Vagueness is embroiled inseveral real phenomena. Whether one contemplates vagueness explicitly whenmodeling such a phenomenon is one of the modeling choices, the outcome of whichwill rest on on the situation. On the other hand, the modeler chooses to reflectvagueness, he or she will have to select the method for modeling it. Someexperts assert that one theory, e.
g. probability theory, is adequate to modelevery kind of vagueness. The excellence of the techniques used in a statisticalanalysis rest on extremely on the presumed probability model or distribution.
Some physical systems, those complexones, are uncompromising to model by an accurate and precise mathematicalprocedure or equation due to the complexity of the system structure,nonlinearity, uncertainty, randomness, etc. Therefore, approximationmodeling is often necessary for real-world applications. But, the important questions are what kind ofapproximation is upright, where the logic of “goodness” has to be firstdefined, of course, and how to formulate such a good approximation in modelinga system such that it is mathematically rigorous and can produce satisfactoryresults in both theory and applications. It is clear that intervalmathematics and fuzzy logic together can provide a promising alternative tomathematical modeling for many physical systems that are too vague or toocomplicated to be described by simple and crisp mathematical formulas orequations. When interval mathematics and fuzzy logic are employed, the intervalof confidence and the fuzzy membership functions are used as approximationmeasures, leading to the so-called fuzzy systems modeling. Zimmermann H.-J. 134proposed a definition of uncertainty: Uncertainty implies that in a certainsituation a person does not dispose about information which quantitatively andqualitatively is appropriate to describe, prescribe or predictdeterministically and numerically a system, its behavior or othercharacteristics.
Buckley 12 define fuzzy probabilities, which will be fuzzynumbers, from a set of confidence intervals and use fuzzy numbers for theparameters in the probability density functions, to produce fuzzy probabilitydensity functions.Once dealing with the usualprobability concept, an occurrence has its specific limit. For take asituation, if an event is X= {2, 4, 7, 9, 11}, its margin is sharp andconsequently, it can be characterized as a crisp set. As soon as we deal anoccurrence whose limit is not sharp, it can be measured as a fuzzy set, thatis, a fuzzy event. We can recognize the probability of two behaviors. One isdealing with the probability of a crisp value (crisp probability) and the otheras a fuzzy set (fuzzy probability). A hormone activity is a verycomplex system, where it secretion processing is narrowly connected tolife-sustaining developments.
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It is evident now that there are a number ofamino acid combinations in the hormone that keep up its activity. Some detailsof hormone activity, like stress or obesity, anxiety are well understood, whileothers, like fetal growth, uterus contraction during cesarean and normaldelivery, primary postpartum hemorrhage effects and many others are stillambiguous. This means that a reasonableexplanation of the performance of a complex organism similar to a hormone’sfunction is expressed in a natural-linguistic method with “sensitive” notationslike great excitability, weak damage, the low anticipation of punishment and soon, which cannot be through statistically assigned.So, if we need to improve anadequate tool for the logical theory of a hormone’s effective, in some sense,we are bound to search for a mathematical tool, which could rightly work with”perceptions” as with mathematical objects. Such mathematical tool was proposedby Zadeh 131 and has been further developed during the last decades. It iscalled fuzzy logic and fuzzy set theory. Guanrong Chen and Trung Tat Pham 50give an example for fuzzy rule-based health monitoring expert systems, fuzzylogic rules to control a focus ring of a camera to allow automatic focusing fora sharp image, application of fuzzy control to a general class of servomechanic systems, the fuzzy controller for the robotic manipulator.
The fuzzyterms and definitions are defined in the following section 67, 135.
