Some Results of Intuitionistic Fuzzy Soft Matrix Theory

Transcription

1 vailable olie at dvaces i pplied Sciece Research, 2012, 3 (1: ISSN: CODEN (US: SRFC Some Reslts of Ititioistic Fzzy Soft Matrix Theory B. Chetia * ad P. K. Das 1 Departmet of Mathematics, Brahmaptra Valley cademy, North Lakhimpr, ssam, Idia 2 Departmet of Mathematics, NERIST, Nirjli, Itaagar, rachal Pradesh, Idia BSTRCT The cocept of soft set is oe of the recet topics developed for dealig with the certaities preset i most of or real life sitatios. The parametrizatio tool of soft set theory ehace the flexibility of its applicatios. I this paper, we defie ititioistic fzzy soft matrices ad their operatios which are more fctioal to make theoretical stdies i the ititioistic fzzy soft set theory. We also defie five types of prodcts ad some reslts are established. Keywords: Soft sets,ititioistic fzzy soft sets, Soft matrices, Ititioistic fzzy soft matrices ad Prodcts of ititioistic fzzy soft matrices. INTRODUCTION Most of or real life problems i medical scieces, egieerig, maagemet, eviromet ad social scieces ofte ivolve data which are ot always all crisp, precise ad determiistic i character becase of varios certaities typical for these problems. Sch certaities are sally beig hadled with the help of the topics le probability, fzzy sets, ititioistic fzzy sets, iterval mathematics ad rogh sets etc. However, Molodtsov[8] has show that each of the above topics sffers from some iheret difficlties de to iadeqacy of their parametrizatio tools ad itrodced a cocept called Soft Set Theory havig parametrizatio tools for sccessflly dealig with varios types of certaities. The absece of ay restrictios o the approximate descrtio i soft set theory makes this theory very coveiet ad easily applicable i practice. Research o soft sets has bee very wide spread ad may importat reslts have bee achieved i the theoretical aspect. Maji et al. itrodced several algebraic operatios i soft set theory ad pblished a detailed theoretical stdy o soft sets[7].the same athors also exteded crisp soft sets to fzzy soft sets [4] ad ititioistic fzzy soft sets[6]. t the same time, there has bee some progress cocerig practical applicatios of soft set theory, especially the se of soft sets i decisio makig. Recetly, Çagma et al.[1] itrodced soft matrix ad applied it i decisio makig problems. I oe of or earlier work [2], we proposed the idea of Fzzy Soft Matrix Theory i seqel to [1] defiig some operatios.the preset paper aims to defie ititioistic fzzy soft matrix ad establish some reslts o them.this style of represetatio is sefl for storig a ittioistic fzzy soft set i compter memory ad which are very sefl ad applicable. 2.Prelimiaries Defiitio 2.1[8] Let U be a iitial iverse, P (U be the power set of U, E be the set of all parameters ad E. soft set o the iverse U is defied by the set of ordered pairs (f, E = {(e, f (e e E, ad f (e P (U }, where f : E P (U sch that f (e = φ if e. Here, f is called a approximate fctio of the soft set (f, E. The set f (e is called e-approximate vale set or e-approximate set which cosists of related objects of the parameter e E. 412

