Fuzzy sets and fuzzy logic - theory and applications
Fuzzy sets and fuzzy logic - theory and applications
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DOI：
10.5860/choice.33-2786
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
G. Klir;B. Yuan
中科院分区：
文献类型：
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作者：
G. Klir;B. Yuan
《模糊集与模糊逻辑》是一部真正的巨著。模糊集，不确定性和信息的扩大-Klir教授和Tina Folger的早期工作-模糊集和模糊逻辑在模糊集理论和模糊逻辑的广泛结合中几乎涉及到每一个重要的主题。对我来说，模糊集和模糊逻辑是一项了不起的成就;它以无可挑剔的权威，深刻的洞察力和对细节的细致关注覆盖了广阔的领土。为了正确地看待模糊集和模糊逻辑，有必要澄清一个与模糊集和模糊逻辑的含义有关的语义学问题。一个经常引起误解的原因与模糊逻辑的解释有关.问题是模糊逻辑这个术语有两种不同的含义。更具体地说，在狭义上，模糊逻辑，FLn，是一个逻辑系统，它可以被看作是一个扩展和推广的经典多值逻辑。但在更广泛的意义上，模糊逻辑，FL^几乎是模糊集理论的同义词。在这种情况下，重要的是要认识到：（a）FLW比FLn广泛得多，并将FLn作为其分支之一;（B）FLn的议程与经典多值逻辑的议程非常不同;以及（c）在这个节骨眼上，术语模糊逻辑通常以其广义而非狭义使用，有效地将模糊逻辑等同于FLW In Fuzzy Sets and Fuzzy Logic，模糊逻辑在某种意义上被解释为接近FLW。然而，为了避免误解，标题同时指模糊集和模糊逻辑。模糊集和模糊逻辑的组织是一个基本事实，即任何域X和任何理论Y都可以通过用模糊集的概念替换X和Y中的清晰集的概念来模糊化。在应用于算术、拓扑、图论、概率论和逻辑等基本领域时，模糊化导致了模糊算术、模糊拓扑、模糊图论、模糊概率论和FLn。同样，在应用领域，如神经网络理论，稳定性理论，模式识别和数学规划，模糊化导致模糊神经网络理论，模糊稳定性理论，模糊模式识别和模糊数学规划。通过模糊化获得的是更大的通用性，更高的表达能力，增强的模拟现实世界问题的能力，最重要的是，一种利用不精确性的方法-一种用于实现易处理性的方法，
Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets, Uncertainty, and Information—an earlier work of Professor Klir and Tina Folger—Fuzzy Sets and Fuzzy Logic addresses practically every significant topic in the broad expanse of the union of fuzzy set theory and fuzzy logic. To me Fuzzy Sets and Fuzzy Logic is a remarkable achievement; it covers its vast territory with impeccable authority, deep insight and a meticulous attention to detail. To view Fuzzy Sets and Fuzzy Logic in a proper perspective, it is necessary to clarify a point of semantics which relates to the meanings of fuzzy sets and fuzzy logic. A frequent source of misunderstanding fias to do with the interpretation of fuzzy logic. The problem is that the term fuzzy logic has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FL^ is almost synonymous with the theory of fuzzy sets. In this context, what is important to recognize is that: (a) FLW is much broader than FLn and subsumes FLn as one of its branches; (b) the agenda of FLn is very different from the agendas of classical multivalued logics; and (c) at this juncture, the term fuzzy logic is usually used in its wide rather than narrow sense, effectively equating fuzzy logic with FLW In Fuzzy Sets and Fuzzy Logic, fuzzy logic is interpreted in a sense that is close to FLW. However, to avoid misunderstanding, the title refers to both fuzzy sets and fuzzy logic. Underlying the organization of Fuzzy Sets and Fuzzy Logic is a fundamental fact, namely, that any field X and any theory Y can be fuzzified by replacing the concept of a crisp set in X and Y by that of a fuzzy set. In application to basic fields such as arithmetic, topology, graph theory, probability theory and logic, fuzzification leads to fuzzy arithmetic, fuzzy topology, fuzzy graph theory, fuzzy probability theory and FLn. Similarly, hi application to applied fields such as neural network theory, stability theory, pattern recognition and mathematical programming, fuzzification leads to fuzzy neural network theory, fuzzy stability theory, fuzzy pattern recognition and fuzzy mathematical programming. What is gained through fuzzification is greater generality, higher expressive power, an enhanced ability to model real-world problems and, most importantly, a methodology for exploiting the tolerance for imprecision—a methodology which serves to achieve tractability,