Distances, Hesitancy Degree and Flexible Querying via Neutrosophic Sets

Transcription

1 Iteratoal Joural of Computer pplcatos Volume 0 No.0 eptember 0 Dstaces Hestacy Degree ad Fleble Queryg va Neutrosophc ets..alama Math ad Computer cece Departmet Faculty of cece Port ad Uversty EGYP Mohamed bdelfattah Iformato ystem Departmet Faculty of Computers & Iformato eha Uversty Egypt Mohamed Esa Computer cece Departmet Port ad Uversty Egypt C ce the world s full of determacy the eutrosophcs foud ther place to cotemporary research. İ ths paper we troduce the dstaces betwee eutrosophc sets: the Hammg dstace he ormalzed Hammg dstace the Eucldea dstace ad ormalzed Eucldea dstace. e wll eted the cocepts of dstaces to the case of eutrosophc hestacy degree. dded to ths paper suggest how to erch tutostc fuzzy queryg by the use of eutrosophc values.. Geeral erms Your geeral terms must be ay term whch ca be used for geeral classfcato of the submtted materal such as Patter ecogto ecurty lgorthms et. al. Keywords Neutrosophc ets; Hammg dstace; Eucldea Dstace; Normalzed Eucldea Dstace; Itutostc Fuzzy Queryg; Queryg Databases; Neutrosophc Queryg.. INODUCION ce the world s full of determacy the eutrosophcs foud ther place to cotemporary research. he fudametal cocepts of eutrosophc set troduced by maradache [5 6] ad alama et al. [ ] provdes a atural foudato for treatg mathematcally the eutrosophc pheomea whch est pervasvely our real world ad for buldg ew braches of eutrosophc mathematcs. Neutrosophy has lad the foudato for a whole famly of ew mathematcal theores geeralzg both ther classcal ad fuzzy couterparts [ ] such as a eutrosophc set theory.he tradtoal query laguages used the database maagemet systems requre a precse ad uambguous specfcato of a query. It seems to be a serous lmtato sce a typcal user ofte formulates hs requremets a atural laguage usg mprecse epressos ad vague terms. For ths reaso several approaches have bee proposed to rela the rgdty of the covetoal queres ad make possble to use queres that allow for a more tellget ad huma cosstet formato retreval see e.g. [5 8 9]. he FQUEY for ccess [ ] s a eample of a computer program that eables to create dfferet kds of fuzzy queres. Usg such fuzzy queres we deal o loger wth bary outputs whether a record fulfll gve requremet or ot but we get a Defto. formato o the degree the record comples wth the requremet. İ ths paper we troduce the dstaces betwee eutrosophc sets: the Hammg dstace he ormalzed Hammg dstace the Eucldea dstace ad ormalzed Eucldea dstace. e wll eted the cocepts of dstaces to the case of eutrosophc hestacy degree.. EMINOLOGIE Neutrosophy has lad the foudato for a whole famly of ew mathematcal theores geeralzg both ther classcal ad fuzzy couterparts [ ] such as a eutrosophc set theory. e recollect some relevat basc prelmares ad partcular the work of maradache [5 6] ad alama et al. [ ]. maradache troduced the eutrosophc compoets I F whch represet the membershp determacy ad o-membershp values respectvely where s ostadard ut terval. alama troduced the followg: Let be a o-empty fed set. eutrosophc set s a obect havg the form where ad whch represet the degree of member shp fucto amely the degree of determacy amely ad the degree of o-member shp amely respectvely of each elemet to the set where ad. maradache troduced the followg: Let I F be real stadard or ostadard subsets of wth up_=t_sup f_=t_f up_i=_sup f_i=_f up_f=f_sup f_f=f_f -sup=t_sup+_sup+f_sup -f=t_f+_f+f_f I F are called eutrosophc compoets. DİNCE EEEN NEUOOPHİC E e wll ow eted the cocepts of dstaces preseted [7] to the case of eutrosophc sets. 7