2 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: Example 2.1 Let U={c 1,c 2,c 3 } be the set of three cars ad E ={costly(e 1, metallic color (e 2, cheap (e 3 } be the set of parameters,where ={e 1,e 2 } E. The f (e 1 ={c 1,c 2,c 3 }, f (e 2 ={c 1,c 3 }, the we write a crisp soft set (f,e={( e 1, {c 1,c 2,c 3 },(e 2,{ c 1,c 3 }}over U which describes the attractiveess of the cars which Mr. S(say is goig to by. Defiitio 2.2[3,5] Let U be a iversal set, E a set of parameters ad E. Let F (U deotes the set of all fzzy sbsets of U. fzzy soft set (f, E o the iverse U is defied as the set of ordered pairs (f, E = {(e, f (e : e E, f (e F (U },where f : E F (U. Here, f is called a approximate fctio of the fzzy soft set (f, E. The set f (e is called e- approximate vale set or e-approximate set which cosists of related objects of the parameter e E. Example 2.2 Let U={c 1,c 2,c 3 } be the set of three cars ad E ={costly(e 1, metallic color(e 2,getp (e 3 } be the set of parameters,where ={e 1,e 2 E. The (G,={G(e 1 ={c 1 /.6,c 2 /.4,c 3 /.3}, G(e 2 ={c 1 /.5,c 2 /.7,c 3 /.8}} is the fzzy soft set over U ad describes the attractiveess of the cars which Mr. S(say is goig to by. Defiitio 2.3[1 ] Let (f, E be a soft set over U. The a sbset of U E is iqely defied by R = {(, e : e, f (e} which is called a relatio form of (f, E. The characteristic fctio of R is writte by χ : U E {0,1}, χ (, e = { 1, (, e R R R 0, (, e R If U = { 1, 2,..., m }, E = {e 1, e 2,..., e } ad E, the the R ca be preseted by a table as give below: R e 1 e 2 e χ (, e χ (, e... χ (, e If a = χ (, e, we ca defie a matrix [ a ] 1 R 1 1 R 1 2 R 1 χ (, e χ (, e... χ (, e 2 R 2 1 R 2 2 R 2 M M M M χ (, e χ (, e... χ (, e m R m 1 R m 2 R m R i j a a a a a a M M M M a a... a = m1 m2 m which is called a soft matrix of the soft set (f,e over U. ccordig to this defiitio, a soft set (f, E is iqely characterized by the matrix [a ]. It meas that a soft set (f, E is formally eqal to its soft matrix [a ]. 3.Fzzy soft matrices: Defiitio 3.1[ 2 ] Let (f, E be a fzzy soft set over U. The a sbset of U E is iqely defied by R = {(, e : e, f (e} which is called a relatio form of (f, E. The characteristic fctio of R is writte by µ : U E [0,1], where µ (, e [0,1] is the membersh vale of U for each e E. R R 413

3 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: If µ = µ (, e, we ca defie a matrix [ µ ] R i j µ 11 µ µ 1 µ µ... µ M M M M µ m1 µ m2... µ m = which is called a fzzy soft matrix of the fzzy soft set (f, E over U. Therefore, we ca say that a fzzy soft set (f,e is iqely characterized by the matrix [ ] cocept are iterchageable. µ ad both The set of all m fzzy soft matrices over U will be deoted by FSM. Example 3.1 ssme that U={ 1, 2, 3, 4, 5 } is a iversal set ad E={e 1,e 2,e 3,e 4 } is a set all parameters. If E={e 2, e 3, e 4 } ad f (e 2 ={ 1 /.4, 2 /.5, 3 /1, 4 /.3, 5 /.6}, f (e 3 ={ 1 /.3, 2 /.4, 3 /.6, 4 /.5, 5 /1}, f (e 4 ={ 1 /.5, 2 /.5, 3 /.4, 4 /.3, 5 /.9}. The the fzzy soft set (f,e is a parametrized family { f (e 2, f (e 3, f (e 4 }of all fzzy sets over U.The the relatio form of (f,e is writte by R e 1 e 2 e 3 e 4 µ (, e µ (, e µ (, e µ (, e 1 R 1 1 R 1 2 R 1 3 R 1 4 µ (, e µ (, e µ (, e µ (, e 2 R 2 1 R 2 2 R 2 3 R 2 4 µ (, e µ (, e µ (, e µ (, e 3 R 3 1 R 3 2 R 3 3 R 3 4 µ (, e µ (, e µ (, e3 µ R ( 4, e4 4 R 4 1 R 4 2 R 4 µ (, e µ (, e µ (, e µ (, e 5 R 5 1 R 5 2 R 5 3 R 5 4 R e e e e Hece the fzzy soft matrix [µ ] is writte as [µ ] = Defiitio 3.2[2] Let [µ ] FSM. The [µ ] is called (a a zero fzzy soft matrix, deoted by [0], if µ =0 for all i ad j. (b a iversal fzzy soft matrix, deoted by [1], if µ =1 for all i ad j. (c [µ ] is a fzzy soft sbmatrix of [λ ], deoted by [µ ] % [λ ], if µ λ for all i ad j. 414

