Fuzzy的隶属度可以理解为概率吗?

答案是不可以,隶属度虽然也在[0,1]内,但和概率不是一码事。
一个很好的reddit blog解释如下:
Fuzzy logic and probability address different forms of uncertainty. While both fuzzy logic and probability theory can represent degrees of certain kinds of subjective belief, fuzzy set theory uses the concept of fuzzy set membership, i.e., how much a variable is in a set (there is not necessarily any uncertainty about this degree), and probability theory uses the concept of subjective probability, i.e., how probable is it that a variable is in a set (it either entirely is or entirely is not in the set in reality, but there is uncertainty around whether it is or is not). The technical consequence of this distinction is that fuzzy set theory relaxes the axioms of classical probability, which are themselves derived from adding uncertainty, but not degree, to the crisp true/false distinctions of classical Aristotelian logic.

也有人将probability(包括 Bayesian 和 frequentist)和fuzzy进行了比较:
From the readings above, I conclude that Fuzzy logic and probability (in general) are different ways to reason about different kinds of uncertainty, but Fuzzy and Bayesian logic share similar concepts, such as degree of belief/truthness. Bayesian probability seems more complete and consistent, but it seems that this is a matter of dispute.
On a practical note, if I have data, any kind of data, I will go with (Bayesian) probability. If I have vague or uncertain human procedures, I will go with Fuzzy logic. For example, if you have a process control problem where you have the knowledge of an operator who controls it manually but no system model (which would be highly nonlinear and multivariate), how would you solve this using Bayesian inference? With Fuzzy control it's really easy, and that is actually what the company I work for does.

以上内容简而言之,Fuzzy理论,概率论是从不同角度刻画不确定性的两种方法,数据多的情况下go with Bayesian probability,若涉及到人类的模糊性的时候go with Fuzzy logic。目前我了解的刻画不确定性的数学工具有三种:

  1. Fuzzy Set
  2. Rough Set
  3. Probability

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