2 Iteratoal Joural of Computer pplcatos Volume 0 No.0 eptember 0 Let ad... the he Hammg dstace s equal to d. he Eucldea dstace s equal to e he ormalzed Hammg dstace s equal to NH v he ormalzed Eucldea dstace s equal to NE Eample. Let us cosder for smplcty degerated eutrosophc sets D G F a. full descrpto of each eutrosophc set.e. a may be eemplfed by 00 a 00 a D 00 a G a E a. Let us calculate four dstaces betwee the above eutrosophc sets usg ad v formulas Fg. geometrcal terpretato of the eutrosophc cosdered Eample 5.. e obta e D e D e e G e G e E G D G NE NE D NE D NE G NE G NE From the above results the tragle D Fg. has edges e D e D e NE NE D NE D NE E G ad D G equal to ad ad NE G NE G ad NE E Gs equal to half of the heght of tragle wth all edges equal to multpled by.e.. NE G e Eample. Let us cosder the followg eutrosophc sets ad a b c d e. he d NH 0. e. 9 ad NE emark. Clearly these dstaces satsfy the codtos of metrc space. emark. It s easy to otce that for formulas ad v the followg s vald: 8

3 Iteratoal Joural of Computer pplcatos Volume 0 No.0 eptember 0 9 a d 0 b 0 NH c e 0 d 0 NE. hs represetato of a eutrosophc set Fg. wll be a pot of departure for eutrosophc crsp dstaces ad etropy of eutrosophc sets. Fg.. three-dmeso represetato of a eutrosophc set. e wll ow eted the cocepts of dstaces to the case of eutrosophc hestacy degree. y takg to accout the four parameters characterzato of eutrosophc sets.e. Defto. Let ad o... For a eutrosophc set we call the eutrosophc de of. İt s a hestacy degree of to t s obvtous that 0. Defto. Let ad... the he Hammg dstace s equal to d.akg to accout that ad we have. v he Eucldea dstace s equal to e we have = + v he ormalzed Hammg dstace s equal to NH

4 Iteratoal Joural of Computer pplcatos Volume 0 No.0 eptember 0 v he ormalzed Eucldea dstace s equal to NE emark. It s easy to otce that for formulas ad v the followg s vald: a 0 d b 0 NH c 0 e d 0 NE.. QUEYING VI NEUOOPHIC E query may be treated as a set of searchg crtera coceved by a user. typcal query epressed QL s wrtte a followg form ELEC < lst of attrbutes > FOM < lst of tables > HEE < codto >. Its role s to select records rows that satsfy gve codto. Each record from the table ether satsfes or does ot satsfy the codto ad as a result we obta a crsp set of database records that come up to query. However as t was metoed above tradtoal query syta requres very rgd formulato of the costrats whle for a huma beg a commo laguage s a atural medum to form ad epress hs thoughts. Now we wll try to costruct a query that eables a drect use of lgustc terms modeled by eutrosophc sets.e. a query wth a followg syta: ELEC < lst of attrbutes > FOM < lst of tables > HEE <eutrosophc codto >. Let us cosder a crsp relatoal database wth a set of... ad a set of records attrbutes r r... r m. Let deote the uverse of dscourse for the attrbute. Moreover let Z :... deote a fucto that determes a vector of values of all attrbutes correspodg to Let us defe a fucto : N each record.e. Z r z... z of the attrbute where z s a value for the record r. o costruct a Nquery a sutable eutrosophc set must be defed for each attrbute used HEE clause. hus actually our Nquery s a operator whch trasforms each attrbute to the correspodg eutrosophc set : where : 0 are the membershp determacy ad o-membershp fucto of the defed by the eutrosophc term for the attrbute respectvely. s soo as we accept vague terms queres we also have to modfy our meag of matchg betwee the query ad a record of database. It would be ureasoable to requre the aswer for a N-query to be completely precse adherg to the classcal yes-o or o logc. Now we epect the system to produce a lst of records matchg a query to a degree hgher tha a specfed threes hold ad to lst the records accordg to the lear sem orderg. However our approach utlzg eutrosophc sets we do ot have such atural lear orderg because we have to look o three fuctos. herefore we wll costruct a desred sem orderg usg dstaces metoed ec.. U whch determes a eutrosophc set for each record U r... z z ad z. I other words It s obvous that a eutrosophc set correspodg to the best record.e. the record satsfyg perfectly all requremets of the query would have a followg form whle a eutrosophc set correspodg to the worst record.e. the record that does ot satsfy ay requremets of the query would look lke : e wll apply eutrosophc sets ad our method of calculatg matchg degrees. hey would smply costtute the upper r a followg way ; where z z z... z z z horzo ad the lower horzo respectvely. Hece d ad d deote the Hammg or Eucldea dstace of the eutrosophc set from the upper ad lower horzo respectvely. hese two umbers show how close s the record r to the best ad to the worst possble record respectvely. Of course whle queryg database we are lookg for records wth possbly low d. ad possbly hgh d. herefore let us defe 0

