Utilization of Rough Neutrosophic Sets In Medical Diagnosis

Transcription

1 ntrnational Journal of Enginring Scinc nvntion (JES) SS (Onlin): , SS (rint): Volum 7 ssu 3 Vr. V March Utilization of ough utrosophic Sts n Mdical Diagnosis. Edward Samul nd.armadhagnanam (amanujan sarch Cntr,.G. & sarch Dpartmnt of Mathmatics / GC(),Kumbakonam,,ndia.) (amanujan sarch Cntr,.G. & sarch Dpartmnt of Mathmatics / GC(),Kumbakonam,,ndia.) Corrsponding author:.edward Samul bstract:ough nutrosophic st is an ssntial tool for daling with uncrtaintis and shortcomings that affct th xisting mthods.n this papr, a nw mthod (ordr function)is proposd and som of its proprtis ar discussd hrin. Excution of mdicaldiagnosis is prsntd to find out th disas impacting th patint. Kywords -Mdical diagnosis, ordr function, rough nutrosophic st, singl valud nutrosophic st Dat of Submission: Dat of accptanc ntroduction numbr of ral lif problms in nginring, mdical scincs, social scincs, conomics tc., involv imprcis data and thir solution involvs th us of mathmatical principls basd on uncrtainty and imprcision. Such uncrtaintis ar bing dalt with th hlp of topics lik probability thory, fuzzy st thory[], rough st thory [] tc., Halthcar industry has bn trying to complmnt th srvics offrd by convntional clinical dcision making systms with th intgration of fuzzy logic tchniqus in thm. s it is not an asy task for a clinician to driv a fool proof diagnosis, it is advantagous to automat fw initial stps of diagnosis which would not rquir intrvntion from an xprt doctor. utrosophic st which is a gnralizd st posssss all attributs ncssary to ncod mdical knowldg bas and captur mdical inputs. s mdical diagnosis dmands larg amount of information procssing, larg portion of which is quantifiabl, also intuitiv thought procss involv rapid unconscious data procssing and combins availabl information by law of avrag, th whol procss offrs low intra and intr prsonal consistncy. So contradictions, inconsistncy, indtrminacy and fuzzinss should b accptd as unavoidabl as thy ar intgratd in th bhavior of biological systms as wll as in thir charactrization. o modl an xprt doctor it is imprativ that it should not disallow uncrtainty as it would b thn inapt to captur fuzzy or incomplt knowldg that might lad to th dangr of fallacis du to misplacd prcision. s mdical diagnosis contains lots of uncrtaintis and incrasd volum of information availabl to physicians from nw mdical tchnologis, th procss of classifying diffrnt sts of symptoms undr a singl nam of disas bcoms difficult. h main advantag of rough st thory is that it dos not nd any prliminary or additional information about data(lik th probability in statistics, th valu of possibility in fuzzy st thory tc.,).so, rough nutrosophic sts play a vital rol in mdical diagnosis. n 965, uzzy st thory was firstly givn by Zadh[] which is applid in many ral applications to handl uncrtainty. Somtims mmbrship function itslf is uncrtain and hard to b dfind by a crisp valu. So th concpt of intrval valud fuzzy sts was proposd to captur th uncrtainty of grad of mmbrship. n 986, tanassov[3] introducd th intuitionistic fuzzy sts which considr both truth-mmbrship and falsitymmbrship. Latr on, intuitionistic fuzzy sts wr xtndd to th intrval