FUZZY-NEURO SYSTEM FOR DECISION-MAKING IN MANAGEMENT

Transcription

1 УДК 683:59 FUZZY-NEURO SYSTEM FOR DECISION-MAKING IN MANAGEMENT GALINA SETLAK Ths paper ntroduces a systematc approach for ntellgent decson support system desgn based on a class of neural fuzzy networks bult upon a general neuron model. The neural fuzzy networks can formally represent and process both the qualtatve (lngustc and quanttatve nformaton, whch usually descrbe a complex, multdmensonal systems or decson makng processes. Presented the results of tests and a practcal mplementaton of applcatons of fuzzy-neuro system for decsonmakng n strategc management and determnaton of product development strategy. INTRODUCTION Computer ntegrated manufacturng (CIM provdes manufacturng ndustry wth the means to produce a varety of products effcently. Effectve plannng, schedulng and control n the CIM envronment depend largely on proper desgn of the decson support system (DSS. A manufacturng system s drven by nput stmul from the market n the form of drect product demand, market condtons and feedback on producton wth a varety of nformaton perspectves. The actvtes of ths system may be broadly classfed as management (ncludng strategc plannng, desgn, producton plannng and producton operaton. Intellgent DSS have evolved as tools that attempt to support decson-makng processes n problem contexts characterzed by novelty and large search spaces. Problems wth these characterstcs are known as unstructured problems. The manageral problem doman s composed of dynamc, temporal relatonshps between varables. Solvng many problems concerned wth modern manufacturng management s connected wth processng of ncomplete, nexact nformaton. Frst of all, these problems are manly aspects of strategc management: market analyss, choce of product strategy and of manufacturng system development, choce of strategy for manufacturng arrangement, and others. To solve such tasks t s necessary to apply unstructured procedures for decson makng, whch use expermental data, sklls and human ntuton. To model and process fuzzy, lngustc or so called qualtatve nformaton fuzzy sets theory and mathematcal apparatus of fuzzy logc are used [, 2, 3, 4]. In such systems of decson makng support, the process of obtanng explanatons and nference engne operaton durng processng of fuzzy knowledge s hghly complcated. Ths paper ams at development of procedures and algorthms for applcaton of artfcal ntellgence tools to acqure and process varous types of knowledge (quanttatve, qualtatve, lngustc, fuzzy and to solve selected unstructured problems and tasks n decson support systems. The proposed envronment ntegrates technques and methods of knowledge and decson process modelng such as artfcal neural networks and fuzzy logc-based reasonng methods. In ths paper possbltes are presented of an approach whch combnes methods based on fuzzy logc and artfcal neural networks, whch results n crea- G. Setlak, ISSN System Research & Informaton Technologes, 2003,

2 Fuzzy-neuro system for decson-makng n management ton of a structure called a fuzzy neural network. The structure of a fuzzy neural network combnes the best propertes of an artfcal neural network, the ablty to learn from examples, and fuzzy logc,.e. converson of fuzzy knowledge. Combnaton of these artfcal ntellgence technologes allows creaton of comprehensve programmng tools that can be used to solve complex decson problems when ncomplete, uncertan or contradctory knowledge has to be processed or t s hard to formalze the knowledge. Fuzzy neural networks presented n ths paper are a generalzaton and expanson of classcal neural networks. These networks are able to process qualtatve and lngustc nformaton apart from quanttatve nformaton through the applcaton of the fuzzy set theory and mechansms of fuzzy decson makng. In ths paper the results of the tests and a practcal mplementaton of applcatons for decson support systems based on fuzzy neural networks used for strategc management and determnaton of product development strategy wll be presented. CLASSICAL ARTIFICIAL NEURAL NETWORK The orgnal source of fuzzy neural networks s a multlayer perceptron, whch s a feedforward neural network characterzed by transferrng of nformaton from the nput level through K addtonal hdden layers to the output layer. Fg. presents the structure of a two-layer perceptron,.e. a perceptron wth one addtonal (hdden layer. In the standard structure of a multlayer perceptron each -th node n k -th layer s connected through synaptc weghts W j wth all the nodes of the prevous layer ( k. Y Y 2 Y... Y n Output layer W W 2 W N W nn Y Y 2 Y Y N Hdden layer W W 2 Wn W Nn X X 2... X n Input layer Fg.. Model of multlayer perceptron [2] Output sgnals are calculated as follows: Системні дослідження та інформаційні технології, 2003, 73