5 Iteratoal Joural of Computer pplcatos Volume 0 No.0 eptember 0 d d. It s clear that a desred record should have both values possble. easy computato shows that for the Hammg dstace we obta: d d = mlarly we ca cosder the Eucldea dstaces e ad e values e e ad as hgh as ad correspodg Now the questo s how to apply ad matchg degrees computato. e suggest here three basc methods for determg matchg degrees. Namely we ca calculate the matchg degree for the - th record ether as a average of V ad.e. mamum of these two values or as the mmum MIN M m hus we get M ma or as a It s easly = MIN see that. Hece usg MIN we restrct our cosderato to the dstace from the record whch fts best whle usg MIN we cosder the dstace from the worst possblty oly. hus MIN gves us a optmstc matchg degree M a pessmstc oe ad V s a balaced oe. e ca also cosder a atural famly of operators for matchg degree q [0] computato. uppose s a costat that characterzes the subectve weght attrbuted to the dstace from the upper ad the lower horzo. he for gve q let us defe the matchg degree for the record -th as follows q q. +. Oe ca see easly that ths operators dscussed above are partcular members of the V 0.5 famly MIN q q. Namely M 0. { : q [0]} ad hatever method for calculatg matchg degrees ote t brefly as we choose ths method duces a sem orderg o a set of records. Hece we may say that a record precedes record r or s some sese better f ad oly f the matchg degree s ot smaller tha r r. Of course ths sem orderg strogly depeds o the method used for calculatg matchg degree. e epect the system to reect the records wth matchg degree lower tha a specfed threshold. herefore we reect the -th record f where s a fed umber from the terval [0;]. Hece we obta a followg algorthm of queryg va eutrosophc values:. ake the record from the database.. Calculate. [0. ccept the record f otherwse reect.. If there are more records go to tep otherwse go to tep Lst all accepted records from the best to the worst accordg to r r r.e. ] 5. CONCLUION I the preset paper we have show how to erch fuzzy queryg by the use of eutrosophc values. ce a codto the clause HEE may volve ot oly mprecse values but also such lgustc terms as fuzzy relatos ad lgustc quatfers some other geeralzatos seem atural. I further work we would try to apply eutrosophc sets for modelg relatos ad defg quatfers too. However we beleve that eve lmted our method eables the user to.