valud intuitionistic fuzzy sts. ntuitionistic fuzzy sts and intrval valud intuitionistic fuzzy sts can only handl incomplt information not th indtrminat information and inconsistnt information which xists commonly in blif systms. So, utrosophic st (gnralization of fuzzy sts, intuitionistic fuzzy sts and so on) dfind by lorntinsmarandach[4] has capability to dal with uncrtainty, imprcis, incomplt and inconsistnt information which xists in ral world from philosophical point of viw. Wang t al [5] proposd th singl valud nutrosophic st. n 98, awlak[] introducd th concpt of rough st (S), as a formal tool for modling and procssing incomplt information in information systms. hr ar two basic lmnts in rough st thory, crisp st and quivalnc rlation, which constitut th mathmatical basis of rough sts. h basic ida of rough st is basd upon th approximation of sts by a pair of sts known as th lowr approximation and th uppr approximation of a st. Hr, th lowr and uppr approximation oprators ar basd on quivalnc rlation. anda and Majumdar [6] xamind fuzzy rough sts. Broumi t al [7] introducd rough nutrosophic sts. ag

2 Utilization of rough nutrosophic sts in mdical diagnosis Surapati ramanik and Kalyan Mondal [8,9] introducd cosin and cotangnt similarity masurs of rough nutrosophic sts. Edward Samul and armadhagnanam [0] proposd tangnt logarithmic distanc and coscant similarity masur of rough nutrosophic sts. ramanik t al [] introducd corrlation cofficint of rough nutrosophic sts. n this papr, by using th notion of rough nutrosophic st, it was providd an xmplary for mdical diagnosis. n ordr to mak this, a novl mthod was xcutd. st of th articl is structurd as follows. n Sction, th basic dfinitions wr brifly prsntd. Sction 3 dals with proposd dfinition and som of its proprtis. Sctions 4, 5 & 6 contain mthodology, algorithm and cas study rlatd to mdical diagnosis rspctivly. Conclusion is givn in Sction 7.. rliminaris. Dfinition [5] Lt H b a univrsal spac of points (objcts) with a gnric lmnt of H dnotd by x. singl valud nutrosophic st S is charactrizd by a truth mmbrship function, a falsity mmbrship function and an indtrminacy function with,, H for all x in H. Whn H is continuous, a SVS S can b writtn as follows: x, x, x S S S S x, x H x and whn H is discrt, a SVS S can b writtn as follows: S S x, S x, S x x, x H t should b obsrvd that for SVS S xsup xsup x 3 x H 0 sup S S S,. Dfinition [] Lt b a fuzzy nutrosophic st in X. Lt b th rlation from X to Y. hn max-min composition of fuzzy nutrosophic st with is anothr fuzzy nutrosophic st B of Y which is dnotd by S. hn th mmbrship function, indtrminat function and non-mmbrship function of B is dfind as: y x x x, y y x x x, y y x x, y x.3 Dfinition [7] Lt U b a non-null st and b an quivalnc rlation on U. Lt b nutrosophic st in U with th mmbrship function, indtrminacy function and non-mmbrship function. h lowr and th uppr approximations of in th approximation U, dnotd by & ar rspctivly dfind as follows: x, x, x, x / y x ( ) whr ( ) ( ) ( ) x, y x, x, x / y x, x U [ x ] [ x] [ x] [ x] y y y y y x y, y y[ x] x y,, x U () ag