3 G. Setlak N Y = f W j= j x j θ j for hdden layer neurons, ( Y N = f Wj Y j θ j for output layer neurons, (2 j= N where W j, W j synaptc weghts; f W j x j actvaton functon; j= θ j, θ j shft values; x j ( j =,2,..., N nput sgnals. In hdden perceptron layers transformaton of nonlnear nformaton takes place. For processng of non-lnearty n the hdden layers sgmod functon s often used, whch can be descrbed as follows: f ( α =. (3 α + e In practce, the man Back-Propagaton algorthm, as well as ts dfferent modfcatons, s used for tranng neural networks of the multlayer perceptron type [4, 5]. Detals of the network tranng process wll be presented n the further part of ths paper concerned wth fuzzy neural networks, whch s the object of the research. MODEL OF A FUZZY NEURAL NETWORK Let us consder a system wth n nputs: x, x2,..., xn ( x X, =,2,..., n and m outputs: y, y 2,..., y m ( y j Y j, j =,2,..., m, respectvely, where x = T ( x, x2,..., xn X X 2 X n =... and y j Y j are lngustc varables. Qualtatve nformaton, whch descrbes the behavor of ths system, s presented as a number of K fuzzy IF THEN rules n the followng form: IF x s A and ( x s A and and ( x n s A ( 2 2 n ( y s B and ( y2 s B2 and and ( y m s Bm THEN and and IF x s A and ( x s A and and ( x s A ( k 2 2k n nk ( y s Bk and ( y2 s B2 k and and ( ym s Bmk THEN (4 where A k, B jk, ( =,2,..., n, ( j =,2,..., m and ( k =,2,..., K are certan lngustc notons whch descrbe approprate system nputs and outputs. A k and B jk are fuzzy sets, where Ak R ( X and B jk R ( Y j and R ( X and R ( Y j mean clusters of all fuzzy sets whch are determned on the sets X and Y j respectvely. 74 ISSN System Research & Informaton Technologes, 2003,

4 Fuzzy-neuro system for decson-makng n management Quanttatve nformaton that descrbes the behavor of the system may be presented as a number of L sets wth numercal data of the followng type: ( x l, x 2l,..., x nl, y l, y 2 l,..., yml, where l =,2,..., L, and ( xl X, ( y jl Y j (y jl Y j. Quanttatve nformaton may also be presented as a system of L condtonal rules n the followng form: IF x = x and and ( x n = x THEN ( n ( y y and and ( yn = yn l =,2,..., = L. (5 The methodology of processng the above-presented nformaton (.e. qualtatve, quanttatve, and mxed s based on the applcaton of a fuzzy neural network. In accordance wth the man dea the detals of whch are presented n papers [, 3], all types of the nput nformaton are as f «bult nto» the structure of a fuzzy neural network durng the process of network tranng. Another mportant task s development of the nference engne, whch wll be able to generate responses of the system to the types of nput data determned above. Fuzzy nput data Determnaton of membershp functons Fuzzy rule base Fuzzy nference engne Interface for processng of output data MULTILAYER PERCEPTION Determnaton of outputs for fuzzy set Fuzzyfcaton Output fuzzy sets y,..., y m Y m Algorthm of correcton Fg. 2. Concepton of fuzzy neural system These problems accordng to the approach presented are solved n the followng way: the nput nformaton and the correspondng output nformaton s processed by means of two nterfaces, whch are developed on the bass of the fuzzy sets theory and fuzzy logc. These nterfaces have the same structure. Man concepton for processng of nput and output fuzzy nformaton may be presented by executng of such operatons n the followng sequence (Fg. 2. The task of the nterfaces s transformaton of the nput nformaton to the form allowng for classcal neural network processng. For performng ths task, let us determne the followng notons from the theory of fuzzy logc and fuzzy decson-makng [4, 5]. Системні дослідження та інформаційні технології, 2003, 75

