Abstract
This chapter offers a concise introduction to lattices, Boolean algebras, topological molecular lattices and shows main relations between them. For details, the readers may refer to [1, 3, 2]. Our purpose is to familiarize the readers with the concepts and fundamental results, which will be exploited in further discussion. Some results listed without proofs is left to the reader.
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References
Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematics Society Providence, RI (1967)
Jacobson, N.: Basic Algebra I. W H Freeman and Company, New York (1985)
Wang, G.J.: Theory of Topological Molecular Lattices. Fuzzy Sets and Systems 47, 351–376 (1992)
Pu, B.M., Liu, Y.M.: Fuzzy Topology I, Neighborhood structure of Fuzzy Point and Moore-Smith Convergence. Journal of Mathematical Analysis and Applications 76, 571–599 (1980)
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Liu, X., Pedrycz, W. (2009). Lattices. In: Axiomatic Fuzzy Set Theory and Its Applications. Studies in Fuzziness and Soft Computing, vol 244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00402-5_2
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DOI: https://doi.org/10.1007/978-3-642-00402-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00401-8
Online ISBN: 978-3-642-00402-5
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