Distributive idempotent uninorms. (English) Zbl 1074.03026

Summary: A characterization of all idempotent uninorms satisfying the distributivity property is given. The special cases of left-continuous and right-continuous idempotent uninorms are presented separately, and it is also proved that all idempotent uninorms are autodistributive. Moreover, all distributive pairs of idempotent uninorms (pairs \(U_{1}, U_{2}\) such that \(U_{1}\) is distributive over \(U_{2}\) and \(U_{2}\) is distributive over \(U_{1}\)) are also characterized.


03E72 Theory of fuzzy sets, etc.
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[1] DOI: 10.1016/0165-0114(95)00133-6 · Zbl 0871.04007 · doi:10.1016/0165-0114(95)00133-6
[2] DOI: 10.1016/S0165-0114(00)00027-0 · Zbl 0978.93007 · doi:10.1016/S0165-0114(00)00027-0
[3] DOI: 10.1142/S0218488597000312 · Zbl 1232.03015 · doi:10.1142/S0218488597000312
[4] DOI: 10.1016/S0377-2217(98)00325-7 · Zbl 0933.03071 · doi:10.1016/S0377-2217(98)00325-7
[5] DOI: 10.1016/S0165-0114(99)00125-6 · Zbl 0977.03026 · doi:10.1016/S0165-0114(99)00125-6
[6] DOI: 10.1016/S0165-0114(01)00123-3 · Zbl 1005.03047 · doi:10.1016/S0165-0114(01)00123-3
[7] DOI: 10.1007/978-94-015-9540-7 · doi:10.1007/978-94-015-9540-7
[8] DOI: 10.1016/0165-0114(84)90072-1 · Zbl 0555.94027 · doi:10.1016/0165-0114(84)90072-1
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