5 G. Setlak Membershp functon s a functon whch assgns a degree of membershp (mostly, n the nterval [0, ] to the fuzzy set: µ A ( x, µ A ( x. k Assumng that A A2 An A k A2 k Ank = A and B B2 Bm B k B2 k Bmk = B, the fuzzy rules (4 and (5 can be nterpreted by the product-operaton rule of fuzzy mplcaton: µ A B x, y = µ A ( x µ A ( y. (6 ( j j Each fuzzy set A R x can be descrbed by means of prmary fuzzy ( sets ncluded n the set χ, and also wth the use of compatblty measure of two fuzzy sets A and A k : { mn [ µ ( x, µ ( x ]} π ( A, Ak = sup A A x X k, k,2,...,a =. (7 If the nput data s quanttatve x X, then they are descrbed by the membershp functon µ x ( x =, f x = x and µ x ( x = 0, f x x (so called fuzzy sngleton. Subsequently, the compatblty measure s used: { mn [ µ ( x, µ ( x ]} = µ ( x π ( x, Ak = sup x A A. (8 x X Let us transform the output data n the same way too, by means of prmary fuzzy sets, the membershp functon, and fuzzy logc. Let j be the number of output Y and, respectvely, fuzzy sets 0 j Y j C F ( ( v } k, jk a, whch s determned by the composton «measure of actvaton» { = and composton prmary fuzzy sets n the followng form: 0 µ c j ( y j = max { mn[ µ B ( y j, v j] mn [ µ B ( y j, v 2 ] j k j j2 j k mn [ µ B jk ( y j, v jk ]}, j =,2,..., m. (9 NEURAL NETWORK TRAINING A multlayer perceptron s subjected to the process of tranng,.e. a classcal neural network, whch s a component of the fuzzy neural network model descrbed above. For other research [2, 3, 5, 6], the Back Propagaton algorthm and ts modfcatons are used for tranng of ths neural network. As t has been known, the above-presented algorthm for network tranng does not guarantee the obtanng of global mnmum for qualty evaluaton (for error. Nevertheless, n research on solvng a number of practcal tasks, t s possble to obtan a very 76 ISSN System Research & Informaton Technologes, 2003,

6 Fuzzy-neuro system for decson-makng n management exact approxmaton of the tranng data, whle the tranng process s takng place, by executon of calculatons for varous parameter values (η, α and, what s most mportant the quantty of neurons n the hdden layer N, after whch the optmal varant s chosen. Consequently, a concluson may be drawn that for solvng of a number of practcal tasks, the obtanng of global mnmum for qualty evaluaton s not a necessary and ndspensable condton of recevng satsfactory results. To avod the problem referred to above, n ths paper research on the use of genetc algorthms s carred out for solvng the task of neural network tranng, and also for determnaton of the optmal topologcal network structure. AN EXAMPLE OF A APPLICATION OF A INTELLIGENT DECISION SUPPORT SYSTEM The fuzzy neural network presented above has been used for development of an ntellgent decson support system. The decson support system has been appled to select a product strategy n the area of household equpment. In ths paper, the selecton method of market-assortment-strategy has been appled for the choce of the product development strategy. For development of the market-assortment-strategy basc notons of the Busness Portfolo Models have been appled. Busness Portfolo Models are tools for product classfcaton used for determnaton of a compettve poston of a busness on the market, and assessment of the market possbltes. In ths paper one of the most popular GE (General Electrc methods s appled, otherwse called the GE s Multfactor Portfolo Matrx. Ths approach has a varety of names, ncludng the nne-cell GE matrx, GE s nne-cell busness portfolo matrx, and the market attractveness-busness strength matrx [8]. The basc approach s shown n Fg. 3. Industry Attractveness Hgh Medum 2 Low Busness Strength Hgh Medum Low I I S I S H S H H Fg. 3. GE Multfactor Portfolo Matrx [8] Each crcle n ths matrx represents the entre market and the shaded porton represents the organzaton s busness market share. Each of an organzaton s busnesses s plotted n the matrx on two dmensons, ndustry attractveness and busness strength. Each of these two major dmensons s a composte measure of a varety of factors. The two dmensons make good sense for strategy formulaton, because a successful busness s Системні дослідження та інформаційні технології, 2003, 77

