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On the algebraic structure of binary lattice-valued fuzzy relations

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Abstract

From a general algebraic point of view, this paper aims at providing an algebraic analysis for binary lattice-valued relations based on lattice implication algebras—a kind of lattice-valued propositional logical algebra. By abstracting away from the concrete lattice-valued relations and the operations on them, such as composition and converse, the notion of lattice-valued relation algebra is introduced, LRA for short. The reduct of an LRA is a lattice implication algebra. Such an algebra generalizes Boolean relation algebras by general distributive lattices and can provide a fundamental algebraic theory for establishing lattice-valued first-order logic. Some important results are generalized from the classical case. The notion of cylindric filter is introduced and the generated cylindric filters are characterized.

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Acknowledgments

The work was partially supported by the National Natural Science Foundation of China (Grant No. 61100046, 61175055) and the application fundamental research plan project of Sichuan Province (Grant No. 2011JY0092) and the Fundamental Research Funds for the Central Universities (Grant No. SWJTU12CX054, SWJTU12ZT14). The authors are highly grateful to referees and Professor Antonio Di Nola, Editor-in-Chief, for their valuable comments and suggestions improving the paper.

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  1. School of Mathematics, Southwest Jiaotong University, 610031, Chengdu, Sichuan, People’s Republic of China

    Xiaodong Pan & Yang Xu

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  1. Xiaodong Pan
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  2. Yang Xu
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Correspondence to Xiaodong Pan.

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Pan, X., Xu, Y. On the algebraic structure of binary lattice-valued fuzzy relations. Soft Comput 17, 411–420 (2013). https://doi.org/10.1007/s00500-012-0916-3

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