THE INFLATION INDEX PROGNOSIS BASED ON THE METHOD OF DECISION-MARKING TREE. Alexei Voloshyn, Victoria Satyr

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1 Internatonal Journal "Informaton Theores & Applcatons" Vol.4 / THE INFLATION INDEX PROGNOSIS BASED ON THE METHOD OF DECISION-MARKING TREE Alexe Voloshyn, Vctora Satyr Abstract: The descrpton of the support system for markng decson n terms of prognosng the nflaton level based on the multfactor dependence represented by the decson markng tree s gven n the paper. The nterrelaton of affectng the nflaton level economc, fnancal, poltcal, soco-demographc ones, s consdered. The perspectves for developng the method of decson markng tree, and pontng out the socalled narrow spaces and further analyss of possble scenaros for nflaton level prognosng n partcular, are defned. Keywords. Method of decson - markng tree, multfactor analyss, nflaton ndex, expert nformaton. Introducton Economc growth s consdered to be one of the most mportant socal problems whch s n the focus of economsts and poltcans attenton. So the mportance of nflaton ndex prognosng means that the man tendences of economc development are reflected n t and the charges n the dynamcs of Gross Domestc Product (GDP) affect the changes of lvng standard of each ctzen of Ukrane. There exst no unversal and perfect approaches to fndng soluton to ths problem nowadays. Some attempts for buldng possble scenaros for developng ether phenomenon n future only have been made. Varous method of qualtatve characterstcs based on usng expert nformaton are used for ths purposes. Economc prognoss should defne and evaluate the man drectons of economc development reflectng total combnaton of nternal and external nterrelatons between the components on the macroeconomc level n the frst place. Macroeconomc prognoss means that the nvestgaton should be amed at strategc level. All the man elements of economc and socal sphere n progress should be consdered n the context of ther cause and effect relatons and nterdependence. Irrespectve of the am any macroeconomc prognoss s based on defnte theoretcal grounds to correspond wth scentfc grounds. In terms of mechansms of achevng adequacy and nformaton unty the apparatus of economc mathematc modelng becomes ndspensable because of usng complex economc-mathematc methods based on apparatus of econometrc modellng too often. The methods of quanttatve prognosng (tme lnes, regressve analyss, mtaton modellng, etc.) based on contnuaton f the past present poor results whle prognosng unstable processes whch are characterzed by breakng the monotony and are based on sudden changes and cannot be referred to as dstnctve features for descrbng the development of the process n the past [Popov, 996]. The problem les n representng the future as a usual thng related to contnuaton of the past as far as the future can acqure some prncpally new shares. Ths prognosng ( qualtatve prognosng ) s based on drect usage of human (expert) knowledge, naccuracy of expert nformaton beng taken nto account n the frst place, whch depends on the expert s professonal and psychologcal characterstcs (competency, ndependence, mpartalty, real vson, rsk takng, etc.) [Ivchenko, 984]. The method of decson - markng tree The method of decson - markng tree represented n ths paper may be referred to as a basc ground for prognosng nflaton level, expert nformaton beng used for buldng the tree tself and method of double comparson [Voloshn, 999]. Expert nformaton can be presented both as determned and naccurate one. In processng expert nformaton for fndng out collectve estmates the algebrac method based on usng Hemmng s metrcs and measure of nonconformty of obect ranks [Ushakov, 979]. The group wth n ( n ) of experts workng together sngles out the problems and sub-problems and bulds the decson - markng tree, and also defnes the mportance (prorty) of each task (each element of the tree). Processng expert nformaton s

