Application of fuzzy mathematics models in hospital management evaluation

Transcription

1 Abstract Applicatio o uzzy mathematics models i hospital t evaluatio Mei Su 1,2, Hui Feg 2, Siyua Tag 2*, Ziqiag Luo 3 1 Postdoctoral research statio o school o basic medicie, Cetral south uiversity, Chagsha City, Hua Provice, Chia, Nursig School o cetral south uiversity, Chagsha City, Hua Provice, Chia, School o basic medicie, cetral south uiversity, Chagsha City, Hua Provice, Chia, Received 15 September 2014, wwwcmtlv To ormulate a hospital t evaluatio system ad coduct empirical research, Delphi, aalytic hierarchy process, ad uzzy comprehesive evaluatio are used to build a hospital t evaluatio system ad coduct hospital t empirical research Ad the a hospital t evaluatio system is built This system cotais ive irst-level idices, amely, admiistrative t, huma resource t, medical t, iacial t ad logistical support, ad 23 secod-level idices Empirical research shows that the comprehesive evaluatio o hospital t is above average ad that service quality ad irastructure costructio have the highest ad lowest evaluatio scores, respectively This evaluatio system is a eective tool or studyig hospital t Chiese hospital t requires urther improvemet, especially i terms o irastructure costructio Keywords: uzzy mathematics, hospital t, evaluatio system, aalytic hierarchy process 1 Itroductio Hospital is a health ad medical istitutio that treats ad prevets diseases ad protects people s health Thus, hospital developmet ad t are importat cocers o all social sectors [1] At preset, hospital uctios chage rom simple diagosis ad treatmet ito prevetio, heath care, diagosis ad treatmet, ad rehabilitatio, makig services withi hospitals exted orward ad backward hospitals [2] Hospital t shall adapt to such chages, adjust service structure ad mode, ad optimize ad reorgaize hospital resources The icreasigly ierce competitios i the medical market ad the icreasig medical service demads have brought ew problems, chages, ad challeges to hospital t Hospital t iovatio is a ievitable requiremet o costatly chagig objective hospital coditios ad is a eteral theme o sustaiable developmet o health cause Hospitals should cotiuously iovate ad improve t cocept to remai ivicible i the ierce market competitio [3] Thereore, hospital admiistrators eed to actively iovate hospital t cocept WHO itroduces a ew ramework to aalyze the perormace o health systems i dieret coutries ad believes that the health system shall have three objectives [4], amely, promote good health, stregthe reactio capacity that people expect, ad esure iacig airess It also proposes that a health system should possess our mai uctios, amely, t, iacig, service provisio, ad raisig resources Hospital t quality ca relect the comprehesive stregth ad level o a hospital The actual situatio o Chiese hospital t relects the urget eed or the guidace o hospital t iovatio theory Curretly, all levels ad categories o Chiese hospitals have iaccurate market ad uctioal positioig, outdated operatio ad t cocepts, low operatig eiciecy, ad weak drivig orce ad capital support or sustaiable developmet [5] Practical exploratio ad theoretical research o hospital t iovatio should be vigorously coducted to make moder Chiese hospitals truly become subjects o market ecoomy with idepedet t, sel-disciplie, ad seldevelopmet Chages i social medical ad health demads urgetly require hospitals to study t system iovatio, t operatio iovatio, ad t techological iovatio, amog others [6] A ew domestic ad iteratioal studies have evaluated hospital t quality Hospital t quality has its ow eatures, ad the particularity o comprehesive evaluatio o hospital t quality is worthy o exploratio ad research This study builds a hospital t evaluatio idex system by aalytic hierarchy process (AHP) This process ca scie- * Correspodig author s sumei1111@yeahet 758