7 G. Setlak typcally one that s an attractve ndustry and has a partcular busness strength requred for succeedng n t. To use ths approach, an organzaton must determne what factors are most crtcal for defnng ndustry attractveness and busness strength. In ths paper a lst of the factors that are commonly used for placng busnesses on the aforesad dmensons has been used, whch s presented n [8]. Dependng on where busnesses are plotted on the matrx, three basc strateges are formulated: I nvest/grow, S Selectve nvestment and H Harvest/dvest. The next step s to wegh each varable on the bass of ts perceved mportance relatve to the other factors (hence the total of the weghts must be,0. Subsequently, a fuzzy-neural system must ndcate, on a scale of to 5, how low or hgh the busness scores on that factor. Table presents ths analyss for one busness. Table. Illustraton of Industry Attractveness and Busness Strength Computatons (source [8] Industry Attractveness Overall market sze Annual market growth rate Hstorcal proft margn Compettve ntensty Technologcal requrements Inflatonary vulnerablty Energy requrements Envronmental mpact Socal/poltcal /legal Weght Value Busness strength Weght Value 0,20 0,8 Market share 0,0 0,40 0,20,0 Share growth 0,5 0,60 0,5 0,6 Product qualty 0,5 0,60 0,5 0,45 Brand reputaton 0,0 0,50 0,5 0,45 0,05 0,0 0,05 0,5 0,05 0,05 Must be acceptable Dstrbuton network Promotonal effectveness Productve capasty Productve effecency 0,05 0,20 0,05 0,25 0,05 0,5 0,05 0,0 Unt costs 0,5 0,45,00 3,60 Materal supples 0,05 0,25 R&D performance 0,0 0,40 Manageral personel 0,05 0,20,00 4,30 Performance of a fuzzy neural expert system has been tested on the followng nput data: N = 22 number neurons n nput layer; L = 68 rules. Fuzzyfcaton wth 3 lngustc varables K = 3 has been appled to the system (Fg ISSN System Research & Informaton Technologes, 2003,

8 Fuzzy-neuro system for decson-makng n management Number neurons n hdden layer: 0, 5, 25, 30, 35 (Fg.5. Number neurons n output layer: 3. The fuzzy set defned n R ( X s characterzed by a membershp functon µ ( : R [0,], and s labeled by a lngustc term A k, such as B jk y j µ 0,5 µ B3 µ B «hgh», «medum», «low» (ndustry attractveness and busness strength. The membershp functon for the fuzzy set nputs, s shown n Fg. 4. Fuzzy set conformty metrcs (or actvaton levels n other words are nputs to the neural network, accordng to (7 (8 formulas. Next, they are processed by the neural network and compared to the requred actvaton levels for outputs. A fuzzy neural network accepts both quanttatve and qualtatve nformaton n the learnng data set. Qualtatve nformaton s represented by the fuzzy set apparatus n the form of an approprate set of membershp functons for each lngustc varable. In the case of the generaton of quanttatve output data, defuzzyfcaton s carred out wth the use of the center average method: y m 0 j= j = m j= y µ µ B j B j ( y. (0 ( y Durng the system testng, mean absolute error was used as a crteron of qualty evaluaton and the assessment of the system, whch for the tranng data assumes the form: Q = PM P M p= l= ( d µ B3 Fg. 4. Membershp functon for the nputs fuzzy set p l Y v p 2 l, p =,2,..., P. ( Another such crteron of system assessment wth respect both to the tranng and testng data s the maxmum system error Q, defned as follows: B max Q Bmax = p P L= = 0,2,,...,,..., M max d p l v p l. (2 The structure of the neural network, namely the number of addtonal layers and quantty of neurons n an addtonal layer, has been chosen expermentally. The structures wth one, two and three addtonal layers have been evaluated. A neural network wth one addtonal layer and non-lnear sgmodal actvaton Системні дослідження та інформаційні технології, 2003, 79

