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Fuzzy Abstract Algebra

  • John N. Mordeson
  • Premchand S. Nair
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 20)

Abstract

In 1971, Azriel Rosenfeld wrote his seminal paper on fuzzy subgroups, [52]. This paper led to a new area in abstract algebra as well as a new area in fuzzy mathematics. Hundreds of papers examining various fuzzy substructures of algebraic structures have since appeared in the literature. In this chapter, we examine those fuzzy substructures which have applications or strong potential for applications outside of mathematics, namely computer science or engineering. We emphasize that the nature of fuzzy abstract algebra differs from that of the algebra of fuzzy numbers such as triangular fuzzy numbers and others.

Keywords

Prime Ideal Commutative Ring Polynomial Ring Formal Power Series Fuzzy Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • John N. Mordeson
    • 1
  • Premchand S. Nair
    • 2
  1. 1.Center for Research in Fuzzy Mathematics and Computer ScienceCreighton UniversityOmahaUSA
  2. 2.Department of Mathematics and Computer ScienceCreighton UniversityOmahaUSA

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