2 tiically, objectively, ad accurately evaluate hospital t perormace ad promote hospitals to stregthe cootatio costructio The, uzzy comprehesive evaluatio is used to assess the t quality o six hospitals i a city The evaluatio results o hospital t quality are discussed or admiistrators to compare work quality ad work developmet amog hospitals i dieret times This study may serve as a basis or evaluatig hospital t quality 2 Methods 21 EXPERT INTERVIEW O the basis o literature readig, experiece reerece, ad idividual visit, this study begis with importat ad key cotets that relect hospital t, prelimiarily selects hospital t evaluatio idices, ad iitially builds a hospital t evaluatio idex system that cotais 5 irst-level idices ad 37 secodlevel idices 22 DELPHI A qualiied expert group ad scree idices are selected rom studies o social idices through Delphi, a scietiic, relatively objective, ad strogly operatioal method [7] We seek advices o experts o selected hospital t evaluatio idex systems by distributig questioaires ad ially determie a evaluatio system that cotais 5 irst-level idices ad 23 secodlevel idices accordig to the advices ad suggestios o experts 23 AHP Weight coeiciets o all levels o idices ca be calculated by AHP [8] 24 FUZZY COMPREHENSIVE EVALUATION Hospital t ivolves a wide scope Hospital t evaluatio is a multiactor ad multilevel process with highly complex iluecig actors Evaluatio idices are both qualitative ad quatitative I additio, medical sta evaluates hospital t o the basis o subjective actors, uzzy idex actors, ad asymmetric iormatio The itroductio o the hybrid multi-attribute evaluatio model ca eicietly solve this problem Triagular uzzy umbers i uzzy multi-attribute decisio makig ca eectively hadle idex quatiicatio ad evaluators subjective preerece values [9,10] Fuzzy comprehesive evaluatio is realized by MATLAB70 program package 3 Buildig o hospital t evaluatio system 31 BUILDING OF INDEX SYSTEM I accordace with the basic priciples o SERVQUAL [11], a large umber o hospital t idices are collected through literature ad semi-structured iterviews, ad the Delphi is used to prelimiarily select 37 idices ad determie hospital t evaluatio idices, icludig 5 irst-level idices (ie, admiistrative t, huma resource t, medical t, iacial t, ad logistical support) ad 23 secod-level idices A evaluatio system is established through experts scores o idices by pairwise compariso combied with AHP A questioaire is desiged accordig to the established system, ad the questioaire is scored by the Likert ive-level scale Fially, a model is established by uzzy mathematical modelig combied with exploratory ad coirmatory aalyses 32 DETERMINE INDEX WEIGHT The weight o hospital t evaluatio idices plays a importat role i the evaluatio system It is related to the importace degree o hospitals t o iluecig actors I terms o social evaluatio, the weights o evaluatio idices are curretly directly determied by a ew experts accordig to experiece, which is a isuiciet basis or data aalysis [12] I additio, their experiece may sigiicatly deviate rom the actual situatio, thereby aectig the accuracy o evaluatio results Thus, this study uses AHP to determie idex weights The idex weight o the hospital t evaluatio system is calculated by AHP accordig to the ollowig steps: Step 1: establish a hierarchical idex system structure, ie, build idex hierarchy accordig to the basic relatios o the evaluatio idex system Step 2: build a pair-wise compariso matrix Step 3: check cosistecy CI 1 CI CR RI max, I this study, CR = 0017 < 010, idicatig that weight coeiciets are available The idex weight coeiciets o the evaluatio idex system ca be determied accordig to the above three steps The weight o all levels o idices ca be ially determied as show i Table 1 o the basis o the scores provided by 10 experts o 5 irst-level idices ad 23 secod-level idices (1) 759 Operatio Research ad Decisio Makig

3 TABLE 1 Evaluatio idex system ad weight First-level idex (U i) Admiistra tive t U1 Huma resource t U2 Medical t U3 Fiacial t U4 Weight (W i) Logistical support U5 016 Secod-level idex (U ii) Weight (W ii) Idex cootatio Orgaizatioal structure U Ratioal hospital t orgaizatioal structure Leaders t resposibilities 031 U12 Leaders devote themselves to hospital t Maagemet accoutability U Maagemet accoutability, to implemet reward ad puishmet system Developmet plaig U Formulate ad implemet developmet plaig ad aual workig pla Huma resource allocatio U Ratioal allocatio o departmet huma resources Talet echelo costructio U Talet echelo costructio system, cotiuig educatio system Physicia structure U Ratioal three-level physicia employmet structure Nursig sta U Ratioal amout ad echelo structure o ursig sta Educatioal backgroud ad proessioal Ratioal educatioal backgroud ad proessioal kowledge structure o 018 kowledge U25 medical sta Medical quality U Medical treatmet, medical matters ad other t orgaizatios, ad workig system Departmet supervisio U Maage ad supervise the quality o cliical ad medicie departmets Medical risk warig U Medical risk warig