Research on Care of Postoperative Patient based on Rough Sets Theory

Transcription

1 International Jornal of Compter Applications ( ) Volme No0, October 0 Research on Care of Postoperative Patient based on Rogh Sets Theory Ynlong X School of Compter Science & Technology, Soochow University, Szho, P R China Yping Cao Department of Basic Corse Lianyngang Technical College, Lianyngang,P R China Songlin Yang School of Mathematical Science Soochow University, Szho, P R China ABSTRACT In this paper, the rogh set theory is sed to deal with the relations between patient s temperatre, oxygen satration, blood pressre and decision ADM-DECS in care of postoperative patients, we select 8 postoperative patients as a sample, take ADM-DECS as a decision attribte and take patient s temperatre, oxygen satration, blood pressre as condition attribtes We are based on rogh-set theory to research importance of condition attribtes with respective to decision attribte and strength of condition attribtes spporting decision attribte Reslts of this research will be helpfl for nrses to raise qality of care Keywords rogh set; importance; strength; blood pressre INTRODUCTION In order to extract sefl information hidden in the sea of data, many methods in addition to classical logic have been proposed Rogh set theory, which was proposed by Z Pawlak in 98[], plays an important role in applications of these methods Their significance has been demonstrated by many sccessfl applications in pattern recognition and artificial intelligence[][][][7][9][0] [] An important application of rogh set theory is to indce decision rles that indicate the decision class of an object based on its vales on some condition attribtes [6][8] The data obtained from the clinical diagnosis and care contain a large amont of information The algorithm which ses the data mining techniqe, especially the techniqe based on the rogh set theory, can be trained throgh the training data set and can be applied to determine the state of an illness with a very high accracy[][][] In this paper we se rogh sets theory to deal with the relations between patient s temperatre, oxygen satration, blood pressre and decision ADM-DECS, to research what is the most important in care of postoperative patients, then find what nrses shold focs on in nrsing For this prpose, we selected 8 postoperative patients from a hospital at random as a sample and recorded their internal temperatre, oxygen satration, lase measrement of blood pressre, stability of core temperatre and stability of blood pressre as the following table PAT I ENT CO RE Table : Postoperative Patient Data O BP CORE STBL BP STBL AD M DE CS No mid excel mid stable stable A No mid excel high stable modsta S No high excel high stable stable A No mid good high stable modsta S No mid excel high stable stable A No6 high good mid stable nstable S No7 mid excel high stable stable A No8 high excel mid nstable modsta S No9 mid good mid stable modsta S No0 high excel mid stable stable A No mid good mid stable stable A No mid good high stable modsta S No high excel high stable nstable A No mid good mid stable modsta A No mid good high nstable modsta S No6 high excel high stable nstable A No7 low good high stable stable A No8 mid good low stable stable A No9 mid good mid stable nstable A No0 mid good mid modsta modsta S No low good mid stable stable A No low excel high stable nstable A No mid good mid stable nstable A No low good high stable stable A No high good mid stable modsta A No6 high good low stable modsta A No7 high good mid nstable nstable I No8 mid good mid stable nstable I Where CORE denotes patient s internal temperatre in C: high(> 7), mid( 6 and 7), low(< 6) O denotes oxygen satration in %: excel(excellent)( 98), good ( 90 and < 98), fair ( 80 and < 90), poor (< 80) BP denotes last measrement of blood pressre: high(>0/90), mid( 0/90 and 90/70), low(< 90/70) CORE-STBL denotes stability of patient s internal temperatre: stable, modstab(mod-stable), nstable BP-STBL denotes stability of patient s blood pressre: stable, modstab(mod-stable), nstable ADM-DECS: I(patient set to Intensive Care Unit), S(patient prepared to go home), A(patient sent to general hospital floor) 8

