IE Paper Template Informatica Economică vol. 14, no. 3/2010 199 Multicriterial Methods used in Expert Systems for Business Decision Making Cornelia MUNTEAN, Mihaela I. MUNTEAN West University of Timisoara, Romania cornelia.muntean@feaa.uvt.ro, mihaela.muntean@feaa.uvt.ro Many organizations are in front of most competitive economic environments, where, in order to survive, they must reduce costs all the time and adopt the most intelligent business strate- gies. In most decision making activities the manager has to decide which variant is the most advantageous, taking into account a multitude of criterions. Expert systems use the expert's knowledge and problem solving skills in a particular subject area throughout an organiza- tion, and can propose the optimal variant to be chosen. In this paper we have outlined the role of multicriterial methods in programming expert systems to decide in favor of the most eligible variant between a multitude of possibilities. We also made a case study and designed the prototype of an expert system for choosing the most profitable offer among many, in the prenegotiation stage, for a company, in order to organize the negotiation processes accor- dingly. In this respect, we tried to highlight the usefulness of multicriterial mathematical me- thods in three negotiation processes of a Romanian negotiation team with foreign negotiation teams for the acquisition of an equipment. Keywords: Business Decision Making, Expert Systems, Multicriterial Methods Introduction Today’s decisions are complex, combin- ing hard facts with experts’ intuition. Rapid business decision-making often requires col- laboration across time zones, organizations and cultural norms. In the field of business decision support, more and more recent research [1] has been concentrating on the human side of the per- son-technology relation in decision making. It has been shown in many works that busi- ness decision making environment is a unity of decision makers’ experience, beliefs and perceptions on one side, and decision support tools and techniques – on the other side. The information environment surrounding busi- ness activities and decisions is getting increa- singly complex due to growing volumes of information of potential relevance to certain business activities [2]. An Expert System (ES) is a knowledge-based computer program containing expert domain knowledge about objects, events, situations and courses of action, which emulates the process of human experts in the particular domain. For long term use, a knowledge base stores rules, facts and other knowledge struc- tures, much as a database stores data. When the ES is used, an inference engine processes the knowledge structures, bringing problem specific information into the system, and makes recommendations to the user based on the information and knowledge structures available [3]. After making a recommendation, users rou- tinely view the decision making logic used by the ES. Since the system remembers its logical chain of reasoning, a user may ask for an explanation of a recommendation and the system will display the factors it considered in providing a particular recommendation. This main attribute, the ability to explain rea- soning, enhances user confidence in the rec- ommendation and acceptance of the ES. Some expert systems are designed to take the place of human experts while others are de- signed to aid them. In negociation, as well as in most other cir- cumstances, people must take a decision from a multitude of possible decisions, in or- der to achieve a certain goal. It is perfectly normal for human reasoning to analyse and to compare the possibilities, in order to adopt that decision which permits the best fulfil- ment of the desired goal. Although we fre- quently use the term "optimal decision", in 1 200 Informatica Economică vol. 14, no. 3/2010 most situations this "optimality" is a very complex concept which can't be defined but by mean of a mathematical model. In our case study we will use three multicriterial methods, implemented in an expert system designed in Exsys Corvid. Corvid provides an object-oriented structure that makes it easy to build systems using me- thods and properties of variables, while not requiring the developer to change the way they think and describe their decision-making steps and logic. The result is a very flexible and powerful development environment that can easily be learned. We used Corvid for implementing our application presented in paragraph 3. 2 Multicriterial Methods. Business Deci- sion Making Theoretical Approaches Mathematical models appeared and were used in the process of decision making in business, particularly in negociation, quite from the necessity to sustain the logical rea- soning in negociation and to manage a great number of factors simultaneously. Furthermore, the applying of these mathe- matical methods grants the approach of some new qualitative problems, so that it is not at all surprising the fact that in negociation as well there are used more and more mathe- matical tools, techiques and models. The process of decision-making is defined by following elements [4]: the decision-maker, the assemblage of decision alternatives, the assemblage of decision criterions, the assem- blage of goals. The decision-maker is the person who