Exact calculations of extended logical operations on fuzzy truth values

Authors:
Zsolt Gera;József Dombi
Affiliations:
Department of Computer Algorithms and Artificial Intelligence, University of Szeged, H-6720 Szeged, Hungary;Department of Computer Algorithms and Artificial Intelligence, University of Szeged, H-6720 Szeged, Hungary
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

In this paper we propose computationally simple, pointwise formulas for extended t-norms and t-conorms on fuzzy truth values. The complex convolutions of the extended operations are shown to be equivalent to simple pointwise expressions for several special cases. Linear fuzzy truth values are defined and it is shown that the extended Lukasiewicz operations preserve linearity. Since linear fuzzy truth values are common in representing linguistic modifiers, the results simplify fuzzy truth value-based reasoning methods. The results can also be applied immediately to type-2 fuzzy set operations.