2 64 Internatonal Journal "Informaton Theores & Applcatons" Vol.4 / 007 carred out takng nto account prortes set by expert and degree of agreement on ther estmates [Kozeletskyy, 979]. The basc are presented at the top of the tree. Then these fall nto smaller sub-problems, etc. As a result the decson - markng tree s bult. The leaves of the tree stand for the whch do no fall nto further sub-problems. After heavng set the prortes n the decson - markng tree the mportance of each factor s evaluated [Seber, 980]. The tree s bult by a group of experts (persons who make decsons). Each of the elements (key ponts) of the tree (expert of the leaves) has ts sub-elements (.e. each problem has a sub-problem). Then the prortes (chances) for comng from one top of the tree to another one are set. The work of the expert group results n buldng the decson - markng tree amed at prognosng the nflaton ndex (Fgure ) whch ncorporates the followng man problems: economc - ndustry, agrondustral complex, fnancal market, commerce, etc; poltcal - rregular economy, nvestment, monetary and antmonopolstc polcy, etc; socal demographc stuaton unemployment, socal-demographc load, tempo of populaton ncrement, etc; fnancal fnancal-budget, monetary polcy, sate regulaton of securtes market, state regulaton of prces, etc. To specfy narrow spaces means to sngle out the affectng at each stage of the sub-problem, for nstance, let s consder the state of economc development: state orders (contracts), prvleges, subsdes, state credts, warrants and taxes, nternal and external nvestments, the allotment of the aggregate ncome expenses on consumer goods. Let s consder the problem of unemployment, the number of obs avalable, the system of allotment of pensons and students grants, state regulaton of labour market. Employment and workng condtons, etc. Havng consdered the mportance the leaves of ths tree we obtan the probable specfc ndces of nflaton fr a certan perod of tme. Each of the experts produces estmates of three types: a - optmstc, a - realstc, and a - pessmstc. The resultng estmate s calculated n such a way. The average estmate of each expert a a a a, s consdered n the frst place, then wth reference to the mportance of all the experts, the resultng estmate s calculated. In ths case: a,,,, n s ntroduced ndstnctly by means of functon (vector of essental qualty and looks lke: a ( a,..., a ),, n. Coeffcents, k,, are calculated emprcally and present numercal characterstcs [Tsurkov, 98]. In accordance wth one of the method, 4 (for expert- realst ), accordng to other -, 0,, 0, (for an optmst ) and (for a pessmst ). To specfy the psychologcal type of the expert (pessmst, optmst, realst) by means nput n the system the psychologcal testng of the experts s carred out and then the coeffcents of realstcty k ( / λ / for realst, 0 λ / for pessmst, / λ for optmst correspondngly are taken nto account). The coeffcents of competency k are calculated on the bass of the prevous prognoses accuracy n conformty wth the methods suggested. The ntal coeffcents k equal [Gladun, 987]. n The theory To analyse the way the decson - markng tree can respond t s necessary to fnd the facts whch dramatcally affect the nflaton level and could be taken nto consderaton n ths model. Bearng ths n mnd we should sngle out the narrow spaces whch depend greatly on beng placed on a certan leaf of the tree the estmate of the prognosed parameter.

3 Internatonal Journal "Informaton Theores & Applcatons" Vol.4 / Quantty and qualty of natural resourses Structural polcy Law s, normatve acts State orders (contracts) Nef export (X) State purchases (G) Investments (I) Consum pton (C) Expenses GDP Supply Demand Quantty and qualty of labour resourses The amount of captal of the country Technology Tax level Interest rate Producton capacty Investment polcy Scentfc techncal regulaton Innovaton polcy Deprecaton polcy Monetary polcy State regulaton of securtes market State regulaton of prces Ant nflaton regulaton State regulaton of enterprses Branch norms, lmts Deprecaton norms Prognoses, ndcatve acts Amed complex programmes Soco economc normatves Prvleges, donatons, subsdes Budgets, state nvestments Interest and bank rates, exchange rate, reserve normatves Systems of fxed margnal prces, prce fxng condton, ndex for consumer prces State credts, quarantees GDP percapta Economc development level, ndces of the effectvenessof the economy: money turnover, money capacty, captal ntensty, resourse capacty, power capacty, labour capacty > Incomes Wages Rent payment Interests Profts Indrect taxes on busness De pres aton Ef f ectve ness Soco cultural, nsttuto nal and other Employ ment Producton effectveness (thrfty utlsaton of natural resourses Dstrbutonal effectveness (producton of the most valuable goods for the publc) Socal clmate Antmonopolstc polcy State regulaton of foregn economc actvtes State regulaton of labour market, employ ment, workng condton Socal polcy, ncome and consumpton regulaton State regulaton of provdng servces for general publc Demographc polcy State regulaton of envronmental protecton measures Shumantaran polcy Preferencal nvestments Soco economc normatves, ndex of ncomes Subsstence level, mnmum wages, pensons Sngle tarff system System of pensons and students grants Customs dutes and leves Import export quotas Means of export stmulaton Means of mport regulaton Ecologcal nvestgaton,norms and standarts Producton of the man tems of consumpton per captal, the level of producton development of some regons The level and qualty of lvng < 6,9 deductons Cultural atmosphere Regonal polcy Taxes Centralsaton of ncomes Poltcal structure of the socety Natonal polcy Unemployment benefts Atttude to w ork Ways of prvatsaton Part of the aggregate ncome on consumer goods