4 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: (d [µ ] ad [λ ] are fzzy soft eqal matrices, deoted by [µ ] = [λ ], if µ = λ for all i ad j. Defiitio 3.3[2 ] Let [µ ], [λ ] FSM. The the fzzy soft matrix [ν ] is called (a io of [µ ] ad [λ ], deoted by [µ ] % [λ ] if ν = max{ µ, λ } for all i ad j. (b itersectio of [µ ] ad [λ ], deoted by [µ ] % [λ ] if ν = mi{ µ, λ } for all i ad j. (c complemet of [µ ], deoted by [µ ], if ν =1- µ for all i ad j. Example 3.2 Let [µ ]= [µ ] % [λ ]= ad [λ ]= ,[µ ] [λ ] = The ad [µ ] = Propositio 3.1[2] Let [µ ], [λ ] FSM. The (i ([µ ] % [λ ] = [µ ] % [λ ] (ii ([µ ] % [λ ] = [µ ] % [λ ] Proof: (i For all i ad j, ([µ ] % [λ ] =[ max{ µ, λ }] =[1-max{ µ, λ }] =[mi{1- µ,1- λ }] =[ µ ] % [λ ] (ii similar to (i. Propositio 3.2[2 ] Let [µ ], [ν ], [λ ] FSM, the (i [µ ] % ([ν ] % [λ ] =([µ ] % [ν ] % ([µ ] % [λ ] (ii [µ ] % ([ν ] % [λ ] =([µ ] % [ν ] % ([µ ] % [λ ] 4. Prodct of fzzy soft matrices I this sectio, for types of prodcts of fzzy soft matrices are defied i cotiatio to for special prodcts of soft matrices itrodced by Çagma et al.[1]. Defiitio 4.1[2 ] Let [µ ], [ν ] FSM. The d-prodct of [µ ] ad [ν ] is defied by : FSM FSM FSM 2, [µ ] [ν ]= [λ ] where λ = mi{µ, ν } sch that p = (j-1+k. Defiitio 4.2[2 ] Let [µ ], [ν ] FSM. The Or-prodct of [µ ] ad [ν ] is defied by : FSM FSM FSM 2, [µ ] [ν ]= [λ ] where λ = max{µ, ν } sch that p = (j-1+k. 415

5 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: Defiitio 4.3[ 2] Let [µ ], [ν ] FSM. The d-not-prodct of [µ ] ad [ν ] is defied by : FSM FSM FSM 2, [µ ] [ν ] = [λ ] where λ = mi{µ, 1-ν } sch that p = (j-1+k. Defiitio 4.4[ 2 ] Let [µ ], [ν ] FSM. The Or-Not-prodct of [µ ] ad [ν ] is defied by : FSM FSM FSM 2, [µ ] [ν ]= [λ ] where λ = max{µ, 1-ν } sch that p = (j-1+k. Example 4.1 Let [µ ], [ν ] FSM 5 4 where [µ ]= ad [ν ]= the [µ ] [ν ]= Similarly, the other prodcts ca also be obtaied. Remark: Commtatively is ot valid for the prodcts of fzzy soft matrices. Propositio 4.1[2 ] Let [µ ], [λ ] FSM, the (i ([µ ] [λ ] = [µ ] [λ ] (ii ([µ ] [λ ] = [µ ] [λ ] (iii ([µ ] [λ ] = [µ ] [λ ] (iv ([µ ] [λ ] = [µ ] [λ ] 5. Ititioistic Fzzy soft matrices (IFSMs. I this sectio, we defie ititioistic fzzy soft matrices. Defiitio 5.1 Let U be a iitial iverse, E be the set of parameters ad E. Let ( f, E be a ititioistic fzzy soft set (IFSS over U. The a sbset of U E is iqely defied by R = {(, e; e, f ( e} which is called a relatio form of ( f, E.The membersh fctio ad o membersh fctio are writte by µ : U E [0,1] ad ν : U E [0,1] where µ : (, e [0,1] ad V : (, e [0,1] R R are the membersh vale ad o membersh vale respectively of If (, = ( (, e, (, e, we ca defie a matrix µ ν µ ν R i j R i j R R U for each e E. 416

