双论域上基于Brouwer－正交补的粗糙近似

南京大学学报(自然科学版) ›› 2016, Vol. 52 ›› Issue (5): 871–.

双论域上基于Brouwer－正交补的粗糙近似

李同军1，2*，吴伟志1，2，顾沈明1，2

出版日期:2016-09-25 发布日期:2016-09-25
作者简介: 1.浙江海洋大学，浙江省海洋大数据挖掘与应用重点实验室，舟山，316022；2．浙江海洋大学数理与信息学院，舟山，316022
基金资助:
基金项目：国家自然科学基金(11071284，41631179，61272021，61573321)，浙江省自然科学基金(LY14F030001)
收稿日期：2016－09－06
*通讯联系人，Email：ltj722@163.com

Rough approximations based on Brouwerorthocomplementations on two universes of discourse

Li Tongjun1，2*，Wu Weizhi1，2，Gu Shenming1，2

Online:2016-09-25 Published:2016-09-25
About author: 1.Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province，Zhejiang Ocean University，Zhoushan，316022，China；2．School of Mathematics，Physics and Information Science，Zhejiang Ocean University，Zhoushan，316022，China

摘要/Abstract

摘要： 主要研究广义近似空间上粗糙近似算子的扩展模型．首先，将Cattaneo提出的抽象近似空间理论具体运用于广义近似空间中的粗糙集模型研究，利用空间中双论域间的二元关系，导出指定论域上的一个Brouwer－正交补算子，据此算子构造性地定义了指定论域上的两对粗糙近似算子．然后，研究了新算子的基本性质和代数表示，将它们与已有近似算子进行对比，指出它们的异同，给出它们之间的大小顺序关系．最后，研究了新近似算子和已有近似算子的等价性，给出它们与邻近算子之间等价的条件，讨论了等价条件之间的关系．

Abstract: The objective of this paper is to establish new rough set models on generalized approximation spaces.One basic notion in a generalized approximation space is the relation between the two universes of discourse.In the original rough set models of generalized approximation spaces，the approximating sets and the approximated sets are located on different universes.Some extended models are thus proposed for many applications，in which the approximating sets and the approximated sets are located on the same universe.According to the theory of abstract approximation spaces presented by Cattaneo，a preclusivity relation on one of the two universes of a generalized approximation space is firstly induced from a relation between two universes，and a Brouwerorthocomplentation operator on the universe is constructed.Consequently，two pairs of lower and upper rough approximation operators are formulized by the Brouwerorthocomplentation operation，which guarantees that the approximating sets and the approximated sets are located on the same universe.Secondly，the representations and properties of the operators defined newly are explored.As a result，it is discovered that one of the two pairs of new operators is equal to existing one，and by the way，an ordered relation among the new operators and the existing operators are given.At last，the equivalence among them and the nearest operators in an ordered chain are investigated.Consequently，some necessary and sufficient conditions are obtained and relations among them are illustrated.

李同军1，2*，吴伟志1，2，顾沈明1，2. 双论域上基于Brouwer－正交补的粗糙近似[J]. 南京大学学报(自然科学版), 2016, 52(5): 871–.

Li Tongjun1，2*，Wu Weizhi1，2，Gu Shenming1，2. Rough approximations based on Brouwerorthocomplementations on two universes of discourse[J]. Journal of Nanjing University(Natural Sciences), 2016, 52(5): 871–.

参考文献

[1]　Zadeh L A．Fuzzy sets and information granularity.In：Gupta N，Ragade R，Yager R R．Advances in Fuzzy Set Theory and Applications.NorthHolland，Amsterdam，1979：3－18.
[2] Yao J T，Vailakos A V，Pedrycz W．Granular computing：Perspectives and challenges.IEEE Transactions on Cybernetics，2013，43：1977－1989.
[3] Pedrycz W，Succi G，Sillitti A，et al.Data description：A general framework of information granules.KnowledgeBased System，2015，80：98－108.
[4] Yao Y Y．Information granulation and rough set approximation.International Journal of Intelligent Systems，2001，16：87－104.
[5] Pawlak Z．Rough sets.International Journal of Computer and Information Science，1982，11：341－356.
[6] Yao Y Y．The superiority of threeway decisions in probabilistic rough set models.Information Sciences，2011，181：1080－1096.
[7] Slowinski R，Vanderpooten D．A generalized definition of rough approximations based on similarity.IEEE Transactions on Knowledge and Data Engineering，2000，12：331－336.
[8] Bonikowski Z，Bryniarski E，Wybraniec U．Extensions and intentions in the rough set theory.Information Sciences，1998，107：149－167.
[9] Yao Y Y．Two views of the theory of rough sets in finite universe.International Journal of Approximate Reasoning，1996，15：291－317.
[10] Wong S K，Wang L S，Yao Y Y．On modeling uncertainty with interval structure.Computational Intelligence，1995，11：406－426.
[11] Yao Y Y．Constructive and algebraic methods of the theory of rough sets.Information Sciences，1998，109：21－47.
[12] Wu W Z，Zhang W X．Constructive and axiomatic approaches of fuzzy approximation operators.Information Sciences，2004，159：233－254.
[13] Wu W Z，Zhang W X．Generalized fuzzy rough sets.Information Sciences，2003，15：263－282.
[14] Pei D W，Xu Z B．Rough set models on two universes.International Journal of General Systems，2004，33(5)：569－581.
[15] Li T J．Rough approximation operators on two universes of discourse and their fuzzy extensions.Fuzzy Sets and Systems，2008，159(22)：3033－3050.
[16] Li T J，Zhang W X．Rough fuzzy approximations on two universes of discourse.Information Sciences，2008，178(3)：892－906.
[17] Abd ElMonsef M E，ElGayar M A，Aqeel R M．A comparison of three types of rough fuzzy sets based on two universal sets.International Journal of Machine Learning & Cybernetics，DOI：10.1007/s13042－015－0327－8.
[18] Sun B Z，Ma W M．Fuzzy rough set model on two different universes and its application.Applied Mathematical Modelling，2011，35：1798－1809.
[19] Yang H L，Li S G，Wang S，et al.Bipolar fuzzy rough set model on two different universes and its application.KnowledgeBased System，2012，35：94－101.
[20] Xu W，Sun W，Liu Y，et al.Fuzzy rough set models over two universes.International Journal of Machine Learning & Cybernetics，2013，4(6)：631－645.
[21] Cattaneo G．Abstract approximation spaces for rough theories.In：Polkowski S．Studies in Fuzziness and Soft Computing 18，Rough Set and Kownoledge Discovery 1.PhysicaVerlag，1998：59－98.

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