3 x y. y[ x] Utilization of rough nutrosophic sts in mdical diagnosis So, 0 x x x 3& 0 x x x 3 whr and man max and min oprators rspctivly, y, y& y ar th mmbrship, indtrminacy and non-mmbrship of y with rspct to. t is asy to s that & ar two nutrosophic sts inu,thus th S mappings : U U lowr and uppr rough nutrosophic st approximation oprators, and th pair nutrosophic st in U,.. roposd Dfinition, ar rspctivly, rfrrd to as th, is calld th rough 3. Dfinition Lt a, b, c b a singl valud nutrosophic numbr, an ordr function of a singl valud nutrosophic valu, basd on th truth-mmbrship dgr, indtrminacy-mmbrship dgr and falsity-mmbrship dgr is dfind as : a c log b 3 3 () 3c[b ] a 3.. roposition 0 roof h proof is straightforward 3.. horm Lt a, b, c and a, b, c B roof By (), a c log b 3 3 B b two singl valud nutrosophic numbrs. f B thn 3c [b a & B 3c [b a ] Sinc B, a a, b b & c c. ( a a) 0, ( b ) b 0& ( c c ) 0. Hnc B 0 a log 3 ] c b 3 V. Mthodology n this sction, it was prsntd an application of rough nutrosophic st in mdical diagnosis. n a givn pathology, suppos S is a st of symptoms, D is a st of disass and is a st of patints and lt Q b a rough nutrosophic rlation from th st of patints to th symptoms. i.., S nutrosophic rlation from th st of symptoms to th disass. i.., S D involvs thr main jobs:. Dtrmination of symptoms. ormulation of mdical knowldg basd on rough nutrosophic sts 3. Dtrmination of diagnosis on th basis of nw computation tchniqu Q and b a rough and thn th mthodology V. lgorithm Stp : h symptoms of th patints ar givn to obtain th patint - symptom rlation Q and ar notd in abl. 3 ag

4 Utilization of rough nutrosophic sts in mdical diagnosis Stp : h mdical knowldg rlating th symptoms with th st of disass undr considration ar givn to obtain th symptom - disas rlation and ar notd in abl. Stp 3 : abl 3 is obtaind by calculating avrag valus of abl. Stp 4 : abl 4 is obtaind by calculating avrag valus of abl. Stp 5 : abl 5 is obtaind by applying () btwn abl 3 & abl 4. Stp 6 : h Computation of th rlation of patints and disass is found using () in abl 5 and ar notd in abl 6. Stp 7 : inally, th minimum valu from abl 6 of ach row ar slctd for possibility of th patint affctd with th rspctiv disas and thn it was concludd that th patint k k,,3 was r,,3,4 suffring from th disas Dr V. Cas study [8] Lt thr b thr patints,, Stomach pain, Cough, Chst pain}.h rough nutrosophic rlation S and th st of symptoms S = {mpratur, Hadach, Q is givn as in abl.lt th st of disass D = {Viral fvr, Malaria, Stomach problm, Chst problm}.h rough nutrosophic rlation S D is givn as in abl. abl atint Symptom rlation (using stp ) Q mpratur Hadach Stomach pain Cough Chst pain 0.6,0.4,0.3, 0.4,0.4,0.4, 0.5,0.3,0., 0.6,0.,0.4, 0.4,0.4,0.4, 0.8,0.,0. 0.6,0.,0. 0.7,0.,0. 0.8,0.0,0. 0.6,0.,0. 0.5,0.3,0.4, 0.5,0.5,0.3, 0.5,0.3,0.4, 0.5,0.3,0.3, 0.5,0.3,0.3, 0.7,0.3,0. 0.7,0.3, ,0., ,0., ,0., ,0.4,0.4, 0.5,0.,0.3, 0.4,0.3,0.4, 0.6,0.,0.4, 0.5,0.3,0.3, 0.8,0.,0. 0.7,0.0,0. 0.8,0.,0. 0.8,0.,0. 0.7,0.,0. mpratur Hadach Stomach pain Cough Chst pain abl Symptom Disas rlation (using stp ) Viral fvr Malaria Stomach roblm Chst problm 0.6,0.5,0.4, 0.,0.4,0.4, 0.3,0.4,0.4, 0.,0.4,0.6, 0.8,0.3,0. 0.5,0.,0. 0.5,0.,0. 0.4,0.4, ,0.3,0.4, 0.,0.3,0.4, 0.,0.3,0.3, 0.,0.5,0.5, 0.7,0.3,0. 0.6,0.3,0. 0.4,0.,0. 0.5,0.3,0.3 0.,0.3,0.4, 0.,0.4,0.4, 0.4,0.3,0.4, 0.,0.4,0.6, 0.4,0.3,0. 0.3,0.,0. 0.6,0.,0. 0.3,0., ,0.3,0.3, 0.3,0.3,0.3, 0.,0.6,0.6, 0.5,0.3,0.4, 0.6,0.,0. 0.5,0., ,0.4, ,0.,0. 0.,0.4,0.4, 0.,0.3,0.3, 0.,0.4,0.4, 0.4,0.4,0.4, 0.4,0.,0. 0.3,0.,0. 0.3,0.,0. 0.6,0.,0. abl 3 vrag (using stp 3) Q mpratur Hadach Stomach pain Cough Chst pain 0.7,0.3,0. 0.5,0.3, ,0.,0. 0.7,0., ,0.3, ,0.3, ,0.4, ,0., ,0., ,0., ,0.3, ,0.,0. 0.6,0., ,0., ,0.,0. 4 ag

