Evaluation as a General Approach to Problem Driven Mathematical Modeling

  • Adalbert Kerber


Many modern applications need evaluation of statements, the truth values “true” and “false” alone may not suffice, a statement can be neither true nor false, it may be true (or false) “in a certain sense.” They also need modeling of linguistic expressions and of fuzzy situations. “Binary thinking” does not suffice in many cases. Moreover, the choice of methods might better be problem driven, depending, for example, if we better use a pessimistic or an optimistic reasoning. Here is a brief introduction of how we can choose tools that are appropriate for mathematically modeling this kind of problems.


Global Warming Potential Standard Norm Complete Lattice Standard Intersection Evaluation Problem 
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Thanks are due to the referees for helpful hints.


  1. Brüggemann R, Kerber A, Restrepo G (2011) Ranking objects using fuzzy orders with an application to refrigerants. MATCH Commun Math Comput Chem 66:581–603MathSciNetGoogle Scholar
  2. Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic (theory and applications). Prentice Hall, Englewood CliffsMATHGoogle Scholar
  3. Restrepo G (2008) Assessment of the environmental acceptability of refrigerants by discrete mathematics: cluster analysis and Hasse diagram technique. Doctoral thesis, University of Bayreuth, Germany. Available via the address\&la=de

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BayreuthBayreuthGermany

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