6 Iteratoal Joural of Computer pplcatos Volume 0 No.0 eptember 0 costruct queres a more fleble way. ome of the propertes of the eutrosophc sets Dstace measures ad Hestacy Degree hese measures ca be used effectvely mage processg ad patter recogto. he future work wll cover the applcato of these measures. 6. CKNOLEDGMEN I gratefully ackowledge the support ad geerosty of eha uversty faculty of computers ad formatcs 7. EFEENCE [] K. taassov 986 Itutostc fuzzy sets Fuzzy ets ad ystems [] K. taassov 999 Itutostc Fuzzy ets:heory ad pplcatos Physca -Verlag. [] K. taassov evew ad ew result o tutostc fuzzy sets preprt IM-MFI--88 ofa 988. [].. lblow.. alama ad Mohmed Esa 0 New Cocepts of Neutrosophc ets Iteratoal Joural of Mathematcs ad Computer pplcatos esearch IJMC Vol. Issue [5] P. osc J. Kacprzyk Eds. 995 Fuzzess Database Maagemet ystems Physca-Verlag Hedelberg. [6] P. Grzegorzewsk 998 Metrcs ad orders space of fuzzy umbers Fuzzy ets ad ystems [7] P. Grzegorzewsk 00 Dstaces betwee tutostc fuzzy sets based o the Hausdorff metrc submtted to Fuzzy ets ad ystems. [8] P. Grzegorzewsk E. Mr owka 00 oft queryg va tutostc fuzzy sets Proceedgs of the 9th Iteratoal coferece o Iformato Processg ad maagemet of Ucertaty Kowledge-ased ystems IMPU 00 ecy July pp [9] J. Kacprzyk. Zadro zy 000 O combg tellget queryg ad data mg usgfuzzy logc cocepts I: ordoga G. Pas G. Eds.: ecet Issues o Fuzzy Databases Physca-Verlag Hedelberg pp [0] I. M. Haafy.. alama ad K. Mahfouz 0"Correlato Coeffcet of Neutrosophc ets by Cetrod Method" Iteratoal Joural of Probablty ad tatstcs pp 9-. [] I. M. Haafy.. alama ad K. Mahfouz 0 Correlato of eutrosophc Data Iteratoal efereed Joural of Egeerg ad cece IJE Vol. Issue PP.9-. [].. alama ad.. lblow 0" Neutrosophc et ad Neutrosophc opologcal paces" IO J. mathematcs IO-JM Vol.. Issue ep-oct. 0. pp -5. [].. alama ad.. lblow 0"Geeralzed Neutrosophc et ad Geeralzed Neutrousophc opologcal paces"joural Computer cece ad EgeergVol. No. 7.pp98-0. [].. alama ad H. Elagamy" Neutrosophc Flters" Iteratoal Joural of Computer cece Egeerg ad Iformato echology eseearch IJCEI Vol. Issue Mar 0 pp [5]F.maradach 00" Neutrosophc set a geeralzato of the tutstc fuzzy sets" Proceedgs of the thrd coferece of the Europea ocety for fuzzy logc ad echolgye EUFL eptamper Zttau Geamay Uv. of ppled ceces at Zttau Goerlt -6. [6]F.maradach 0 INODUCION ONEUOOPHIC MEUENEUOOPHIC INEGLND NEUOOPHIC POILIY EN: [7] Eulalazmdt ad Jaus Koeprzyk 000 Dstace betwee tutostc fuzzy sets Fuzzy ets ad ystems [8].. alama"neutrosophc Crsp Pots &Neutrosophc Crsp Ideals" Neutrosophc ets ad ystems Vol. No. 0 pp [9].. alama ad F. maradache Flters va Neutrosophc Crsp ets" Neutrosophc ets ad ystems Vol. No. 0 pp-8. [0]... alama" he Cocept of Neutrosophc et ad asc Propertes of Neutrosophc et Operatos" E 0 PI FNC Iteratoal Uversty of cece Egeerg ad echology 0 [].. alama F. maradache ad ValerKroumov " Neutrosophc Crsp ets &Neutrosophc Crsp opologcal paces" Neutrosophc ets ad ystems Vol. pp [].. alama F. maradache ad.. lblow " he Characterstc Fucto of a eutrosophc et " Neutrosophc ets ad ystem ccepted 0. [].. alama Mohamed Esa ad M. M. bdelmoghy "Neutrosophc elatos Database" Iteratoal Joural of Iformato cece ad Itellget ystem 0. [] uprya Kumar De at swas ad khlaa oy Itustotc Fuzzy Database ecod It. Cof. o IF ofa - Oct. 998 NIF [5] L.. Zadeh Fuzzy ets Iform ad Cotrol IJC M :