Fuzzy logic principles

A fuzzy perception is an assessment of a physical condition that is not measured with precision, but assigned with an inmitive value. It is asserted that everything in the universe has some fuzziness, no matter how good the measurement equipment is. By using meaningful words to name the fuzzy description, the construction of engineering process is easy to understand and can be built up intuitively. 

Measured non-fuzzy data is one of the primary inputs for the fuzzy logic models. Examples are temperature measurements by thermometers, rainfall by rain-gages, groundwater levels by sounders, etc. Additionally, humans with their fuzzy perceptions could also provide inputs with linguistic statements. 

In order to model a problem through fuzzy logic principles, first of all the variables (cause-reasons-inputs and effect-resnlts-ontpnts) must be attached with meaningful words such as rainfall, benefit, income, resistance, temperature, etc. For example, in a disarmament model finance, armament, enmity, weapon quantity and modernity of the weapons etc. are the variables. Each one of these words inclndes uncertainty in terms of vagueness, incompleteness, doubt, and incompleteness. They can be sub-classified in model construction. 

The second question is which variables are inpnts or outputs This is tantamount to identify antecedent and conseqnent variables. It is similar to any mathematical expression, where there are dependent and independent variables. In the disarmament problem armament is the conseqnent variable and other four are antecedent variables. In the classical logic, each variable exists due to its opposite like armament-disarmament, snpport-not snpport, modem-not modern and alike. Such two alternatives are demolished in the fuzzy logic and instead more general classifications with middle classes are taken into consideration as multiple alternatives. Thus there are many relationships between sub-classes. 

Sub-classifications should be completed for each variable. They can be subclassified according to the following. 

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Potential human errors and equipment failures are combined in dynamic event trees for the final evaluation of event probabilities as identified initially from the bow tie diagrams. Data about Human Error Probabilities (HEPs) are estimated with the use of the FPE tool on the basis of expert judgement and theoretical insight (i.e., the CREAM methodology HoUnagel 1998) applied in combination with fuzzy logic principles (Zadeh 2008). 

The principle of applying fuzzy logic to matching of spectra is that, given a sample spectrum and a collection of reference spectra, in a first step the reference spectra are unified and fuzzed, i.e., around each characteristic line at a certain wavenumber k, a certain fuzzy interval [/ o - Ak, + Afe] is laid. The resulting fuzzy set is then intersected with the crisp sample spectrum. A membership function analogous to the one in Figure 9-25 is applied. If a line of the sample spec-... 

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... 

An unambiguous algorithm. The intent of this principle is to ensure the transparency of the modeling algorithm. Sometimes, it is a difficult task to satisfy this principle, particularly when complex methods like neural networks or fuzzy logic techniques are used for modeling. 

The term fuzzy logic is often interpreted in two ways. In a broad interpretation, fuzzy logic is viewed as a system of concepts, principles, and methods for dealing with modes of reasoning that are approximate rather than exact. In a narrow interpretation, it is viewed as a generalization of the various many-valued logics. This narrow interpretation of fuzzy logic is not of interest in this chapter. 

The general principle in fuzzy logic is that a reference value Xq is associated with a fuzzy interval dx, and experimental data within an interval of Xq dx are identified as reference data. Since natural, or experimental, data are always inaccurate, and the representation of knowledge is quite like that in fuzzy logic, expert systems have to use fuzzy logic or some techniques similar to fuzzy logic [33]. In a computer system based on the fuzzy logic approach, fuzzy intervals for reference values are defined a priori. 

Fuzzy logic represents one of the main elements of soft computing. The latter differs from conventional hard computing as it is tolerant to imprecision, uncertainty, partial truth, and approximation. The principle behind soft computing is to exploit the tolerance for imprecision, uncertainty, partial truth, and approximation to achieve tractability, robustness, and low cost. 

In this paper we presented an approach where fuzzy logic and BBN concepts are combined to estimate human error probability. This combination leads to a fuzzy Bayesian network approach based on the concept o fuzzy number and on extension principles applied to discrete fuzzy probabilities calculation. 

Objective entities in the process operation system, such as reactor, distillation column units and processes, are used and conducted by the different operation tasks. Modeling methods for the units and processes objects are first principle rules, statistical regression, artificial neural network, and fuzzy logic relation. 

However, the mentioned above single models have some shortages unavoidably. To remedy the defects of single models, hybrid models are actively researched recently. One kind of hybrid models (Qi, 1999) combines part of first principle equations with ANN, in which ANN is used to determine parameters of the first principle models. Fuzzy logic approach (Qian, 1999) is used for representing imprecision and approximation of the relationship among process variables. It is successfully incorporated into conventional process simulators. Several efforts (Baffi, 1999) have been made to combine statistical analysis with non-linear regression, which are polynomial, spline function and ANN. 

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