6 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: [( µ, ν ] ( µ 11, ν 11 ( µ 12, ν 12 L ( µ 1, ν1 ( µ, ν ( µ, ν L ( µ, ν M M M M ( µ m1, ν m1 ( µ m2, ν m2 L ( µ m, ν m = which is called a m IFSM of the IFSS ( f, E over U. Therefore, we ca say that a IFSS ( f, E is iqely characterized by the matrix [( µ, ν ] cocepts are iterchageable. The set of all m IFS matrices over U will deoted by IFSM. m ad both Example 5.1 ssme that U = { 1, 2, 3, 4, 5} is a iversal set ad E={ e1, e2, e3, e4} is a set of all parameters. If E = { e e e } ad 2, 3, 4 2 = f ( e { / (.4,.5, / (.5,.3, / (1,0, / (.3,.6, / (.6,.2} f ( e = { / (.3,.5, / (.4,.6, / (.6,.2, / (.5,.5, / ( 1, 0} f ( e = { / (.5,.2, / (.5,.5, / (.4,.6, / (.3,.6, / (.9,.1} The the IFS set ( f, E is a parameterized family { f ( e2, f ( e3, f ( e4 } of all IFS sets over U. The the relatio form of ( f, E is writte as R e e e e (.4,.5 (.3,.5 (.5,.2 0 (.5,.3 (.4,.6 (.5,.5 0 ( 1, 0 (.6,.2 (.4,.6 0 (.3,.6 (.5,.5 (.3,.6 0 (.6,.2 ( 1, 0 (.9,.1 Hece the IFSM [( µ, ν ] is writte by 0 (.4,.5 (.3,.5 (.5,.2 0 (.5,.3 (.4,.6 (.5,.5 [( µ 54, ν 54] = 0 (1,0 (.6,.2 (.4,.6 0 (.3,.6 (.5,.5 (.3,.6 0 (.6,.2 ( 1,0 (.9,.1 Defiitio 5.2 % = [( µ ν ] IFSM m. The % is called Let, (a a zero IFSM, deoted by 0 % = [(0,0], if µ = 0 ad ν = 0 for all i ad j. (b a µ - iversal IFSM, deoted by Ι = [(1,0],if µ = 1 ad ν = 0 % for all i ad j. (c a ν - iversal IFSM, deoted by I = [(0,1],if µ = 0 ad ν = 1 for all i ad j. (d % = [( µ, ν ] is a ititioistic fzzy soft sb matrix of B = [( µ, ν ], % B % if µ µ ad ν ν % for all i ad j. % deoted by 417

7 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: (e % = [( µ, ν ] ad B% = [( µ, ν ] are ititioistic fzzy soft eqal matrices, deoted by ( % o % B% = ([( µ ν ] % [( µ ν ],,, = [(max{ µ, µ },mi{ ν, ν }] = [{mi{ ν, ν },max{ µ, µ }] = [( ν, µ ] % [( ν, µ ] = % o % B% o % = B % if µ = µ ad ν = ν for all i ad j. Defiitio 5.3 Let % = [( µ, ν ], B% = [( µ, ν ] IFSM m.the the IFSM C = [( µ, ν ] (a io of % ad B %, deoted by for all i ad j. (b itersectio of ad ν max{ ν, ν } o o % is called % % B % µ = µ µ ν = ν ν '' if max{(, } ad mi{, } % B %, deoted by % % B % if µ = mi{( µ, µ " } ad = for all i ad j. (c complemet of, Example 5.2 % = [( µ ν ], deoted by o (.1,.2 (.5,.4 (.3,.6 (.4,.4 (.2,.3 (.5,.1 Let % = ad (.5,.2 (.3,.4 (.6,.2 (.7,.2 (.6,.1 (.5,.3 The (.5,.2 (.5,.4 (.7,.1 (.8,.1 (.4,.3 (.5,.1 % B= % (.5,.2 (.3,.4 (.6,.2 (.7,.2 (.6,.1 (.5,.1 (.2,.1 (.4,.5 (.6,.3 (.4,.4 (.3,.2 (.1,.5 o = (.2,.5 (.4,.3 (.2,.6 (.2,.7 (.1,.6 (.3,.5 Propositio 5.1 % =, %, Let % =[( µ, ν ], B% = [( µ, ν ] IFSM m The (i ( % o o o % B% = % % B% (ii ( % % B% = % % B% o o o Proof : For all i ad j (i (ii Similar to (i. [( ν µ ] for all i ad j. (.5,.3 (.1,.6 (.7,.1 (.8,.1 (.4,.3 (.5,.2 B = (.2,.5 (.3,.6 (.4,.5 (.1,.7 (.2,.5 (.5,.1 %. (.1,.3 (.1,.6 (.3,.6 (.4,.4 (.2,.3 (.5,.2 % B= % (.2,.5 (.3,.6 (.4,.5 (.1,.7 (.2,.5 (.5,.3 % ad 418

