Advertisement

Abstract

The notion of MI-group introduced in [1], [2] and later on elaborated in [3] is redefined and its structure analysed. In our approach, the role of the “Many Identities” set is replaced by an involutive anti-automorphism. Every finite MI-group coincides with some classical group, whilst infinite MI-groups comprise two parts: a group part and a semigroup part.

Keywords

many identities group algebraic structures fuzzy numbers involutive anti-automorphism 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Holčapek, M., Štěpnička, M.: Arithmetics of extensional fuzzy numbers – part I: Introduction. In: Proc. IEEE Int. Conf. on Fuzzy Systems, Brisbane, pp. 1517–1524 (2012)Google Scholar
  2. 2.
    Holčapek, M., Štěpnička, M.: Arithmetics of extensional fuzzy numbers – part II: Algebraic framework. In: Proc. IEEE Int. Conf. on Fuzzy Systems, Brisbane, pp. 1525–1532 (2012)Google Scholar
  3. 3.
    Holčapek, M., Štěpnička, M.: MI-algebras: A new framework for arithmetics of (extensional) fuzzy numbers. Fuzzy Sets and Systems (2014), http://dx.doi.org/10.1016/j.fss.2014.02.016
  4. 4.
    Hage, J., Harju, T.: On Involutive Anti-Automorphisms of Finite Abelian Groups. Technical UU WINFI Informatica en Informatiekunde (2007)Google Scholar
  5. 5.
    Hage, J., Harju, T.: The size of switching classes with skew gains. Discrete Math. 215, 81–92 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Dummit, D.S., Foote, R.M.: Abstract Algebra. Wiley (2003)Google Scholar
  7. 7.
    Mareš, M.: Computation over Fuzzy Quantities. CRC Press, Boca Raton (1994)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Martin Bacovský
    • 1
  1. 1.Faculty of Science Department of MathematicsUniversity of OstravaOstravaCzech Republic

Personalised recommendations