Weighted Neutrosophic Soft Sets
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Transcript of Weighted Neutrosophic Soft Sets
Weighted Neutrosophic Soft SetsPabitra Kumar Maji1'21 Departmet o! "athematics, #. $. $olle%e, &sasol, 'est #e%al, (13 304, )dia. *-mail+ pa,itra-ma.i/yahoo.com 2 Departmet o! "athematics, 0. N. 1i2ersity, &sasol, 'est #e%al, (13 301, )dia. *-mail+ pa,itra-ma.i/yahoo.comAbstract. ) this paper we st3dy the cocept o!e3trosophicso!t sets. )mposi%somewei%hts otheparameters cosidered we itrod3ce here wei%htede3trosophic so!t sets. 4ome operatios li5e 3io,itersectio, complemet, &ND, 6R etc. ha2e ,eede!iedothisewcocept. 4omepropertieso!theseewly de!ied operatios ha2e also ,ee 2eri!ied .Keywords: 4o!t sets, e3trosophic sets, e3trosophic so!t sets, wei%hted e3trosophic so!t sets.1Introduction7he so!t set theory iitiated ,y "olodtso2 8 1 9 has,eepro2edasa%eericmathematicaltooltodealwithpro,lems i2ol2i% 3certaities or imprecise data. 4ocalled traditioal tools s3ch as!3::y sets 8 2 9, ro3%h sets 8 3 9, 2a%3e sets 8 4 9, pro,a,ility theory etc. ca ot ,e3seds3ccess!3lly,eca3se o! iade;3ecypreset itheparametri:atio o! the tools.$ose;3etly, "olodtso2 hasshow that so!t set theory has a potetial to 3se i 2arietyo! may !ields 8 1 9. &!ter its iitiatio a detailedtheoretical costr3ctio has ,ee itrod3ced ,y "a.i et ali 8 5 9 .'or5s o so!t set theory is %rowi% 2ery rapidlywith all its potetiality ad is ,ei% 3sed i di!!eret !ields8 < = 11, 1(,1> 9.) case o! so!t set the parametri:atio isdoe with the help o! words, seteces, !3ctios etc..?ordi!!eret characteristicso!theparameterspreset iso!tset theory di!!eret hy,ridi:atio 2i:. !3::y so!t sets8 12 9,so!t ro3%h sets 8 13 9, it3itioistic !3::y so!t sets 8 14 9,2a%3e so!t sets 8 15 9, e3trosophic so!t sets 8 1< 9 etc. ha2e,eeitrod3ced. )81>3 ), 9D. $he, *. $. $. 7sa%, D. 4.^e3%ad@. 'a%, 7heNarametri:atio Red3ctio o! 4o!t sets ad its &pplicatios,$omp3t. "ath. &ppl. 4> ( 5 - < ) ( 2005 ), (5( - ( ( 2001 ), 5V> - (3)( 2001 ),.81V9 ?.4maradache,Ne3trosophic 4et, a Oeeralisatio o! the)t3itioistic ?3::y 4ets, )t. \.N3re &ppl. "ath. 24( 2005 ), 2V( = 2>(.81>9N. 0. "a.i, 'ei%htedNe3trosophic4o!t 4etsiDecisio"a5i% Nro,lem, comm3icated.Received: September 6, 2014. Accepted: September 27, 2014Neutrosophic Sets and Systems, Vol. 6, 2014P. K. Maji, Weighted Neutrosophic Soft Sets11