must select the most advantageous variant from a multitude of possible ones, variant called the optimum choice. The assemblage of decision alternatives, V, is the assemblage of action possibilities at a given moment. The assemblage of decision criterions, C, is the assemblage of parameters which defines the process and in respect of which we have in view the comparison of alternatives. The decision criterions are characterized by a number of levels according to the different alternatives and/or status of unbiased condi- tions. All these levels can make up decision goals that are possible to achieve, from the point of view of that particular criterion. Decision models with an assemblage of crite- rions, called also multicriterial decision mod- els, could be multi-attribute decision models, which are presented below, or multi- objective decision models, which are subject of linear programming [5]. Multi-attribute decision models subsist in the determination of the optimum variant from a finite variant assemblage V={V1, V2, ...,Vm}, variants that are compared one with another in respect with numerical or non-numerical criterions belonging to a finite assemblage C={ C1, C2, ...,Cn}. Each criterion has a min- imum or maximum goal. For some multi-attribute decision problems, in which the matrix of consequences contains heterogeneous data, numerical or non- numerical, the homogenization of these data is done by the normalization procedure [6], which transforms the matrix of consequences in a matrix R=(rij)i=1,m; j=1,n} with elements in the interval [0,1]. In almost all multi-attribute decision prob- lems there is information regarding the im- portance of each criterion. This is generally expressed by the vector P={p1, p2, ..., pn} and indicates the level of importance given by the decision-maker to each criterion. rij =          ≤≤ ≤≤ criterionsfor a a criterionsfor a a ij ij mi ij mi ij min, min max, max 1 1 (1) Every multi-attribute decision problem could be expressed by a matrix A, called the matrix of consequences (Table 1), with elements aij indicating the evaluation (consequence) of Informatica Economică vol. 14, no. 3/2010 201 variant i, i=1, 2, ..., m (Vi), by criterion j, j=1, 2, ..., n, (Cj). Table 1. The matrix of consequences Ci Vj C1 ... Cn V1 a11 ... a1n ... ... ... ... Vm am1 ... amn P p1 ... pn Source: [5] Multi-attribute decision problems could be classified into three categories [7]: direct me- thods, indirect methods and methods which use a certain distance for the construction of hierarchies. Direct methods build a function defined on the assemblage of variants with real values and selects variants for which the function takes the greatest value. Indirect methods determine a hierarchy on the assemblage of variants based on an algo- rithm. Methods which use the distance select a va- riant which is the closest to the ideal solution. In our case study we will use a direct method (the method of simple additive weight) and a method which uses the distance (TOPSIS), methods that are presented below: The method of simple additive weight The method consists in defining the function f : V→R, given by: f(Vi) = mi p rp n j j n j ijj ,1, 1 1 = ∑ ∑ = = (2) where rij are the elements of the normalized matrix R, calculated with relation (1) and pj are the elements of the importance rates vec- tor P, given as last row in Table 1. The opti- mum variant will be that for which f(Vi) takes the maximum value. The TOPSIS method The TOPSIS method (Technique for Order Preference by Similarity to Ideal Solution) is based on the idea that the optimum variant must have the minimum distance to the ideal solution. The steps of the TOPSIS method are: • Step 1. We build the normalized matrix R=(rij), i=1,...,m, j=1,...,n; • Step 2. We build the weighted normalized matrix V=(vij), i=1,...,m, j=1,...,n, where vij = ∑ = n j j ijj p rp 1 (3) • Step 3. We calculate the ideal solution A and the ideal negative solution B, defined as: A= (a1, a2, ..., an), B= (b1, b2, ..., bn) (4) where: aj =     ≤≤ ≤≤ min,min max,max 1 1 isCcriteriontheifv isCcriteriontheifv jijmi jij mi (5) bj =     ≤≤ ≤≤ max,min min,max 1 1 isCcriteriontheifv isCcriteriontheifv jijmi jij mi (6) • Step 4. We calculate the distance between the solutions: Si = ( )∑ = − n j ij ajv 1 2 , i = 1, 2, … ,m; (7) Ti = ( )∑ = − n j jij bv 1 2 , i = 1, 2, ... , m; (8) • Step 5. We calculate the relative nearness from the ideal solution: Ci = ii i TS T + (9) • Step 6. We make a classification on the assemblage V according to the descending values of Ci obtained in step 5. 