Decision Making: system lexicon.

Transcription

1 Decson Makng: syste con Z Abarashv,V Zhukovn, N Chkhkvadze Abstract : There s gven the progra reazaton syste "con" by the usng cographca procedure Key words: Decson akng, cographca procedure Introducton The cographca procedure wdey spread n the decson akng probes It s used n the varous sphere of the huan acton for exape: The words are cographcay reguated n the dctonary 2 The base-ten syste of the nuber recordng s defned by cographca prncpe 3 The tares use the cographca prncpe n the probe of the obectve aocaton 4 The Aercan scentsts experentay proved, that the huans use the cographca prncpe for decson akng 2 Mutcrtera cographca procedure Mutcrtera decson akng probe has been atheatca forazed wth L Zade n 960 After that cographca procedure of choce has atheatca base for ts descrpton, deveopent and generaton new procedures Mutcrtera probe of decson akng s presented n vector nterpretaton n ths way: D = X, K, ( where, X - s fnte set of copettve aternatves x X, = n Let ntroduce the set of ordered pars E wth the eeents ( x, x E, x, x X { K x, K ( x,, K ( x,, K ( x } K = (2 ( 2 Ths s vector crteron of effcency; where K x, ( k =, are scaar functons are type of wn Besdes defned on the set X We can suppose, that a K ( x they are defned wth the content and athough each of the has ts scae of easurng the type of scae s dentty Snce we aways can trade paces the coponents at vector crteron K of portance, we coud say that K x crterons are ordered by the reevance The ( order concurs wth the nuber s order, n other words ost portant crteron s =, next = 2 and so dstances = It s ped that ths order s cographca We expan ths affraton beow Now we foruate cographca structure on the set E For t s necessary to defne bnary cographca preference reatons It defnes n the foowng way Let consder the decsons pars ( x, x E R R : It s sad, that the decsons x X, are cographca preference than k

2 x X, f one of foowng condtons fufs: K x > K ( x, or ( ( x K( 2 K = and K 2 ( x > K 2 (, or ( K ( x = K( and and K ( x = K ( and K ( x > K ( or n K ( x = K( and and Kn ( x = Kn ( and K n ( x > K n ( The stop happens on the row where the nequaty s fufed If the nequaty s not executed on n row too, e K n( x = Kn(, then ths par s cographcay equvaent decson Brefy ths procedure s desgnatng n that way: Let expore characterstcs of pars fro transtve Superorty reaton o rder e R x f~ R E are congruous wth R x (4 In the frst pace t s nked, e a decson ths reaton It s aso asyetrca and s equvaence too Such superorty reaton s near s near order Now we sha appy a arsena of resut, theores, whch are avaabe at present n the theores of decson akng estabshed us and other scentsts, to research of the presented cographca procedure (3 And here the frst It s proved that the near order has nonepty set Pareto (ts kerne and ths set contans one decson, f t soe they are equvaent So procedure (3 aways gve out one decson 3 Lexcographca coeffcents of portance Crteron K ( x of effcency are ordered on portance accordng to nubers: the ess nuber the ore portant crtera for a choce Ths fact can be fxed, havng attrbuted crtera coeffcents of portance: λ K ( x, = In ths case n the theory of decson akng near convouton of vector crtera of effcency K s consdered: L( x = λ K = ( x Ths convouton possesses any very good propertes whch we sha consder ater, n the sae secton The unque requreent to portance coeffcents are λ 0 for λ = a = Soetes use aso a condton =, but t not defntey Wth ths the condton s executed: f L( x L( then f, and (6 x on the contrary f f x then L( x L( x Cear that f λ are nubers and K ( x scaar functon, then L( x scaar functon defnte on X The freedo of a choce λ, = n n ths case us s not arranged (5

3 Sef-wed coecton of portant coeffcents Λ = {λ } dsturbs cographca condtons representng by the forua (3Whether there s a queston s there such coecton of portance coeffcents whch woud not break, and kept a condton cographc (3? Yes, t s and not ony one but whoe cass Therefore we desgnate cographca coeffcents of portance wth λ (, = and a coecton of coeffcents wth λ ( = Λ( { } (7 When near convouton wrtes so for cographca choce (basc forua: L ( x = λ ( K = ( x (8 There are worked speca procedures for the accountng of portance coeffcents λ (, =, by severa scentsts and by us too These procedures do not concde and use dfferent scaes of easurng Now we descrbe basc property of near convouton: a L ex s a functon of usefuness defnte on the X It assgns near order accordng to rues: L ( x L ( x x f x (9 b Ths order s adusted wth the order presented by forua (3, ths s: f f x correspondence wth forua (3, that x L( x L( (0 and on the contrary The foruas (8 and (9 are dentca c Any new presentaton ust be adusted wth (3 and t eans that the presentaton w be adusted wth (7 too d Pareto set XΠ ( contans one decson (kerne of near orders Ths best decson s snge and does not depend for the vew of the presentaton e Ths best eeent w be fnd, f we decde spe optzaton probe: x = ax L( x ( x X ~ where x X and t s best decson n cographca procedure of choce (3 f Now about scae of easure A known us coecton of cographc coeffcents are presented by orderng scae: Ш = K Λ, Φ( K, (2, ex wth ths Φ s the cass of perttng transforaton It s onotone functon (ncreasng or decreasng Usuay the decson x s nstabe n the orderng scae e the expresson (0 does not nvarant concernng onotone transforaton of the coeffcents But ths coon rue breaks n cographca procedure The decson x s stabty concernng the transforaton The expresson (0 s nvarant n orderng scae It s reated to ths ax s searchng wth one crteron and whch s defned by copare par of decson g Cevery, cographca choce nk to superorty degree: Z( x, = 0 ( t s nuber of ne where s executed the choce

