Metamathematics of Fuzzy Logic
Metamathematics of Fuzzy Logic
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DOI：
10.1007/978-94-011-5300-3
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发表时间：
1998-08
期刊：
影响因子：
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通讯作者：
P. Hájek
中科院分区：
文献类型：
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作者：
P. Hájek
这本书提出了一个系统的处理演绎方面和结构的模糊逻辑理解为许多价值的逻辑自成一类。定义并研究了一些重要的实值命题和谓词演算系统。其目的是表明，模糊逻辑作为一种不精确（模糊）命题的逻辑确实有发达的形式基础，大多数通常被称为模糊推理的东西可以自然地理解为逻辑推理。主要有两类目标读者。第一，逻辑学家：他们可以看到模糊逻辑确实是逻辑的一个分支，可能会发现几个非常有趣的开放问题。第二，同样重要的是，研究人员参与模糊逻辑应用和软计算。事实上，他们中的大多数人都不是专业的逻辑学家，因此很容易发生这样的情况：一个应用程序，尽管它可能是聪明和成功的，但在逻辑上并不完全正确，或者可能显得头脑简单。（模糊控制器的逻辑方面的标准表示是最典型的例子。这一事实不会是非常重要的，如果只有邦顿的逻辑学家受到伤害，但它是作者的意见（谁是一个数学逻辑学家），更好地理解严格的逻辑基础模糊逻辑（在通常的广义）是非常有用的模糊逻辑应用程序，因为如果他们知道更好地他们在做什么，他们可能希望做得更好。此外，（经典）逻辑学家和模糊逻辑研究人员之间更好的相互理解，有望导致更深入的合作和新的成果。
This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually namedfuzzy inference'can be naturally understood as logical deduction. There are two main groups of intended readers. First, logicians: they can see that fuzzy logic is indeed a branch of logic and may find several very interesting open problems. Second, equally important, researchers involved in fuzzy logic applications and soft computing. As a matter of fact, most of these are not professional logicians so that it can easily happen that an application, clever and successful as it may be, is presented in a way which is logically not entirely correct or may appear simple-minded.(Standard presentations of the logical aspects of fuzzy controllers are the most typical example.) This fact would not be very important if only the bon ton of logicians were harmed; but it is the opinion of the author (who is a mathematical logician) that a better understanding of the strictly logical basis of fuzzy logic (in the usual broad sense) is very useful for fuzzy logic appliers since if they know better what they are doing, they may hope to do it better. In addition, a better mutual understanding between (classical) logicians and researchers in fuzzy logic, promises to lead to deeper cooperation and new results.