "low pH" set for those pHs that also have some membership in the "medium pH" set. The effect of "very very" is even more marked, as we would expect. 

An early application of fuzzy logic was in the control of a cement kiln and applications to similar or identical systems have continued to appear (see, for example, Jarvensivu et al.1). This is an example of a practical application in which generation of high quality product may depend on the skill and experience of a small number of workers. Even when computer control is available, workers may describe the way that they adjust conditions to provide a high-quality product by statements such as, "The kiln rotation rate should be lowered slightly," and that, in order to compensate, "The temperature should be diminished just a bit." Fuzzy logic now has a lengthening track record of use in such situations. 

Control problems represent a major area of application for fuzzy logic since reliable process control may rely on the long-term expertise of one or a few people, and those people may be able to frame their knowledge of the system only in imprecise terms. A typical example is the control of pH in a crystallization reactor.2 A similar application was described by Puig and co-... 

Fuzzy logic is often presented as an extension in books that cover expert systems. Few texts exist in which the applications of fuzzy logic to scientific problems are described, but several texts include more general discussions of the principles and practical implementation of this method. Among the best is Negnevitsky s text on intelligent systems.9... 

In order to estimate the region of this approximation applicability, it is necessary to examine macrokinetics of a polymeranalogous reaction with explicit allowance for the diffusion of a reagent Z into a globule. In this case, the profile of its constituent monomeric units will be fuzzy rather than stepwise (see Fig. 1). This brings up two questions. The first one is how this profile depends on kinetic and diffusion parameters of a reaction system. The second question is concerned with the effect of the profile shape on the statistical characteristics of the chemical structure of the products of a polymeranalogous reaction. A rigorous theory has been developed [22,23] which enables us to answer these questions. The main concepts of this theory are outlined in the subsequent Sections. 

Fuzzy and Neurofuzzy Applications in European Washing Machines 1191... 

In order to understand the application of FUZZY CONTROL in the development of washing processes, a short explanation of conventional washing techniques will be necessary. 

Wallace TF (ed) (1992) APICS Dictionary, 7th edn. American Production and Inventory Control Society, Falls Church VA Wang R, Liang T (2004) Application of fuzzy multi-objective linear programming to aggregate production planning. Computers Industrial Engineering 46 17-41... 

Costel Sarbu and Horia Pop, Fuzzy Soft-Computing Methods and Their Applications in Chemistry. 

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