新型软粗糙集:软粗糙半群
|
摘要
为进一步简化处理不确定性问题的方法,在半群上研究了一种新型的软粗糙集(MSR-半群)。首先,基于软集、粗糙集和半群的一些基本理论,对它们之间的关系进行深入研究,并讨论了软粗糙集的运算和基本性质;接着,为了进一步了解软逼近空间,应用了下软粗糙逼近和上软粗糙逼近的概念;同时,在半群上提出了两种特殊软集即G-软集和GG-软集的概念,对其做相应的运算,并给出实例进行了证明;接着,对MSR-逼近空间的粗糙性进行讨论,提出了MSR-半群的概念,并且研究了上MSR-半群和下MSR-半群的基本特征;最后,通过实例进行比较分析,说明了软粗糙半群的研究价值。
In order to further simplify the method of dealing with the problem of uncertainty,this paper studied a new type of soft rough set(MSR-semigroup)on semigroups.First of all,based on some basic theories of soft sets,rough sets and semigroups,the relationship among them were deeply studied,and the operation and basic properties of soft rough sets were discussed.Then,in order to further understand the soft approximation space,the concepts of the lower and upper soft rough approximation were applied.At the same time,two special soft sets G-soft sets and GG-soft sets were proposed on semigroups,corresponding operations were given and some examples were given.Then,the roughness of the soft approximation space was discussed,the concept of MSR-semigroups was proposed,and the basic characteristics of the upper and lower MSR-semigroups were studied.Finally,a comparative analysis of example shows the research value of the soft rough semigroup.
In order to further simplify the method of dealing with the problem of uncertainty,this paper studied a new type of soft rough set(MSR-semigroup)on semigroups.First of all,based on some basic theories of soft sets,rough sets and semigroups,the relationship among them were deeply studied,and the operation and basic properties of soft rough sets were discussed.Then,in order to further understand the soft approximation space,the concepts of the lower and upper soft rough approximation were applied.At the same time,two special soft sets G-soft sets and GG-soft sets were proposed on semigroups,corresponding operations were given and some examples were given.Then,the roughness of the soft approximation space was discussed,the concept of MSR-semigroups was proposed,and the basic characteristics of the upper and lower MSR-semigroups were studied.Finally,a comparative analysis of example shows the research value of the soft rough semigroup.
引文
[1] CHEN J,LI J,LIN Y,et al.Relations of reduction between covering generalized rough sets and concept lattices[J].Information Sciences,2015,304(C):16-27.
[2] XIAO Q,LI Q,GUO L.Rough sets induced by ideals in lattices[J].Information Sciences,2014,271(7):82-92.
[3] ALI M I,SHABIR M,TANVEER S.Roughness in hemirings[J].Neural Computing&Applications,2012,21(1):171-180.
[4] SHI W F,SHANG L.A method for determining the number of fuzzy C-means clustering based on decision rough sets[J].Computer Science,2017,44(9):45-48.(in Chinese)石文峰,商琳.一种基于决策粗糙集的模糊C均值聚类数的确定方法[J].计算机科学,2017,44(9):45-48.
[5] KANDIL A,YAKOUT M M,ZAKARIA A.New Approaches of Rough Sets via Ideals[M]∥Handbook of Research on Genera-lized and Hybrid Set Structures and Applications for Soft Computing.2016.
[6] ALI M I,SHABIR M.Logic Connectives for Soft Sets and Fuzzy Soft Sets[J].IEEE Transactions on Fuzzy Systems,2014,22(6):1431-1442.
[7]AGMAN N,ENGINOGLU S.Soft Set theory and uni-int decision making[J].European Journal of Operational Research,2010,207(2):848-855.
[8] MUKHERJEE A,DAS A K.Application of Interval Valued Intuitionistic Fuzzy Soft Set in Investment Decision Making[C]//Fifth International Conference on Advances in Computing and Communications.IEEE,2016:61-64.
[9] AKTAS,,H,AGˇMAN N.Soft sets and soft groups[J].Information Sciences,2007,177(13):2726-2735.
[10]FENG F,LI C,DAVVAZ B,et al.Soft sets combined with fuzzy sets and rough sets:a tentative approach[J].Soft Computing,2010,14(9):899-911.
[11]MAJI P K,ROY A R,BISWAS R.An application of soft sets in a decision making problem[J].Computers&Mathematics with Applications,2002,44(8-9):1077-1083.
[12]MOLODTSOV D.Soft set theory——First results[J].Computers&Mathematics with Applications,1999,37(4-5):19-31.