5 Utilization of rough nutrosophic sts in mdical diagnosis abl 4 vrag (Using stp 4) Viral fvr Malaria Stomach problm Chstproblm mpratur [0.7,0.4,0.3 ] [0.3,0.3,0.3 ] [0.4,0.3,0.3 ] [0.3,0.4,0.5 ] Hadach [0.6,0.3,0.3 ] [0.4,0.3,0.3 ] [0.3,0.,0. ] [0.3,0.4,0.4 ] Stomach pain [0.3,0.3,0.3 ] [0.,0.3,0.3 ] [0.5,0.,0.3 ] [0.,0.3,0.5 ] Cough [0.5,0.,0. ] [0.4,0.,0.3 ] [0.,0.5,0. 5] [0.6,0.,0.3 ] Chst pain [0.3,0.3,0.3 ] [0.,0.,0. ] [0.,0.3,0.3 ] [ 0.5,0.3,0.3 ] abl 5 Max-Min composition (using stp 5) Viral fvr Malaria Stomach problm Chst problm [0.7,0.3,0.3 ] [0.4,0.3,0.3 ] [0.5,0.3,0. 3] [0.6,0.3,0.3 ] [0.6,0.3,0.3 ] [0.4,0.3,0.3 ] [0.5,0.3,0.3 ] [0.6,0.4,0. 3] [0.7,0.3,0.3 ] [0.4,0.3,0. ] [0.5,0.3,0. ] [0.6,0.3,0.3 ] abl 6 Ordr function (using stp 6 & stp 7) Viral fvr Malaria Stomach problm Chst problm rom abl 6,it is obvious that, if th doctor agrs, thn, & 3 suffrs from viral fvr. V. Conclusion n this papr, it was analyzd th rlationship btwn th st of symptoms found with th patints and th st of disass and mployd a novl mthod (ordr function) to find out th disas possibly affctd th patint. h tchniqus considrd in this study wr mor rliabl to handl mdical diagnosis problms quit comfortably. n futur, ths mthods can b nhancd to othr typs of nutrosophic sts also. frncs [] L.. Zadh, uzzy sts, nformation and Control, 8(3),965, [] Z.awlak, ough sts, ntrnational Journal of nformation and Computr Scincs, (5),98, [3] Krassimir.tanassov, ntuitionistic fuzzy sts, uzzy Sts and Systms, 0 (),986,87-96 [4] lorntinsmarandach, unifying fild in logics, nutrosophy: nutrosophic probability,st& logic, hoboth:mrican sarch rss, 998. [5] Haibin Wang, lorntinsmarandach, Yan Qing Zhang and ajshkar Sundrraman, Singl valud nutrosophic sts, Multispac and Multistructur,4,00, [6] S.anda ands.majumdar, uzzy rough sts, uzzy Sts and Systms,45,99, [7] Said Broumi,lorntinSmarandach and Mamoni Dhar, ough nutrosophic sts, talian Journal of ur and pplid Mathmatics,3,04, [8] Surapatiramanik and KalyanMondal, Cosin Similarity Masur of ough utrosophic Sts and its application in mdical diagnosis, Global Journal of dvancd sarch,(), 05,-0. [9] Surapatiramanik and KalyanMondal, Cotangnt Similarity Masur of ough utrosophic Sts and its application to mdical diagnosis,journal of w hory,4,05,90-0. [0].Edward Samul and.armadhagnanam,ough nutrosophic sts in mdical diagnosis, roc. of th ntrnational conf. on Mathmatical and Computr Enginring,V.. Chnnai, amilnadu, ndia,07(ovmbr 3 to 4),8-9. [] Surapatiramanik, umi oy, apan Kumar oy and lorntinsmarandach,multicritria dcision making using corrlation cofficint undr rough nutrosophic nvironmnt,utrosophic sts and systms,7,07,9-36. [] YildirayClik., modl for mdical diagnosis via fuzzy nutrosophic soft sts, sian Journal of Mathmatics and Computr sarch,0(), 06, Edward Samul"Utilization of ough utrosophic Sts n Mdical Diagnosis"ntrnational Journal of Enginring Scinc nvntion (JES), vol. 07, no. 03, 08, pp ag