8 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: Propositio 5.2 L e t % = [ ( µ i j, ν i j ] I F S M m. T h e ( i ( ( % o o = % ( i i (% o I = I o ( i i i ( I = % I ( i v % % % I ( v % % I Propositio 5.3 Let % = [( µ, ν ] IFSM. The ( i % % % = % ( iv % % % = % ( ii % % I% = I% ( v % % I% = % ( iii % % I = % ( vi % % I = I Propositio 5.4 Let % = [( µ, ν ], B% = [( µ, ν ] ad C% = [( µ, ν ] IFSM m The ( i % % B% = B% % % ( ii % % B% = B% % % ( iii( % % B% % C% = % % ( B% % C ( iv( % % B% % C% = % % ( B% % C% ( v % % ( B% % C% = ( % % B% % ( % % C% ( vi % % ( B% % C% = ( % % B% % ( % % C% Propositio 5.5 Let %, B% IFSM as i the Example The (.2,.5 (.4,.5 (.1,.7 (.1,.8 (.3,.4 (.1,.5 ( % o o o % B% = % B% = (.2,.5 (.4,.3 (.2,.6 (.2,.7 (.1,.6 (.1,.5 (.3,.1 (.6,.1 (.6,.3 (.4,.4 (.3,.2 (.2,.5 ( % B% o = % o o % B% = (.5,.2 (.6,.3 (.5,.4 (.7,.1 (.5,.2 (.3,.5 419

9 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: Defiitio 5.4 If % = [( µ, ν ], B% = [( µ, ν ] IFSM The the IFSM C% = [( µ, ν ] is called ( i the '.' opeartio of % ad B%, deoted by C% = %. B% if µ = µ. µ ad ν = ν + ν ν. ν for all i ad j. " µ + µ ν + ν if µ =, ν = for all i ad j 2 2 ( iv the '$' operatio of % ad B%,deoted by C% = % $ B% if µ = µ. µ, ν = ν. ν for all i ad j. Propositio 5.5 Defiitio 5.5 ( ii the' + ' operatio of % ad B%, deoted by C% = % + B% if µ = µ + µ - µ. µ ν = ν. ν for all i ad j. ( iii the '@' operatio of % ad B%, deoted by C% = B% Let %, B%, C% IFSM. The ( i %. B% = B%. % ( ii % + B% = B% + % ( iii B% = % ( iv % $ B% = B% $ % ( v ( % + B% + C% = ( % + ( B% + C% ( vi ( %. B%. C% = %.( B%. C% ( vii ( % % B% + C% = ( % + C% ( B% + C% ( Viii ( % % B%. C% = ( C %.% % ( B%. C% ( ix ( % % C% = ( C% % ( C% ( x ( % % B% + C% = ( % + C% % ( B% + C% ( xi ( % % B%. C% = ( %. C% % ( B%. C% If % = [( µ, ν ] IFSM. The ( i the ecessity operatio of % deoted by % if µ = µ, ν = 1 ν for all i ad j. ( ii the possibility operatio of % deoted by % if µ = 1 ν, ν = ν for all i ad j. 420

10 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: Propositio 5.6 Let %, B% IFSM. The ( i ( % % B% = % % B% (ii ( % % B% = % % B% ( iii % = % ( iv ( % B% = % % B% ( v ( % % B% = % % B% ( vi % = % Example 5.5 Let %, B % IFSM 4 3 as i the Example 4.2 The (.5,.5 (.5,.5 (.7,.3 (.8,.2 (.4,.6 (.5,.5 ( % B% = % B% = (.5,.5 (.3,.7 (.6,.4 (.7,.3 (.6,.4 (.5,.5 ad (.8,.2 (.6,.4 (.9,.1 (.9,.1 (.7,.3 (.9,.1 ( % B% = % B% = (.8,.2 (.6,.4 (.8,.2 (.8,.2 (.9,.1 (.9,.1 6. Prodct of Ititioistic Fzzy Soft Matrices (IFSMs I this sectio, five types of prodcts of IFSM are defied i cotiatio to for special prodcts of fzzy soft matrices. Defiitio 6.1 Let % = [( µ, ν ], B% = [( µ, ν ] IFSM.The ' ' prodct of % ad B% is defied by : IFSM IFSM IFSM sch that % B% = [( µ, ν ] [( µ, ν ] = [( µ, ν ] where µ = µ. µ ' ad ν = ν. ν sch that p = ( j i + k. Defiitio 6.2 Let % = [( µ, ν ], B% = [( µ, ν ] IFSM.The ' ' prodct of % ad B% is dified by :IFSM IFSM IFSM sch that % B% = [( µ, ν ] [( µ, ν ] =[( µ, ν ] where ' µ = µ + µ µ. µ ad ν = ν. ν sch that p = ( j i k

