JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (10): 78-82.doi: 10.6040/j.issn.1671-9352.0.2014.105

Previous Articles     Next Articles

The characterizations of lattice-valued fuzzy lower approximation operators by a unique axiom

LI Ling-qiang1,2, LI Qing-guo1   

  1. 1. College of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan, China;
    2. Department of Mathematics Science, Liaocheng University, Liaocheng 252059, Shandong, China
  • Received:2014-03-20 Online:2014-10-20 Published:2014-11-10

PDF (PC)

769

Abstract: Axiomatic approaches are important in the study of rough set theory. Generally, the axiomatic systems of rough sets consist of more than one axiom. In this paper, under the residuated lattice-valued context, we use only one axiom to describe the lower approximation generated by the lattice-valued fuzzy relations and a series of special lattice-valued fuzzy relations.

Key words: lattice-valued fuzzy relations, lattice-valued fuzzy rough sets, out products, axioms

CLC Number: 

  • O159.1
[1] PAWLAK Z. Rough set[J]. International Journal of Computer and Information Sciences, 1982, 11(5):341-356.
[2] YAO Yiyu. Relational Interpretations of neighborhood operators and rough set approximations operators[J]. Information Science, 1998, 111:239-259.
[3] 林国平,李进金,陈锦坤. 覆盖广义粗糙集的一般化方法[J]. 山东大学学报:理学版, 2012, 47(1):83-86. LIN Guoping, LI Jinjin, CHEN Jinkun. Generalization for covering generalized rough sets [J]. Journal of Shandong University: Natural Science, 2012, 47(1):83-86.
[4] ZHU W. Relationship between generalized rough sets based on binary relation and covering[J]. Information Sciences, 2009, 179:210-225.
[5] LIU Guilong. Generalized rough sets over fuzzy lattices[J]. Information Sciences, 2008, 178:1651-1662.
[6] SHE Yanhong, WANG Guojun. An axiomatic approach of fuzzy rough sets based on residuated lattices[J]. Computers and Mathematics with Applications, 2009, 58:189-201.
[7] HAO Jing, LI Qingguo. The relationship between L-fuzzy rough set and L-topology[J]. Fuzzy Sets and Systems, 2011, (178):74-83.
[8] 李令强,金秋,孙守斌,等. 多值近似空间的上下近似诱导的拓扑结构[J].系统科学与数学, 2012,32(2):226-236. LI Lingqiang, JIN Qiu, SUN Shoubin, et al. The topological structures induced by upper and lower approximations of many-valued approximation spaces[J]. Journal of Systems Science and Mathematics Science, 2012, 32(2):226-236.
[9] MA Zhenming, HU Baoqing. Topological and lattice structures of L-fuzzy rough sets determined by lower and upper sets[J]. Information Sciences, 2013, 218:194--204.
[10] MI Jusheng, ZHANG Wenxiu. An axiomatic characterization of a fuzzy generalization of rough sets[J]. Information Sciences, 2004, 160:235-249.
[11] LIU Guilong. Axiomatic systems for rough sets and fuzzy rough sets[J]. International Journal of Approximate Reasoning, 2008, 48:857-867.
[12] LIU Guilong. Using one axiom to characterize rough set and fuzzy rough set approximations[J].Information Sciences, 2013, 223:285-296.
[13] Hjek P. Metamathematics of fuzzy logic[M]. Dordrecht: Kluwer Academic Publishers, 1998.
[1] MA Hai-cheng, LI Sheng-gang. The digraphs representation of finite topologies [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 100-104.
[2] YU Yue,MENG Guang-wu . A note on ultra separation axioms of L-topological spaces [J]. J4, 2008, 43(2): 44-47 .
[3] ZHAO Mei-xiang, . ［0,1］-fuzzy separation axioms [J]. J4, 2007, 42(11): 98-100 .
[4] ZHAO Mei-xiangsup>,HU Kai,MENG Guang-wu . Bifuzzy separation axioms(Ⅱ) [J]. J4, 2006, 41(4): 44-47 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd