@ARTICLE{FUZIMPL3.MIZ,
  AUTHOR = {Grabowski, Adam},
  TITLE = {On Fuzzy Negations Generated by Fuzzy Implications},
  DAY = {26},
  MONTH = {February},
  YEAR = {2020},
  ADDRESS1 = {Institute of Informatics\\University of Bia{\l}ystok\\Cio{\l}kowskiego 1M, 15-245 Bia{\l}ystok\\Poland},
  SECTION1 = {Preliminaries},
  SECTION2 = {Conjugate Fuzzy Implications},
  SECTION3 = {Fuzzy Negations},
  SECTION4 = {Generating Fuzzy Negations from Fuzzy Implications},
  SECTION5 = {Boundary Fuzzy Negations},
  SECTION6 = {Fuzzy Negations Generated by Nine Fuzzy Implications},
  SECTION7 = {Sugeno Negation},
  SECTION8 = {Conjugate Fuzzy Negations},
  SUMMARY = {We continue in the Mizar system
  \cite{Mizar-State-2015} the formalization of
  fuzzy implications according to the book of Baczy\'nski and Jayaram
  ``Fuzzy Implications''.
  In this article we define fuzzy negations and show their connections
  with previously defined fuzzy implications.
  Additionally, we introduce formally Sugeno negation, boundary negations
  and show how these operators are pointwise ordered.
  This work is a continuation of the development
  of fuzzy sets in Mizar \cite{GrabowskiFuzzy:2013}.}}