11 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: Defiitio 6.3 Let % = [( µ, ν ], B% = [( µ, ν ] IFSM.The ' ' prodct of % ad B% is defied by : IFSM IFSM IFSM sch that % B% = [( µ, ν ] [( µ, ν ]=[( µ, ν ] where µ = µ. µ ad ν = ν + ν ν. ν sch that p = ( j i + k. Defiitio 6.4 Defiitio 6.5 Propositio 6.1 % = % = % ' ' Let [( µ, ν ], B [( µ, ν ] ad C=[( µ, ν ] IFSM.The ( i( % B% C% = % ( B% C% ( ii( % % B% C% = ( % C% % ( B% C% ( iii( % % B% C% = ( % C% % ( B% C% Example 6.1 Let %, B% IFSM as i the Example 4.2 The B = 1 The B = 2 Let % = [( µ, ν ], B% = [( µ, ν ] IFSM.The ' ' prodct of % ad B% is defied by : IFSM IFSM IFSM sch that % B% = [( µ, ν ] [( µ, ν ]=[( µ, ν ] where µ = mi{ µ, µ } ad ν = max{ ν, ν } sch that p = ( j i + k. Let % = [( µ, ν ], B% = [( µ, ν ] IFSM.The ' ' prodct of % ad B% is defied by : IFSM IFSM IFSM sch that % B% = [( µ, ν ] [( µ, ν ]=[( µ, ν ] where µ = max{ µ, µ } ad ν = mi{ ν, ν } sch that p = ( j - i + k. 4 3 (.05,.06 (.01,.12 (.07,.02 (.25,.12 (.05,.24 (.35,.04 (.15,.18 (.03,.36 (.21,.06 (.32,.04 (.12,.16 (.20,.08 (.16,.03 (.08,.09 (.10,.06 (.40,.01 (.20,.03 (.25,.02 (.10,.10 (.15,.12 (.20,.10 (.06,.20 (.09,.24 (.12,.20 (.12,.10 (.18,.12 (.24,.10 (.07,.14 (.14,.10 (.35,.02 (.06,.07 (.12,.05 (.30,.01 (.05,.21 (.10,.15 (.25,.03 (.55,.06 (.19,.12 (.73,.02 (.75,.12 (.55,.24 (.85,.04 (.65,.18 (.37,.36 (.79,.06 (.88,.04 (.64,.12 (.7,.08 (.84,.03 (.52,.09 (.06,.06 (.90,.01 (.7,. 03 (.75,.02 (.6,.10 (.65,.12 (.7,.10 (.44,.20 (.51,.24 (.58,.20 (.68,.10 (.72,.12 (.76,.10 (.73,.14 (.76,.10 (.85,.02 (.64,.07 (.68,.05 (.80,.01 (.55,.21 (.6,.15 (.75,.03 CONCLUSION Molodtsov itrodced the cocept of soft sets,which is oe of the recet topics developed for dealig with the certaities preset i most of or real life sitatios. The parametrizatio tool of soft set theory ehace the flexibility of its applicatios. I this paper, we defie ititioistic fzzy soft matrices some reslts are established ( i cotiatio to soft matrices itrodced by Cagma et al.[ 1]. &

12 B. Chetia et al dv. ppl. Sci. Res., 2012, 3(1: ckowledgemets The athors wold le to thak Dr. B.K.Saia, Departmet of Mathematics, Lakhimpr Girls College, ssam, Idia for providig very helpfl sggestios. ( [1] Cagma & REFERENCES (, N. & Egiogl, S., Compters & Mathematics with pplicatios, 2010, [2] Chetia, B.,& Das, P.K.,Joral of the ssam cademy of Mathematics, 2010,2, [3] Chetia,B., & Das,P.K., Iteratioal Joral of Mathematical rchive,2011, 2(8, 1-6. [4] Chetia, B. ad Das,P.K., applicatio of ititioistic fzzy soft matrices i decisio makig problems (commicated. [5] Maji.,P.K., Biswas,R., ad Roy,.R., The Joral of Fzzy Mathematics, 2001,9(3, [6] Maji.,P.K., Biswas R. ad Roy,.R., The Joral of Fzzy Mathematics, 2001, 9(3, [7] Maji.,P.K., Biswas,R. ad Roy,.R., Compters & Mathematics with pplicatios, 2003,45, [8] Molodtsov, D., Compters ad Mathematics with pplicatio, 37(1999,