于秀清,董化玲,徐鳳生

(德州學(xué)院 數(shù)學(xué)系,山東 德州 253023)

0 引言與預(yù)備知識(shí)

αF=α∪{α′|βα,f(β)=α′∈α,f∈F},

(1)

(2)

這里:β∈V,βα;f∈F把β變成f(β)=α′∈α.

(3)

則稱XF是X生成的外P-集合(outer P-setXF),簡稱XF是外P-集合,且

XF=X∪{u|u∈U,uX,f(u)=x′∈X,f∈F},

(4)

1 內(nèi)P-集合副集的σ-生成和σ-強(qiáng)生成

定義2如果

(5)

(6)

(7)

由定義1和定義2,可得如下結(jié)論.

?.

由定理3知: 對(duì)于?σ*∈(σ1,σ2],

所以

?,

于是

(8)

(9)

(10)

[1] SHI Kai-quan.P-Sets [J].Journal of Shandong University: Natural Science,2008,43(11): 77-84.(史開泉.P-集合 [J].山東大學(xué)學(xué)報(bào): 理學(xué)版,2008,43(11): 77-84.)

[2] SHI Kai-quan.P-Sets and Its Applications [J].An International Journal Advances in Systems Science and Applications,2009,9(2): 209-219.

[3] YU Xiu-qing.P(ρ,σ)-Sets and Its Random Characteristics [J].Computer Science,2010,37(9): 218-221.(于秀清.P(ρ,σ)-集合與它的隨機(jī)特性 [J].計(jì)算機(jī)科學(xué),2010,37(9): 218-221.)

[4] ZHANG Li,CUI Yu-quan,SHI Kai-quan.Outer P-Set and Internal-Outer Recovery [J].System Engineering and Electronics,2010,32(6): 1233-1238.(張麗,崔玉泉,史開泉.外P-集合與數(shù)據(jù)內(nèi)-外恢復(fù) [J].系統(tǒng)工程與電子技術(shù),2010,32(6): 1233-1238.)

[5] LIN Hong-kang,FAN Cheng-xian.The Dual Form of P-Reasoning and Idengtification of Unknown Attribute [J].International Journal of Digital Content Technology and Its Applications,2012,6(1): 121-131.

[6] ZHANG Fei,CHEN Ping,ZHANG Li.P-Separation of P-Sets and Its Applications [J].Journal of Shandong University: Natural Science,2010,45(3): 71-75.(張飛,陳萍,張麗.P-集合的P-分離與應(yīng)用 [J].山東大學(xué)學(xué)報(bào): 理學(xué)版,2010,45(3): 71-75.)

[7] LI Yu-ying.Half P-Sets (XF,X) and Noise Data Rejction-Application [J].Computer Science,2011,38(8): 221-225.(李豫穎.半P-集合(XF,X)與噪聲數(shù)據(jù)剔除-應(yīng)用 [J].計(jì)算機(jī)科學(xué),2011,38(8): 221-225.)

[8] YU Xiu-qing.P-Sets and the Identification-Recovery ofF-Outer Embedding in Formation [J].Computer Science,2010,38(1): 250-253.(于秀清.P-集合與F-外嵌入信息辨識(shí)-發(fā)現(xiàn) [J].計(jì)算機(jī)科學(xué),2010,38(1): 250-253.)

[9] XU Feng-sheng,YU Xiu-qing,SHI Kai-quan.Internal P-Reasoning and Identification of Internal Convergence Information [J].Computer Science,2012,39(3): 212-215.(徐鳳生,于秀清,史開泉.內(nèi)P-推理與內(nèi)收斂信息的辨識(shí) [J].計(jì)算機(jī)科學(xué),2012,39(3): 212-215.)

[10] FAN Cheng-xian,LIN Hong-kang.P-Sets and the Reasoning-Identification of Disaster Information [J].International Journal of Convergence Information Technology,2012,7(1): 337-345.