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Residual coimplicators of left and right uninorms on a complete lattice. (English) Zbl 1183.03027
A left (right) uninorm \(U\) on a complete lattice \(L\) is an associative, non-decreasing binary operation with left (right) neutral element. If a left (right) uninorm has one neutral element, then \(U\) is called a pseudo-uninorm. The authors of this paper discuss some basic properties of the residual coimplications of infinitely \(\wedge\)-distributive left (right) uninorms and pseudo-uninorms. They also investigate the relations between them and residual implications presented by the authors in [“Residual operations of left and right uninorms on a complete lattice”, Fuzzy Sets Syst. 160, No. 1, 22–31 (2009; Zbl 1183.06003)].

MSC:
03B52 Fuzzy logic; logic of vagueness
03E72 Theory of fuzzy sets, etc.
06B23 Complete lattices, completions
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[1] De Baets, B., Coimplicators, the forgotten connectives, Tatra mountains math. publications, 12, 229-240, (1997) · Zbl 0954.03029
[2] De Baets, B., Idempotent uninorms, European J. oper. res., 118, 631-642, (1999) · Zbl 0933.03071
[3] De Baets, B.; Fodor, J., Residual operators of uninorms, Soft comput., 3, 89-100, (1999)
[4] De Baets, B.; Fodor, J., Van Melle’s combining function in MYCIN is a representable uninorm: an alternative proof, Fuzzy sets and systems, 104, 133-136, (1999) · Zbl 0928.03060
[5] De Baets, B.; Tsiporkova, E.; Mesiar, R., Conditioning in possibility theory with strict order norms, Fuzzy sets and systems, 106, 221-229, (1999) · Zbl 0985.28015
[6] Birkhoff, G., Lattice theory, (1967), American Mathematical Society Colloquium Publishers Providence, RI · Zbl 0126.03801
[7] Deschrijver, G.; Kerre, E.E., Uninorms in \(L^*\)-fuzzy set theory, Fuzzy sets and systems, 148, 243-262, (2004) · Zbl 1058.03056
[8] Fodor, J.; De Baets, B., Uninorm basics, (), 49-64 · Zbl 1128.03014
[9] J. Fodor, M. Roubens, Fuzzy Preference Modeling and Multicriteria Decision Support, Theory and Decision Library, Series D: System Theory, Knowledge Engineering and Problem Solving, Kluwer Academic Publishers, Dordrecht, 1994.
[10] Fodor, J.; Yager, R.R.; Rybalov, A., Structure of uninorms, Internat. J. uncertainly fuzziness knowledge-based systems, 5, 411-427, (1997) · Zbl 1232.03015
[11] Gabbay, D.; Metcalfe, G., Fuzzy logics based on \([0, 1)\)-continuous uninorms, Arch. math. logic, 46, 425-449, (2007) · Zbl 1128.03015
[12] Hu, S.K.; Li, Z.F., The structure of continuous uni-norms, Fuzzy sets and systems, 124, 43-52, (2001) · Zbl 0989.03058
[13] Klement, E.P.; Mesiar, R.; Pap, E., Triangular norms, (2000), Kluwer Academic Publishers Dordrecht · Zbl 0972.03002
[14] Mas, M.; Monserrat, M.; Torrens, J., On left and right uninorms, Internat. J. uncertainly fuzziness knowledge-based systems, 9, 491-507, (2001) · Zbl 1113.03341
[15] Mas, M.; Monserrat, M.; Torrens, J., On left and right uninorms on a finite chain, Fuzzy sets and systems, 146, 3-17, (2004) · Zbl 1045.03029
[16] Mas, M.; Monserrat, M.; Torrens, J., Two types of implications derived from uninorms, Fuzzy sets and systems, 158, 2612-2626, (2007) · Zbl 1125.03018
[17] Ruiz, D.; Torrens, J., Residual implications and co-implications from idempotent uninorms, Kybernetika, 40, 21-38, (2004) · Zbl 1249.94095
[18] Tsadiras, A.K.; Margaritis, K.G., The MYCIN certainty factor handling function as uninorm operator and its use as a threshold function in artificial neurons, Fuzzy sets and systems, 93, 263-274, (1998)
[19] Wang, Z.D.; Fang, J.X., Residual operations of left and right uninorms on a complete lattice, Fuzzy sets and systems, 160, 22-31, (2009) · Zbl 1183.06003
[20] Yager, R.R., Uninorms in fuzzy systems modeling, Fuzzy sets and systems, 122, 167-175, (2001) · Zbl 0978.93007
[21] Yager, R.R., Defending against strategic manipulation in uninorm-based multi-agent decision making, European J. oper. res., 141, 217-232, (2002) · Zbl 0998.90046
[22] Yager, R.R.; Kreinovich, V., Universal approximation theorem for uninorm-based fuzzy systems modeling, Fuzzy sets and systems, 140, 331-339, (2003) · Zbl 1040.93043
[23] Yager, R.R.; Rybalov, A., Uninorm aggregation operators, Fuzzy sets and systems, 80, 111-120, (1996) · Zbl 0871.04007
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