Abstract
This paper shows many relations among fuzzy switching functions and fuzzy integrals. First, we show that monotone fuzzy switching functions with constants are extended Sugeno integrals and fuzzy switching functions are Sugeno integrals whose inputs are double inputs, that is, true and false inputs. Next, we propose a Choquet integral based fuzzy binary switching function, which is calculated by a Choquet integral of double inputs and which uses adjusted fuzzy measure of complementary sets. The functions satisfy the complementary law and monotonicity under the monotonicity on binary inputs. Finally, we propose a logical Choquet integral and we discuss its properties.
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References
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© 2004 Springer-Verlag Berlin Heidelberg
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Takahagi, E. (2004). Fuzzy Integral Based Fuzzy Switching Functions. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds) Transactions on Rough Sets II. Lecture Notes in Computer Science, vol 3135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27778-1_8
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DOI: https://doi.org/10.1007/978-3-540-27778-1_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23990-1
Online ISBN: 978-3-540-27778-1
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