system, respose ad hadlig capacities Doctor patiet relatioship U Deal with medical disputes timely ad properly, ad coordiate doctor patiet relatioship Emergecy t U Deal with emergecies ad public disasters Medical attitude U Attitude o medical sta toward patiets Accoutig posts U Set accoutig posts scietiically accordig to eeds Accoutig U Set accoutig items or iacial accoutig accordig to provisios Budgetig U Formulate ad implemet budget or reveues ad expeditures scietiically ad ratioally Fiacial cotrol U Stregthe cost accoutig ad cotrol, ad reduce operatig costs Basic acility costructio U Carry out basic costructio items accordig to atioal laws ad regulatios Equipmet t U Maage equipmet scietiically Equipmet reewal U Perect medical equipmet purchasig, maiteace ad reewal system Logistical work U Meet eeds o cliical work ad patiets treatmet 33 EVALUATION METHODS Fuzzy comprehesive evaluatio mathematical models ca be divided ito oe-level models ad multilevel models Aalysis o evaluatio actors shows that some actors are coordiatig while some are causal I other words, evaluatio actors have dieret levels, causig a practical issue that objectively exists Multilevel uzzy comprehesive evaluatio model: low-level actors are iitially comprehesively evaluated, ad the results are subjected to high-level comprehesive evaluatio by the ollowig speciic steps: 1) Coirm the actor set o evaluatio object F={ 1, 2,, } For hospital t evaluatio idices, irst-level evaluatio actors iclude (admiistrative 1 t), 2 (huma resources), 3 (medical t), 4 (iacial t), ad 5 (logistical support) while secod-level evaluatio sub-actors iclude those o the idices i Table 1 2) Coirm evaluatio category set E={ e 1, e 2,, e } Hospital t evaluatio grades are determied as E= {very high, quite high, geeral, quite low, very low} grades, which correspod to scores o 90, 80, 70, 60, ad 50, respectively 3) Determie weight set W 4) Perorm sigle-actor evaluatio Establish uzzy mappig rom actor set F to commet set E, derive a uzzy relatio R rom, ad its matrix represetatio ca be deoted as R = R =( ikj m ) i 5) Comprehesive evaluatio Calculate comprehedsive evaluatio vector S ad comprehesive evaluatio value T accordig to the ollowig ormulas S W R, WS 4 Empirical research o hospital t based o uzzy mathematics A questioaire is ormulated i accordace with a hospital t evaluatio system to ivestigate hospital t quality, ad the questioaire is scored by the Likert ive-level scale with 1 represetig dissatisied ad 5 represetig very satisied Medical sta members select accordig to perceived actual situatio ad thus complete the test o hospital t quality A total o 600 questioaires are set out, ad 586 valid oes are recovered with a eective recovery rate o 9767% With dieret emphasis o actors i U, each actor shall be give dieret weights, which ca be expressed as a uzzy subset Aa1, a2,, a o U, ad stipulate ai 1 i1 With R ad A, comprehesive evaluatio is B A R, B b1, b2,, bm is a uzzy subset o V, where b V ( a r )( j 1,2,, m) (2) j i ij i1 The statistical data rom the sample survey are substituted ito the established model, ad the vectors o all levels o uzzy comprehesive evaluatio are calculated e 760 Operatio Research ad Decisio Makig

4 41 ESTABLISH AN EVALUATION SET A evaluatio set cosists the evaluatio o all idices ad all possible results o total evaluatio Hospital t evaluatio may have ive possible results The evaluatio set ca be deoted as R = {r 1, r 2, r 3, r 4, r 5 ) = {very low, quite low, geeral, quite high, very high} The idex orgaizatioal structure U11 is very high or 48 people, quite high or 169 people, geeral or 228 people, quite low or 37 people, ad very low or 104 people O the basis o ormalizatio calculatio, the evaluatio set o orgaizatioal structure U11 is r1 = (0178, 0063, 0389, 0289, 0081) Similarly, the sigle-actor evaluatio matrix o admiistrative t obtaied by combiig the evaluatio grades o the sub-idices o admiistrative t is as ollow: r1 r2 R1 r 3 r TABLE 2 Idex evaluatio scores First-level idex Admiistrative t U1 Huma resource t U2 Medical t U3 Fiacial t U4 Logistical support U5 Secod-level idex Evaluatio scores Orgaizatioal structure U Leaders t resposibilities U Maagemet accoutability U Developmet plaig ad t U Huma resource allocatio U Talet echelo costructio U Physicia structure U Nursig stas U Educatioal backgroud ad proessioal kowledge U Medical quality U Departmet supervisio U Medical risk warig U Doctor patiet relatioship U Emergecy t U Medical attitude U