2 International Jornal of Compter Applications ( ) Volme No0, October 0 PRELIMINARIES In this section, we recall some basic concepts from rogh set theory[][6][7][8] Definition : S ( U, A, V, f ) is called an information system () U, a nonempty finite set, is called the niverse of discorse () A C D is a finite set of attribtes, where C and D are disjoint nonempty sets of condition attribtes and decision attribtes respectively () f : U A V is an information fnction () V V : A}, where V f (, ) : U} If we distingish in the information system two disjoint classes of attribtes, called condition and decision attribtes, respectively, then system will be called a decision table and will be denoted by S = (U, C,, where C and D are disjoint sets of condition and decision attribtes, respectively, and C D A Colmns of a decision table are labeled by elements of A, rows of a decision table are labeled by elements of U Definition : Let S ( U, C D, V, f ) be an information system () For a C D, we define an eqivalence relation ~ on U as follows: i ~ j f ( i, a) f ( j, a) U / a denotes the family consisting of all eqivalence classes with respect to ~ Notation [] denotes the eqivalence class with respect to ~ containing U () For B C D, U / b : b B} is a partition of U, which is denoted U / B The eqivalence relation indced by U / B is also denoted by B Definition : Let R be an eqivalence relation on an niverse U of discorse, and X U Pt R( X ) [ ] [ ] U / R,[ ] X} R (X ) is called lower approximation of X Definition : Let R be a family of eqivalence relations on U and R 0 R Let Q be an eqivalence relation on U () Pt pos R ( Q) R( X ) : X U / Q} pos R (Q) is called positive region of Q with respect to R posr ( Q) () Pt R( Q) is called dependable U degree of Q with respect to R where U denotes the cardinal of U () Pt ( R) ( Q) ( Q) (R) is RQ R RR called importance of R with respect to Q Definition : For information system S ( U, C, let W U and c C () Pt S c ( W) [ ]:[ ] U / c and [ ] W} S c (W) is called a spport sbset of W with respect to condition attribte c Sc ( W ) () Pt sptc ( W ) is called the spport deg- U ree of W with respect to condition attribte c RQ () Pt Sc( d) Sc( W) : W U / d} S c (d) is called a spport sbset of decision attribte d with respect to condition attribte c Theorem : Let S = (U, C S be an information system, c C and D d} Then the following hold () Sc( d) Sc( W ) Sc( W ) Sc( W ) () Sc( Wi ) Sc( Wj ) for all i, j,, and i j () sptc ( d) sptc ( W ) sptc ( W ) sptc ( W ) ROUGH SET MODEL AND DECISION TABLE In this section, we establish a rogh set model of Postoperative Patient Data for or investigation, which is expressed by the following decision table we transform Table into a decision table(table ) of or rogh set model Table : Decision Table U c c c c c d c c c c c d c c c c c d c c c c c d c c c c c d c c c c c d 6 c c c c c d 7 c c c c c d 8 c c c c c d 9 c c c c c d 0 c c c c c d c c c c c d c c c c c d c c c c c d c c c c c d c c c c c d 6 c c c c c d 7 c c c c c d 8 c c c c c d 9 c c c c c d 0 c c c c c d c c c c c d c c c c c d c c c c c d c c c c c d c c c c c d 6 c c c c c d 7 c c c c c d 8 c c c c c d where c, c, c, c, c are five condition attribtes