4 Let anayze deta the crterons K It s scaar functon defnte on X Let consder these coeffcents Every crteron has own nae (energy, ength, expendture, whch represents any property of the estatng obect x X The nae enabes us the group of crteron K, =, w be ordered wth portance Every nuber crteron has the scae of estatng There s exape pc ı ı ı ı ı ı ı 0 2 ν q -2 q pc Usuay the scae s begnnng fro the zero, but t s possbe begnnng fro ether of eanng (for exape p Let consder the crteron of wn It eans that ν >ν where ν s ndcator of scae rank Ths dependence s transtve and nked Now defne scae dapason of crteron K d = axν ( nν (, (3 f the scae s begnnng fro zero d = axν ( = q,where q s quantty of scae rank Let defne the condtons of cographca group crterons K, = : Affraton Assue the portance of crteron s ncreasng fro the rght to the eft and ts nuber of poston fro the eft to the rght (foruae 3, then f the condton n ν ( f axν ( + s fufed for a =, then crterons group K, = s cographc ordered Notce: Zero takes not n part of the nu defnng (ony n the affraton 2 The ark f sgnfes the portance 3 Ths dependence s nked and transtvty Now we can assgn the forua for the accountng cographca coeffcents of portance: λ ( = d, = (4 May be the scaes of the crteron are dverse (for exape: the speed /h, energy k/h In ths case the foruae (3 works, but L( oses the sense One of the ethod the forng unforty syste of the crteron s the ratonng Instead of K, ncude foowng crterons: K ( x γ ( x = a where a > 0 (5 ax K Ths gves the freedo for the varaton ( for exape a = 0 scae of Saaty Unforty of crtera Let consder two exape of cographca structure for the presentng unforty crterons a Deca syste of nuber presentng: =

5 The poston s correspondng wth the crteron The nuberng of the poston s fro the rght to the eft The portance grows up sae drecton too There s sae the scae n each poston Ths s the unforty of the crteron (poston b Lexcon The drecton of portance ncreasng s fro the rght to the eft and poston nuberng on the contrary fro the eft to the rght The nuber of the poston s unted It s bad for the dctonary For ths we assgn axa possbe ength of the word ( 20 etter One etter contans n each poston ( gap s paced n the begnnng of the aphabet or n end The etters are ordered by the preference (fro A to Z There s unforty structure too Notce: Each word s ascrbed the nuber then we order these nubers The accountng cographca coeffcents of portance are for Georgan aphabet: λ ( = 33 for a 4 Syste con Now because our artce s about the con (Georgan-Engsh, Engsh-Georgan, Russan-Georgan, Georgan- Russan e we consder one of the exape for the coputer There are soe restrcton taton whch we pertted durng the prograng The nuber of postons s 20 2 The base of preference we take 6 (nstead of 33 n Georgan and 26 n Engsh 30 3 Frst poston of preference s λ = 6 (top t of the eory 4 The preference s ncreasng fro the eft to the rght For the unque of each poston λ λ = The dapason of preference dfference s fro λ = 6 - to λ = 6 8, because nuber of poston s 20 The progra part of the syste "con" s fored n syste Deph syste "con" coposes two progras and they work daogc rege Frst of the progras "an" search the font of the words, the context and the correspondng data base After a t pasts the rung second progra Second progra s "con" There are the coentares whch reaze recess operaton There are consdered: Get the word and context 2 The word and context are effaced f they are wrong 3 Speca code weght and paces correspondng to ts pace n data base 4 The con ay be carred to EXCEL and t gves possbty the pubcaton con for wde custoer References Жуковин ВЕ Многокритериальные модели принятия решений с неопределенностью-тбилиси:мецниереба,983,с05 2 Жуковин ВЕ Нечеткие многокритериальные модели принятия решений- Тбилиси:Мецниереба,988,с72