Accoutig posts U Accoutig U Budgetig U Fiacial cotrol U Basic acility costructio U Equipmet t U Equipmet reewal U Logistical work U Accordig to uzzy membership degree, the evaluatio matrix shows that the orgaizatioal structure ad leader t resposibilities are geeral while the t accoutability ad developmet plaig are low I terms o comprehesive evaluatio scores, physicia structure evaluatio has the highest scores; whereas medical attitude evaluatio has the lowest scores (Table 2) Similarly, the sigle-actor evaluatio matrix o huma resource t obtaied by combiig the evaluatio grades o sub-idices o huma resource t is show as ollow: r r r r r I terms o uzzy membership degree, the evaluatio o huma resource allocatio, talet echelo costructio, physicia structure, ad ursig sta is geeral, whereas the evaluatio o educatioal backgroud ad proessioal kowledge is low I terms o evaluatio scores, huma resource allocatio has the highest scores, whereas educatioal backgroud ad proessioal kowledge have the lowest scores Similarly, the sigle-actor evaluatio matrix o medical t obtaied by combiig the evaluatio grades o sub-idices o medical t is show as ollow: r r r r r r I terms o uzzy membership degree, medical quality ad departmet supervisio have geeral evaluatio, whereas medical risk warig, doctor patiet relatioship, emergecy t, ad medical attitude have low evaluatio I terms o evaluatio scores, medical quality has the highest scores, whereas medical attitude has the lowest scores Similarly, the sigle-actor evaluatio matrix o iacial t obtaied by combiig the evaluatio grades o the sub-idices o iacial t is show as ollow: r r r r I terms o uzzy membership degree, accoutig posts, accoutig, ad iacial cotrol have low evaluatio, whereas budgetig has geeral evaluatio I terms o evaluatio scores, budgetig has geeral scores, the other aspects o iacial t have low scores, ad iacial cotrol has the lowest scores Similarly, the sigle-actor evaluatio matrix o logistical support obtaied by combiig the evaluatio grades o sub-idices o logistical support is show as ollow: r r r r I terms o uzzy membership degree, basic acility costructio ad equipmet t have geeral eva- 761 Operatio Research ad Decisio Makig

5 luatio, ad equipmet reewal ad logistical work have low evaluatio Basic acility costructio has the highest scores, whereas logistical work has the lowest scores 42 ESTABLISH A WEIGHT SET Weight set o secod-level idex layer: The correspodig weight o each idex is provided accordig to the above expert scorig ad AHP aalysis results Weights o admiistrative t idices: A 1 = c (022, 031, 021, 026) Weights o huma resource t idices: A 2 = c (023, 022, 018, 019, 018) Weights o medical t idices: A 3 = c (021, 019, 009, 019, 015, 017) Weights o iacial t idices: A 4 = c (024, 027, 022, 027) Weights o logistical support idices: A 5 = c (028, 026, 019, 027) Weight set o irst-level idex layer: The correspodig weight o each idex is provided accordig to the AHP aalysis results: W = c (018, 021, 032, 013, 016) 43 COMPREHENSIVE EVALUATION With the above weight sets ad sigle actor evaluatio sets, we ca calculate the ollowig: The comprehesive evaluatio vector o admiistrative t is: B1 A1 R I terms o uzzy membership degree, at admiistrative t has low evaluatio, ad its comprehesive Similarly, the comprehesive evaluatio vector o huma resource t is: B I terms o uzzy membership degree, huma resource t has geeral evaluatio, ad its comprehedsive Similarly, the comprehesive evaluatio vector o medical t is: B I terms o uzzy membership degree, medical t has geeral comprehesive evaluatio, ad its Similarly, the comprehesive evaluatio sector o iacial t is: B I terms o uzzy membership degree, iacial t has quite low comprehesive evaluatio, ad its comprehesive Similarly, the comprehesive evaluatio sector o logistical support is: B I terms o uzzy membership degree, logistical support has geeral comprehesive evaluatio, ad its comprehesive With the above comprehesive evaluatio ad weights o three irst-level idices, the comprehesive evaluatio scores o hospital t ca be calculated as ollow: B1 B2 C W B B4 B I terms o uzzy membership degree, comprehesive evaluatio is geeral, ad the comprehesive evaluatio scores o hospital t are: =7189 O the basis o the above results, a summary table o irst-level idices ad comprehesive evaluatio scores ca be obtaied (Table 3) TABLE 3 First-level idices ad comprehesive evaluatio First-level idex Ui Satisactio membership Evaluatio scores Admiistrative t U1 Quite low Huma resource t U2 Geeral Medical t U3 Geeral Fiacial t U4 Quite low Logistical support U5 Geeral Comprehesive evaluatio Geeral Operatio Research ad Decisio Makig