in the information system, c, c, c, c, c denote patient s internal temperatre, oxygen satration, last measrement of blood pressre, stability of core temperatre and stability of blood pressre d is the decision attribte, d denotes decision ADM-DECS Remark : () c indicates patient s internal temperatre more than 7, c indicates patient s internal temperatre between 6 and 7, c indicates patient s internal temperatre lower than 6 () c indicates patient s oxygen satration more than 98%, c indicates patient s internal temperatre between 90% and 98%, c indicates patient s internal temperatre between 80% and 90%, c indicates patient s internal 9

3 International Jornal of Compter Applications ( ) Volme No0, October 0 temperatre lower than 80% () c indicates patient s last measrement of blood pressre more than 0/90, c indicates patient s last measrement of blood pressre between 0/90 and 90/70, c indicates patient s internal temperatre lower than 90/70 () c indicates that patient s core temperatre is stable, c indicates that patient s core temperatre is mod-stable, c indicates that patient s core temperatre is nstable () c indicates that patient s blood pressre is stable, c indicates that patient s blood pressre is mod-stable, c indicates that patient s blood pressre is nstable Remark : d indicates that patient is sent to Intensive Care Unit, d indicates that patient prepare to go home, d indicates that patient is sent to general hospital floor Let U,,, 8}, C c, c, c, c, c}, D d}, S U, C D} is a decision table of an information system Some related partitions of U and related rogh sets are following Related partitions of U By some simple calclating, we have the following related partitions of U () U/ c =, 0, 7},,,,,,,,,,,,, },, , }} () U / c=,,, 0, 7},,,,, 0,, 8}} () U / c=,,,, },, 0,, 0, 7, 6}} () U/ c=,,, 0,,,, 8} 8,, 7}} () U / c=,, 0, },,,, 0, 6} 9, 8}} (6) U / C= } } } } 6}, } 0} } 6} } } 8}, 0} } } } 6} (7) U / D= 7,,,, 0,, 0,,,, 6}} (8) U/( C c}) =, 0} }, }, 6,, } } }, 6, } } } 0} 6} 7}} (9) U/( C c}) =, }, } } 7} 6} } 0} 6} } }, 0} } } } 6}, 7 }} (0) U/( C c}) =, }, 0}, } } }, }, } }, 9, , } 0} } } 6}, 7 }} () U/( C c}) = } } }, }, },, } },, } } }, , 6} } } }, } 6}} () U/( C c}) = },, 6},, } 6} 9} 0}, 8}, } 7, } 0} } } } 6}, 7 }} Related rogh sets of U By Definition, we have the following positive regions by some simple calclating pos ( ),,,,,,,,,, () C D ,, 0, 7} () pos,,,,,,,,, C c }( 7 8 0,, 0, 7} () pos,,,,,,,,, C c }( ,, 0, 7} () pos,,,,,,,,, C c }( , 0, 7} () pos,,,,,,,,, C c }( 7 8 0,, 6} (6) posc c }(,, 0,,, 0, 7} IMPORTANCE AND SUPPORT DEGREES For an information system S ( U, C, let c C Pt CD( c}) C ( C c} ( According to Z Pawlak rogh-set theory, CD (c }) is the importance of condition attribte c with respect to decision attribte d By Definition and some simple calclating, we have the following proposition Proposition : The following hold posc ( () C ( 0 8 U posc () C 0 7 U posc () C 0 79 U posc () C 0 7 U 0

4 International Jornal of Compter Applications ( ) Volme No0, October 0 posc () C 0 7 U posc (6) C 0 7 U By Proposition, we have the following proposition, which gives the importance of condition attribte C with respect to decision attribte d Proposition : The following hold () CD( c }) C ( C 0 07 () CD( c }) C ( C 0 0 () CD( c }) C ( C 0 07 () CD( c }) C ( C 0 () CD( c }) C ( C 0 For an information system S ( U, C, let c C Sc( d) Pt sptc ( d) According to rogh-set theory, U spt c (d) reflects the strength of condition attribte c C spporting decision attribte d Let W 8}, W, 0,, 0}, W,,,,, 6} Then U / D W, W, W} By Definition and some simple calclating, we have the following spport sets Proposition : The following hold () Sc ( W ), S ( W ), S ( W ) c c } () Sc ( W ), Sc ( W ), S ( W ) c () Sc ( W ), S ( W ), S ( W ) 6} c c () Sc ( W ), S ( W ) 0}, S ( W ) c c () Sc ( W ), S ( W ), S ( W ),, c c 7, 0, } By Definition and Proposition, we have the following proposition Proposition : The following hold () sptc ( W ) 0, sptc ( W ) 0, sptc ( W ) 0 () sptc ( W ) 0, sptc ( W ) 0, sptc ( W ) 0 () sptc ( W ) 0, sptc ( W ) 0, sptc ( W ) 007 () sptc ( W ) 0, sptc ( W ) 00, sptc ( W ) 0 () sptc ( W ) 0, sptc ( W ) 0, sptc ( W ) 06 From Proposition, we get the strength of condition attribte C spporting decision attribte d Proposition : The following hold () sptc ( spt ( W ) spt ( W ) spt ( W ) c c c 0 () sptc ( sptc ( W ) sptc ( W ) sptc ( W ) 0 () sptc ( sptc ( W ) sptc ( W ) sptc ( W ) 0 07 () spt spt ( W ) spt ( W ) spt ( W ) c ( c c c 0 0 () spt spt ( W ) spt ( W ) spt ( W ) 0 6 c ( c c c CONCLUSION By Proposition, we have the following conclsions () Stability of patient s core temperatre and Stability of patient s blood pressre to ADM-DECS have the same importance(the importance is 00), which are more important than others () Importance of patient s internal temperatre and last measrement of blood pressre to ADM-DECS are eqal(the importance is 007), which are more than importance of oxygen satration So nrses mst pay more attention to the stability of patient s blood pressre and stability of patient s blood pressre in care of postoperative patient By Proposition, we have the following conclsions () The strength of stability of blood pressre is maximal(the strength is 06) () The strength of patient s internal temperatre is less than the strength of stability of blood pressre is maximal(the strength(the strength is 0) and more than the strength of last measrement of blood pressre(the strength is 007) () The strengths of oxygen satration and stability of core temperatre are 0 Hence nrses make frther focs on the stability of patient s blood pressre in care of postoperative patient 6 ACKNOWLEDGMENT This project is spported by the Fok Ying Tong Edcation Fondation(No 00) 7 REFERENCES [] G Alvatore, M Bentto and S Roman, Rogh set theory for mlti criteria decision analysis, Eropean Jornal of Operational Research 9(00), -7 [] A Bdihardjo, J Grzymala-Bsse and L Woolery, Program LERS-LB as a tool for knowledge acqisition in nesing, Proceeding of the th Int Conference on Indstrial & Engineering Applications of AI&Expert Sytems, (99), 7-70 [] R Golan and W Ziarko, Methodology for stock market analysis tilizing rogh set theory, Proc of IEEE/IAFE Conference on Comptational Intelligence for Financial Engineering (99), -0 [] Q Li,G Xie and Y MU, The application of data mining technology based on rogh sets to medical diagnosis, CHINESE MEDICAL EQUIPMENT JOURNAL, (00), -7 [] Z Pawlak, Rogh sets, International Jornal of Compter and Information Sciences (98), -6 [6] Z Pawlak, Rogh Sets: Theoretical Aspects of

5 International Jornal of Compter Applications ( ) Volme No0, October 0 Reasoning Abot Data, Klwer Academic Pblishers, 99 [7] Z Pawlak, Vageness and ncertainty: a rogh set perspective, Comptational Intelligence (99), 7- [8] Pawlak, Z, Decision rles and flow networks, Eropean Jornal of Operational Research, 00, 8-90 [9] S Padmini and H Donald, Vocablary mining for information retrieval: rogh sets and fzzy sets, Information Processing and Management 7(00), -8 [0] K Qin, Y Gao and Z Pei, On covering rogh sets, LNAI 8(007), - [] S Tsmoto, Atomated discovery of medical expert system rles from clinical databases based on rogh set, Proc of Second International Conf on Knowledge discovery and data Mining, (996), 6-7 [] M Yahia, R Mahmodr and N Slaimann, Rogh neral expert systems, Expert system with Applications 8(00), 87-99