Algebraic Structures of Truth Values in Fuzzy Logic
IJCAI '91 Proceedings of the Workshops on Fuzzy Logic and Fuzzy Control
ISMVL '00 Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic
de Morgan Bisemilattice of Fuzzy Truth Value
ISMVL '02 Proceedings of the 32nd International Symposium on Multiple-Valued Logic
A First Course in Fuzzy Logic, Third Edition
A First Course in Fuzzy Logic, Third Edition
Efficient triangular type-2 fuzzy logic systems
International Journal of Approximate Reasoning
The variety generated by the truth value algebra of type-2 fuzzy sets
Fuzzy Sets and Systems
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International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Design of interval type-2 fuzzy models through optimal granularity allocation
Applied Soft Computing
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Information Sciences: an International Journal
Exact inversion of decomposable interval type-2 fuzzy logic systems
International Journal of Approximate Reasoning
On type-2 fuzzy sets and their t-norm operations
Information Sciences: an International Journal
On type-2 fuzzy relations and interval-valued type-2 fuzzy sets
Fuzzy Sets and Systems
Type-2 operations on finite chains
Fuzzy Sets and Systems
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The algebra of truth values of type-2 fuzzy sets consists of all mappings of the unit interval to itself, with type-2 operations that are convolutions of ordinary max and min operations. This paper is concerned with a special subalgebra of this truth value algebra, namely the set of nonzero functions with values in the two-element set {0,1}. This algebra can be identified with the set of all non-empty subsets of the unit interval, but the operations are not the usual union and intersection. We give simplified descriptions of the operations and derive the basic algebraic properties of this algebra, including the identification of its automorphism group. We also discuss some subalgebras and homomorphisms between them and look briefly at t-norms on this algebra of sets.