6 5 Coclusios This study establishes a hospital t evaluatio system cotaiig 5 irst-level idices (ie, admiistrative t, huma resource t, medical t, iacial t, ad logistical support) ad 23 secod-level idices It also determies the weights ad evaluatio methods o idices i this evaluatio system The hospital t evaluatio system i this study ca scietiically ad ratioally solve the problem o irratioal evaluatio by cosiderig the mai quatitative actors i previous evaluatio methods Empirical aalysis o hospital t shows that the comprehesive evaluatio score o curret hospital Reereces t is 7189 while that o hospital t level eeds urther improvemet Particularly, admiistrative ad iacial ts have low evaluatio scores ad eed to be improved urgetly Meawhile, huma resource t, logistical support, ad medical t have geeral evaluatio scores ad also eed urther improvemet Ackowledgemet Ziqiag Luo ad Siyua Tag are co-correspodig authors The authors ackowledge A Project Supported by Postdoctoral sciece oudatio uded project o cetral south uiversity provided by Mei Su [1] Zhag Y, Xu L, Pa X 2007 Aalysis o Hospital Maagemet ad Social Awareess Chiese Hospital Maagemet 27(11) 4-5 (i Chiese) [2] Ta T, Huo M, Feg G, Ou B, Liao T 2007 Ivestigatio o the Preset Situatio o Medical Sta Resources i Public Medical Istitutios o Xidu District i Chegdu Joural o Military Surgeo i Southwest Chia 9(6) (i Chiese) [3] Wag Y 2003 Maagemet Cocepts That Hospitals Shall Stregthe durig Trasitio Jiagsu Health Care Maagemet 14(6) 21-2 (i Chiese) [4] Braiga E T, Murray E, Holmes A 2009 Where does iectio cotrol it ito a hospital t structure? Joural o Hospital Iectio 73(4) [5] Diggs L A, Yusu J E, De Leo G 2014 A update o out-o-hospital airway t practices i the Uited States Resuscitatio 85(7) [6] Bakker A R, Leguit F A 1999 Evolutio o a itegrated HIS i the Netherlads It J Med I 54(3) [7] Zhou D, Yu D 2007 Research o Moderizatio Idex System o Capital PE Joural o Beijig Sport Uiversity 30(5) (i Chiese) [8] Liu H C 2013 A theoretical ramework or holistic hospital t i the Japaese healthcare cotext Health Policy 113(1-2) [9] Guo L, Gao J, Yag J, Kag J 2009 Criticality evaluatio o petrochemical equipmet based o uzzy comprehesive evaluatio ad a BP eural etwork Joural o Loss Prevetio i the Process Idustries 22(4) [10] Ahmed A H 2014 Prevetio ad Maagemet o Hospital- Acquired Aemia Hospital Medicie Cliics 3(1) e71-e84 [11] Zou K, Gog Z 2007 Aalysis o Customer Satisactio Idex o Commuity s Iormatio Service Library Tribue 27(5) [12] Lu Z, She Y 2011 The Study o Veture Capital Project Appraisal usig AHP-Fuzzy Comprehesive Evaluatio Methods Iteratioal Joural o Advacemets i Computig Techology 3(8) 50-6 Authors Mei Su, bor i August 1982, Taiyua City, Shaxi Provice, PR Chia Curret positio, grades: lecturer o Nursig school, Cetral South Uiversity, Chia Uiversity studies: Doctor degree at Cetral South Uiversity i Chia Scietiic iterests: ursig quality cotrol, chroic disease t Publicatios: more tha 12 papers Experiece: teachig experiece o 2 years, 4 scietiic research projects Hui Feg, bor i Jue 1973, Chagsha City, Hua Provice, PR Chia Curret positio, grades: Associate Proessor o Nursig school, Cetral South Uiversity, PR Chia Uiversity studies: Bachelor, Master ad Doctor degree i Medicie at Cetral South Uiversity o Hua i Chia Scietiic iterests: ursig educatio ad chroic disease t Publicatios: more tha 20 papers Experiece: teachig experiece o 21 years, 7 scietiic research projects Siyua Tag, bor i April 1966, Hegyag City, Hua Provice, PR Chia Curret positio, grades: Proessor at Nursig school, Cetral South Uiversity, Chia Uiversity studies: Bachelor, Master ad Doctor degree i Medicie at Cetral South Uiversity o Hua i Chia Scietiic iterests: ursig educatio, chroic disease t Publicatios: more tha 120 papers Experiece: teachig experiece o 26 years, 12 scietiic research projects Ziqiag Luo, bor i April 1962, Chagsha City, Hua Provice, PR Chia Curret positio, grades: Proessor at the basic medical school, Cetral South Uiversity, Chia Uiversity studies: Bachelor, Master ad Doctor degree i Medicie at Cetral South Uiversity o Hua i Chia Scietiic iterests: respiratory physiology Publicatios: more tha 102 papers Experiece: teachig experiece o 30 years, 18 scietiic research projects 763 Operatio Research ad Decisio Makig