Abstract
This paper mainly addresses the connection between fuzzy rough sets and lattices. Based on a complete lattice equipped with a t-norm, the concepts of TL-fuzzy lower and upper rough approximation operators induced by an L-fuzzy set on a lattice are introduced, and their basic properties are investigated. Particularly, some characterizations of TL-fuzzy ideals on distributive lattices are developed in terms of the TL-fuzzy rough approximation operators. In addition, we use these operators to define a new class of fuzzy structures, called TL-fuzzy quasi-rough ideals induced by an L-fuzzy set on a lattice, and investigate the relationships among TL-fuzzy ideals, TL-fuzzy rough ideals and TL-fuzzy quasi-rough ideals on a given lattice.
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Acknowledgements
This work is supported by the National Science Foundation of China (Nos. 11371130; 11401195); the High School Doctoral Foundation of Ministry of Education of China (No. 20120161110017); the Hunan Provincial Natural Science Foundation of China (No. 2015JJ3050).
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Huang, X., Li, Q. & Guo, L. The TL-fuzzy rough approximation operators on a lattice. Soft Comput 22, 17–29 (2018). https://doi.org/10.1007/s00500-016-2448-8
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DOI: https://doi.org/10.1007/s00500-016-2448-8