[13]FENG F,LIU X,LEOREANU-FOTEA V,et al.Soft sets and soft roughsets[J].Information Sciences,2011,181(6):1125-1137.
[14]PAWLAK Z.Rough sets[J].International Journal of Computer&Information Sciences,1982,11(5):341-356.
[15]PAWLAK Z.Rough Sets:Theoretical Aspects of Reasoning about Data[M].London:Kluwer Academic Publishers,1992.
[16]SHABIR M,ALI M I,SHAHEEN T.Another approach to soft rough sets[J].Knowledge-Based Systems,2013,40(1):72-80.
[17]FENG F.Soft rough sets applied to multicriteria group decision making[J].Annals of Fuzzy Mathematics and Informatics,2010,2(1):69-80.
[18]LIANG D,PEDRYCZ W,LIU D,et al.Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making[J].Applied Soft Computing,2015,29(C):256-269.
[19]XUE Z A,ZHU T L,XUE T Y,et al.Three-branch decision model based on Intuitionistic Fuzzy Sets[J].Computer Science,2016,43(6):283-288.(in Chinese)薛占熬,朱泰隆,薛天宇,等.基于直觉模糊集的三支决策模型[J].计算机科学,2016,43(6):283-288.
[2] XIAO Q,LI Q,GUO L.Rough sets induced by ideals in lattices[J].Information Sciences,2014,271(7):82-92.
[3] ALI M I,SHABIR M,TANVEER S.Roughness in hemirings[J].Neural Computing&Applications,2012,21(1):171-180.
[4] SHI W F,SHANG L.A method for determining the number of fuzzy C-means clustering based on decision rough sets[J].Computer Science,2017,44(9):45-48.(in Chinese)石文峰,商琳.一种基于决策粗糙集的模糊C均值聚类数的确定方法[J].计算机科学,2017,44(9):45-48.
[5] KANDIL A,YAKOUT M M,ZAKARIA A.New Approaches of Rough Sets via Ideals[M]∥Handbook of Research on Genera-lized and Hybrid Set Structures and Applications for Soft Computing.2016.
[6] ALI M I,SHABIR M.Logic Connectives for Soft Sets and Fuzzy Soft Sets[J].IEEE Transactions on Fuzzy Systems,2014,22(6):1431-1442.
[7]AGMAN N,ENGINOGLU S.Soft Set theory and uni-int decision making[J].European Journal of Operational Research,2010,207(2):848-855.
[8] MUKHERJEE A,DAS A K.Application of Interval Valued Intuitionistic Fuzzy Soft Set in Investment Decision Making[C]//Fifth International Conference on Advances in Computing and Communications.IEEE,2016:61-64.
[9] AKTAS,,H,AGˇMAN N.Soft sets and soft groups[J].Information Sciences,2007,177(13):2726-2735.
[10]FENG F,LI C,DAVVAZ B,et al.Soft sets combined with fuzzy sets and rough sets:a tentative approach[J].Soft Computing,2010,14(9):899-911.
[11]MAJI P K,ROY A R,BISWAS R.An application of soft sets in a decision making problem[J].Computers&Mathematics with Applications,2002,44(8-9):1077-1083.
[12]MOLODTSOV D.Soft set theory——First results[J].Computers&Mathematics with Applications,1999,37(4-5):19-31.
[13]FENG F,LIU X,LEOREANU-FOTEA V,et al.Soft sets and soft roughsets[J].Information Sciences,2011,181(6):1125-1137.
[14]PAWLAK Z.Rough sets[J].International Journal of Computer&Information Sciences,1982,11(5):341-356.
[15]PAWLAK Z.Rough Sets:Theoretical Aspects of Reasoning about Data[M].London:Kluwer Academic Publishers,1992.
[16]SHABIR M,ALI M I,SHAHEEN T.Another approach to soft rough sets[J].Knowledge-Based Systems,2013,40(1):72-80.
[17]FENG F.Soft rough sets applied to multicriteria group decision making[J].Annals of Fuzzy Mathematics and Informatics,2010,2(1):69-80.
[18]LIANG D,PEDRYCZ W,LIU D,et al.Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making[J].Applied Soft Computing,2015,29(C):256-269.
[19]XUE Z A,ZHU T L,XUE T Y,et al.Three-branch decision model based on Intuitionistic Fuzzy Sets[J].Computer Science,2016,43(6):283-288.(in Chinese)薛占熬,朱泰隆,薛天宇,等.基于直觉模糊集的三支决策模型[J].计算机科学,2016,43(6):283-288.