Negation and affirmation: the role of involutive negators

Authors:
Koen C. Maes;Bernard De Baets
Affiliations:
Ghent University, Department of Applied Mathematics, Biometrics and Process Control, Coupure links 653, 9000, Gent, Belgium;Ghent University, Department of Applied Mathematics, Biometrics and Process Control, Coupure links 653, 9000, Gent, Belgium
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Year:
2007

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Abstract

Strict negators and automorphisms are prevalently used to fuzzify the Boolean negation and affirmation. Involutive negators are of particular interest. Every monotone [0,1] → [0,1] bijection is a composition of at most four involutive negators. Involutive negators are geometrically recognized by the symmetry of their graph w.r.t. the first bisector. If the graph of an automorphism has an alternating behavior, we can generate the automorphism by a pair of involutive negators.