9 G. Setlak functon returns as good results as does a network wth two addtonal layers. A neural network wth more addtonal layers requres large amount of tranng data n order to learn effectvely. It s not necessary then to extend the network structure as t leads to ncreased quantty of data and learnng tme. That s why ths paper presents the results for the neural network wth one addtonal layer and wth a layer wth varous quanttes of neurons. All experments have been run wth varous quantty of neurons n the addtonal layer (N. The results of smulaton researches are shown on Fg.5. Ths very mportant problem has been wdely dscussed n the lterature. The present research just confrm the opnon that the neural network wth one addtonal layer and wth non-lnear sgmodal actvaton functon s able to approxmate any functon, practcally, wth requred accuracy. Q mn 0,04 0,03 0,02 0,0 N Fg. 5. Results of tranng phase for fuzzy neural network The tranng data are prepared for a specfc decson problem on the bass of data receved from an expert (strategc management dvson. The data form a set of fuzzy rules for preparng a Multfactor Portfolo Matrx. CONCLUSIONS The paper uses fuzzy neural networks to model and process fuzzy, lngustc or mxed knowledge. The developed programmng modules provde user nterfaces that (based on fuzzy logc theores allow converson of the nput nformaton nto numerc form and subsequent processng by a classc neural network. On the bass of the results t may be supposed that fuzzy neural networks are a more unversal theoretcal nstrument, whch can be used for complex processes modelng and for developng ntellgent decson support systems, characterzed by the ablty to process quanttatve, as well as qualtatve, and lngustc nformaton, and thus to solve unstructured tasks n a fuzzy envronment. Fuzzy neural network models show very good features for nterpolaton and extrapolaton of tranng data used durng the tranng process. The research conducted proves that fuzzy neural networks are a very effectve and useful nstrument of mplementaton of ntellgent manageral systems. REFERENCES. Gorczałczany M. Fuzzy neural networks n expert systems and n process modelng, (n pol.. Kelce: p. 80 ISSN System Research & Informaton Technologes, 2003,

10 Fuzzy-neuro system for decson-makng n management 2. Brown M., Harrs C. Neurofuzzy adaptve modellng and control. Prentce Hall, New York p. 3. Buckley J.J., Hayash Y. Fuzzy neural networks: A survey, Fuzzy Sets and Systems, P. l Hayash Y., Buckley J.J., Czogala E. Fuzzy neural networks wth fuzzy sgnals and weghts. Internatonal Journal of Intellgent Systems N 8. P Zadeh L.A. Fuzzy sets as a bass for a theory of possblty. Fuzry sets and Systems N l. P Masters T. Practcal neural network recpes n C++. New York: Academc Press P Rutkowska D. Intelgentne systemy oblczenowe. Warszawa: Akademcka Ofcyna Wydawncza PLJ P Schaffer J.D., Whtley L. Eshelman J. Combnatons of genetc algorthms and neural networks: A Survey of the State of the Art., Proceed. of Internatonal Workshop «Combnatons of Genetc Algorthms and Neural Networks», COGANN P Certo C. Samuel, Peter J. Paul. Strategc management. New York: Random House, Inc p. Receved Системні дослідження та інформаційні технології, 2003, 8