4 66 Internatonal Journal "Informaton Theores & Applcatons" Vol.4 / 007 After ths t s desrable to consder several scenaros for descrbng dfferent swtchovers n the tree. Under such condtons there s a possblty to obtan current statstc data for the model parameters to be estmated and usng them to test statstc and economc effectveness of the model and develop the more effectve prognoss. To decde on what should be chosen for the model of ths knd the theory of economc ndcators mght be of great mportance. Commonly all ndcators are nterrelated and affect each other so nflaton tself may be referred to as an economc ndcator and there exst a number of ndcators closed related to t. The wde range of ndcators allows them to be grouped nto certan system or models n conformty wth the requrements specfc for them. One of the methods of changng economc stuaton s combnng economc ndcators nto a system n terms of ther economc contents and the nature of statstc nterrelaton wth nflaton. There economc ndcators can be grouped though certan elements n them can overlap. Among these ndcators there may be dstngushed such of them whch characterse economy and economc growth, populaton and employment, state fscal polcy, consumpton, nvestments ndustry and commerce, external cash flows, exchange rates, money and nterest rates and salares and wages. Whle consderng ndcators of each group as separate elements of the system and comparng ther dynamcs wth the dynamcs of GDD changes we may sngle out such of them whch are drectly related to nflaton level and those whch are not. The ndcators whch tend to be the components of nflaton belong to the frst group. They are: part of the aggregate ncome expenses on consumer goods, prvleges, donatons and subsdes, etc. In ths context t s possble to defne one more crteron of ther relaton to nflaton whether they change together wth economc stuaton or wth the postve or negatve lag. There are the moments whch form the bass of the statstc prognosng ndcators system whch s used to prognoses the nflaton level. So, the ndcator approach gves an opportunty to take nto consderaton those crtcal moments n the tree and the nfluence of dfferent by ther nature ndces on the common result. It s also by means of other methods to change the data obtaned from the experts accordng to ther characterstcs. Let - expert gve the approxmate estmate a ( a,..., ak ) of the problem that mght become one of the tops of the decson makng tree. If for example, the expert s not rsk takng enough t s advsable to process the obtaned estmate n such a way [Zagoruko, 999]. The maxmum a max and the mnmum a mn values are calculated then the average value a s ( a mn) ( max a ) calculated. Any a s changed n such a way: a a. ( max mn) Ths changer wll change the type of the functon essental qualty: (Fgure.) Judgng from ths fgure we may arrve to the concluson that ths knd of transformaton makes the functon more vvdly expressed. Ths may be understood as ncreasng the degree of expert s rsk takng. Besdes, n accordance wth the task t s also possble to perform certan transformatons n terms of ncreasng expert s realstcty, ndependence, etc. The man advantages of such approach are: It allows to solve effectvely the tasks of technologcal forecast dong the research of unstable processes and phenomena wth nsuffcent descrpton as far as they are based on the experts knowledge and do not depend on the nformaton abut the behavour of these phenomena n the past; It allows the structurng of colletng expert nformaton dvdng the subect area nto certan segments whch makes t possble to select more hghly specalzed and hence more sklled experts/

5 Internatonal Journal "Informaton Theores & Applcatons" Vol.4 / Concluson Ths system was used for prognosng the nflaton ndex on , the system was used n July, 005, the nflaton ndex obtaned was equal.8%, the prognosed estmates of the offcal nsttutes and external experts were fluctuatng between 8% to 0% and plus. The offcal statstc data of the mnstry of Economy of Ukrane come up to 0,5% and the Insttute for Economcs and Prognosng suggested,5% - %. Takng nto consderaton the level of rregular economy the second fgure seems much more realstc. Bblography [Popov, 988] E. V. Popov Expert systems. M.: Nauka, p [Popov, 988] E. V. Popov, I. B. Fomnykn, E. B. Ksel. Statstc and dynamc expert systems: Educatonal materal M.: Fnance and statstcs, p. [Ivchenko, 984] G. I. Ivchenko, I. Medvedev. Mathematcal statstcs/ M.: Publshng House Vysshaya Shkola, p. [Seder, 980] J. Seber. Lnear regressve analyss. M.: Mr, p. [Voloshn, 999] A. F. Voloshyn, M. B. Panchenko, E. P. Pkhotnk. The expert system of supportng the prognosng hrvna exchange rate Artfcal ntellect Pp [Ushakov, 979] I. A. Ushakov the tasks of optmal reservng. M.: Znanye, p. [Tsurkov, 98] U. I. Tsurkov Decomposton n great demensons sums M.: Scence, 98. 5p. [Koseletskyy, 979] Yu. P. Koseleletskyy. Psychologcal theory of makng decsons. M.: Progress, p. [Gladun, 987] V. P. Gladun Decson Plannng. Kev: Naukova dumka, p. [Zagoruko, 999] N. G. Zagoruko. The appled methods of analyzng data and Knowledge. Novosbrsk: Publ. House NM SB RAN. Authors' Informaton Voloshyn Alexe Fodorovch Kev Natonal Unversty "Taras Shevchenko", Faculty of Cybernetcs, professor, Kev, Ukrane; e-mal: Satyr Vktora Valervna Kev Natonal Unversty "Taras Shevchenko"; Faculty Cybernetcs, master of scences, Kev, Ukrane; e-mal: vcsatr@hotmal.com SYNERGETIC METHODS OF COMPLEXATION IN DECISION MAKING PROBLEMS Albert Voronn, Yury Mkheev Abstract. Synergetc methods of data complexaton are proposed that make t possble to obtan a maxmal amount of avalable nformaton usng a lmted number of channels. Along wth freedom degrees reducers, a mechansm of freedom degrees dscrmnators s proposed that enables all the channels to take part n the development of a cooperatve decson n accordance wth ther nformatveness n a current stuaton. Keywords: Synergetcs, data complexaton, nformaton channels, decson makng Introducton In advanced nformaton systems, nformaton on the same obect (a process or an event) s usually transmtted over several channels. The problem les n determnng the channels over whch more sgnfcant data are transmtted. Dependng on ths, t s requred to combne (ntegrate) obtaned data to develop a cooperatve decson on the state of an obect.