Abstract
The algebra of truth values for fuzzy sets of type-2, due to Zadeh, contains as subalgebras those of type-1 and of interval-valued fuzzy sets. It also contains many other interesting subalgebras, some of which could possibly serve as a basis of a useful fuzzy set theory. This paper is about one such subalgebra which we call the subalgebra of points, and which generalizes type-1. We investigate it as an algebra, and determine its automorphism group. In particular, we show that is it a characteristic subalgebra and that its automorphisms are exactly those induced by automorphisms of the containing truth value algebra of fuzzy sets of type-2.
Keywords
- Fuzzy truth values
- type-2 fuzzy set
- type-1 fuzzy set
- interval-valued fuzzy set
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Walker, C.L., Walker, E.A. (2007). Points with Type-2 Operations. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_6
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DOI: https://doi.org/10.1007/978-3-540-72950-1_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72917-4
Online ISBN: 978-3-540-72950-1
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