Homomorphisms on the Monoid of Fuzzy Implications \((\mathbb{I}, \circledast)\) - A Complete Characterization

  • Nageswara Rao Vemuri
  • Balasubramaniam Jayaram
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8251)

Abstract

In [4], we had proposed a novel generating methods of fuzzy implications and investigated algebraic structures on the set of all fuzzy implications, which is denoted by \(\mathbb{I}\). Again in [5], we had defined a particular function g K on the monoid \((\mathbb{I}, \circledast)\) (See Def. 16) and characterised the function K for which g K is a semigroup homomorphism (s.g.h) in two special cases, i.e., K is with trivial range and K(1,y) = y for all y ∈ [0,1](neutrality property). In this work we characterise the nontrivial range non neutral implications K such that g K is an s.g.h. and also present their representations.

Keywords

Fuzzy implication neutrality property homomorphism 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nageswara Rao Vemuri
    • 1
  • Balasubramaniam Jayaram
    • 1
  1. 1.Department of MathematicsIndian Institute of Technology HyderabadYeddumailaramIndia

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