Fuzzy Set Theory by Shin-Yun Wang
Before illustrating the fuzzy t theory which makes decision under uncertainty, it is important to realize what uncertainty actually is.
Uncertainty is a term ud in subtly different ways in a number of fields, including philosophy, statistics, 新年展望economics, finance, 入党日期怎么查insurance, psychology, engineering and science. It applies to predictions of future events, to physical measurements already made, or to the unknown. Uncertainty must be taken in a n radically distinct from the familiar notion of risk, from which it has never been The esntial fact is that 'risk' means in some cas a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really prent It will appear that a measurable uncertainty, or 'risk' proper, as we shall u the term, is so far different from an immeasurable one that it is not in effect an uncertainty at all.
压力的作用效果
What is relationship between uncertainty, probability, vagueness and risk? Risk is defined a
s uncertainty bad on a well grounded (quantitative) probability. Formally, Risk = (the probability that some event will occur) X (the conquences if it does occur). Genuine uncertainty, on the other hand, cannot be assigned such a (well grounded) probability. Furthermore, genuine uncertainty can often not be reduced significantly by attempting to gain more information about the phenomena in question and their caus. Moreover the relationship between uncertainty, accuracy, precision, standard deviation, standard error, and confidence interval is that the uncertainty of a measurement is stated by giving a range of values which are likely to enclo the true value. This may be denoted by error bars on a graph, or as value ± uncertainty, or as decimal fraction (uncertainty).
滕州生活网Often, the uncertainty of a measurement is found by repeating the measurement enough times to get a good estimate of the standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation. However, if the values are averaged and the mean is reported, then the averaged measurement has uncertainty equal to the standard error which is the standard deviation divided by the square root of the number of measurements. When the uncertainty reprents the standard error of the
measurement, then about 68.2% of the time, the true value of the measured quantity falls within the stated uncertainty range.
Therefore no matter how accurate our measurements are, some uncertainty always remains. The possibility is the degree that thing happens, but the probability is the probability that things be happen or not. So the methods that we deal with uncertainty are to avoid the uncertainty, statistical mechanics and fuzzy t (Zadeh in 1965).
(Figure from Klir&Yuan)
Fuzzy ts萨博出场集数 have been introduced by Lotfi A. Zadeh (1965). What Zadeh propod is very much a paradigm shift that first gained acceptance in the Far East and its successful application has ensured its adoption around the world. Fuzzy ts are an extension of classical t theory and are ud in fuzzy logic. In classical t theory the membership of elements in relation to a t is assd in binary terms according to a crisp condition — an element either belongs or does not belong to the t. By contrast, fuzzy t theory permits the gradual asssment of the membership of elements in relation to a t; this is described with the aid of a membership function valued in the real unit interval [0, 1]. Fuzzy ts are an extension of classical t theory since, for a certain univer, a membership function may act as an indicator function, mapping all elements to either 1 or 0, as in the classical notion.
Specifically, A fuzzy t is any t that allows its members to have different grades of membership (membership function) in the interval [0,1]. A fuzzy t on a classical t Χ is defined as follows:
The membership function μA(x) quantifies the grade of membership of the elements x to the fundamental t Χ. An element mapping to the value 0 means that the member is not included in the given t, 1 describes a fully included member. Values strictly between 0 and 1 characterize the fuzzy members.
520告白日
非全日制职工Membership function terminology
Univer of Discour滑炒里脊丝: the univer of discour is the range of all possible values for an input to a fuzzy system.
