CONCEPT OF A LINGUISTIC VARIABLE AND ITS APPLICATION TO APPROXIMATE REASONING .3.
CONCEPT OF A LINGUISTIC VARIABLE AND ITS APPLICATION TO APPROXIMATE REASONING .3.
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DOI：
10.1016/0020-0255(75)90017-1
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发表时间：
1975-01-01
影响因子：
8.1
通讯作者：
ZADEH, LA
中科院分区：
文献类型：
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作者：
ZADEH, LA
在概率论的经典方法中，事件A被定义为样本空间ft的子集的o-域d的成员。因此，若P是可测空间（a，_#）上的赋范测度，则A的概率定义为P（A），即的测度。4，并且是区间[0，I]中的数。有许多现实世界的问题，其中一个或多个基本假设是隐含在上述定义被违反。首先，事件A经常是定义不清的，如在问题“明天是温暖的一天的概率是多少？”在这种情况下，暖日事件是一个模糊事件，因为它的发生和不发生之间没有明显的分界线。如[48]所示，这样的事件可以被表征为样本空间Q的模糊子集A，其中A的隶属函数tiA是可测量函数。第二，即使A是一个定义明确的非模糊事件，它的概率P（A）也可能是不明确的。例如，在回答“道琼斯平均股价在一个月内上涨的概率是多少？”如果给出一个明确的数字答案，例如0.7，显然是不合理的。在这种情况下，一个模糊的回答，如“很有可能”，将更符合我们缺乏对股票价格动态的理解，因此，一个更现实的，如果不太精确的描述概率的问题。
In the classical approach to probability theory, an event, A, is defined as a member of a o-field,, d, of subsets of a sample space ft. Thus, ifP is a normed measure over a measurable space (a, _~#), the probabibty of A is defined as P (A), the measure of. 4, and is a number in the interval [0, I]. There are many real-world problems in which one or more of the basic assumptions which are implicit in the above definition are violated. First, the event, A, is frequently ill-defined, as in the question,“What is the probability that it will be a warm day tomorrow?” In this instance, the event warm day is a fuzzy event in the sense that there is no sharp dividing line between its occurrence and nonoccurrence. As shown in [48], such an event may be characterized as a fuzzy subset, A, of the sample space Q, with tiA, the membership function of A, being a measurable function. Second, even if A is a well-defined nonfuzzy event, its probability, P (A), may be ill-defined. For example, in response to the question,“What is the probability that the Dow Jones average of stock prices will be higher in a month from now?” it would be patently unreasonable to give an unequivocal numerical answer, eg, 0.7. In this instance, a vague response like “quite probable,” would be much more commensurate with our lack of understanding of the dynamics of stock prices, and hence a more realistic-if less precisecharacterization of the probability in question.