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Introduction to Fuzzy Sets

In: Fuzzy Set Theory—and Its Applications

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  • H.-J. Zimmermann

Abstract

Most of our traditional tools for formal modeling, reasoning, and computing are crisp, deterministic, and precise in character. By crisp we mean dichotomous, that is, yes-or-no-type rather than more-or-less type. In conventional dual logic, for instance, a statement can be true or false—and nothing in between. In set theory, an element can either belong to a set or not; and in optimization, a solution is either feasible or not. Precision assumes that the parameters of a model represent exactly either our perception of the phenomenon modeled or the features of the real system that has been modeled. Generally, precision also implies that the model is unequivocal, that is, that it contains no ambiguities.

Suggested Citation

  • H.-J. Zimmermann, 2001. "Introduction to Fuzzy Sets," Springer Books, in: Fuzzy Set Theory—and Its Applications, edition 0, chapter 1, pages 1-8, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-0646-0_1
    DOI: 10.1007/978-94-010-0646-0_1
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