Abstract
In this paper, we study the decomposability of S-implications, R-implications, n-reciprocal R-implications and n-reciprocal QL-implications.
Foundation item: Ningbo Natural Science Foundation and Science Foundation of Zhejiang Wanli University.
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References
De Baets, B., Mesiar, R.: Triangular norms on product lattices. Fuzzy Sets and Systems 104, 61–75 (1999)
Karacal, F.: On the direct decomposability of strong negations and S-implication operators on product lattices. Information Sciences 176, 3011–3015 (2006)
Wang, Z.D.: Generating pseudo-t-norms and implication operators. Fuzzy Sets and Systems 157, 398–410 (2006)
Wang, Z.D.: Notes on the pseudo-tnorms and implication operators on a complete Brouwerian lattice (I). Fuzzy Systems and Mathematics 20(1), 107–111 (2006)
Wang, Z.D., Yu, Y.D.: Pseudo-t-norms and implication operators on a complete Brouwerian lattice. Fuzzy Sets and Systems 132, 113–124 (2002)
Wang, Z.D., Yu, Y.D.: Pseudo-t-norms and implication operators: direct products and direct product decompositions. Fuzzy Sets and Systems 139, 673–683 (2003)
Birkhoff, G.: Lattice Theory. Amer. Math. Soc. Coll. Publ., Rhode Island (1967)
Ma, Z., Wu, W.M.: Logical operators on complete lattices. Information Sciences 55, 77–97 (1991)
Wang, Z.D.: On L-subsets and TL-subalgebras. Fuzzy Sets and Systems 65, 59–69 (1994)
Dubois, D., Prade, H.: Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions. Fuzzy Sets and Systems 40, 143–202 (1991)
Fodor, J.C.: Contrapositive symmetry of fuzzy implications. Fuzzy Sets and Systems 69, 141–156 (1995)
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Wang, Z. (2007). Decomposability of Implication Operators. In: Apolloni, B., Howlett, R.J., Jain, L. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2007. Lecture Notes in Computer Science(), vol 4693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74827-4_24
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DOI: https://doi.org/10.1007/978-3-540-74827-4_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74826-7
Online ISBN: 978-3-540-74827-4
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