202 Informatica Economică vol. 14, no. 3/2010 3 Multicriterial Methods. Case Study The case study in this paper wants to mark out the role of mathematical methods imple- mented in an expert system for the stage of preparation in an international negotiation process. For that purpose we tried to highlight the usefulness of multicriterial methods in three business negotiation processes of a same Romanian negotiation team with three other international negotiation teams in order to purchase an industrial equipment. In order to achieve the chased goal we made a case study at S.C. Chimcomplex S.A., us- ing the two multicriterial methods presented in paragraph 2 (the method of simple additive weight and the TOPSIS method) for select- ing, in the stage of prenegotiation, the best offer and for organizing the negotiation processes thereafter. Chimcomplex will have to decide between three offers of three for- eign companies, taking into account eight se- lection criterions:  C1 : the account of the good that has to be purchased (million Euro);  C2 : requested advance money (%);  C3 : time period allowed for the payments (years);  C4 : payment staggering (month);  C5 : rate of interest (%);  C6 : time of delivery of the equipment (month);  C7 :guarantee period (years);  C8 : offer validity (month). The following three offers of three foreign companies will be approached further as po- tential variants of the Romanian company Chimcomplex S.A:  the offer of Vichem Company, from France – variant 1 (V1);  the offer of Michelis Company, from Germany – variant 2 (V2);  the offer of Itochu Corporation, from Ja- pan – variant 3 (V3) The Romanian company Chimcomplex S.A. confers to each invoked criterion a specific rate of importance on a scale from 1 to 10 (rate 10 for the most important criterion and 1 for the lowest importance criterion). So the importance rates are: For C1 : 10; for C2 : 9; for C3 : 8; for C4 : 6; for C5 : 6; for C6 : 5; for C7 : 4; for C8 : 3. In following table are presented the offers of the three companies according to the crite- rions invoked by Chimcomplex S.A and the importance rates given by the Romanian ne- gotiation team (Table 2). Table 2. The characteristics of the variants according to the criterions and the impor- tance rates for each of the criterions C1 Mil.Euro C2 % C3 years C4 Month C5 % C6 month C7 years C8 Month V1 5 10 7 6 7,5 1 1 2 V2 4,75 11 6 12 7 2 2 1 V3 5,25 9 5 5 6,5 1,5 1,5 1,5 P 10 9 8 6 6 5 4 3 For doing all calculations more quickly, we used the expert system generator Corvid, and put all entrance data into an input files, con- taining the characteristics of each variant in respect to each criterion and the importance rates of the eight criterions. Further we will apply, using Corvid va- riables, the two mathematical methods de- scribed in paragraph 2 (the method of simple additive weight and the TOPSIS method) for deriving the best variant between the three offers for the Romanian company. Finally we will compare the results obtained with the two methods. Considering that the matrix in Figure 1 con- tains heterogeneous data, there will be neces- sary a normalization procedure. This occurs by minimization for C1, C2, C5, C6 and by maximization for C3, C4, C7, C8. For the max- imum and minimum criterions we used rela- Informatica Economică vol. 14, no. 3/2010 203 tion (1) and calculated the elements of the normalized matrix R=(rij) with i= ;3,1 j= 8,1 , like in Figure1. Fig. 1. Determination of the normalized matrix in a Corvid logic block. Next, for applying the simple additive weight method, we calculate the values for the func- tions f(Vi) using relation (2), like in Figure 2. Fig. 2. Determination of fV1, fV2 and fV3 for classifying the variants with the simple addi- tive weight method We obtain following results: → fV1 = 0,85882 → fV2 = 0,85867 → fV3 = 0,80088 According to this method, the order of the variants is: V1 → V2 → V3, like in figure 3. It is easy to observe that the values for the variants 1 and 2 are very close (they differ only at the forth decimal), so we can con- clude that this method is unconvincing, and it can't help much in selecting the optimal va- riant. Next we apply the TOPSIS method. Here we also need the normalized matrix R=(rij), i=1,...,m, j=1,...,n and then we build the weighted normalized matrix V=(vij), i=1,...,m, j=1,...,n, using relation (3). Thereaf- ter we calculate the ideal solution A and the ideal negative solution B, like in Figure 4. 204 Informatica Economică vol. 14, no. 3/2010 Fig. 3: Results calculated by the Expert System with the simple additive weight method After calculating the distance between the so- lution and the ideal solution with relation (7) and the distance between the solution and the ideal negative solution with relation (8), we determine the relative nearness from the ideal solution Ci, with i= 3,1 using relation (9) and we obtain: →C1= 0.407 →C2= 0.706 →C3= 0.323. Fig. 4. Part of the logic block calculating the ideal solution A and the ideal negative solution B We make a classification on the assemblage V according to the descending values of Ci , and we obtain following order of variants: V2 → V1 → V3 , like in figure 5, a little different from the simple additive weight method, where the order was V1 → V2 → V3., but the function value for V1 was very close to that of V2. Fig. 5. Results calculated by the Expert System with the TOPSIS method 4 Conclusions For some business negotiations the stakes are much too high to be lost. That's why it is de- sired to select and to apply the most efficient strategy which could grant the winning of the negotiation. In this respect it is useful to call on mathematical methods for identifying the best variants for overcoming a deadlock by anticipating the movements of the partner. Sometimes there are situations in which the negotiators must choose from a multitude of variants, must make a hierarchy and select the optimal offer. In such cases the most ap- propriate tool are multicriterial methods. The purpose of this paper was to relieve the usefulness and importance of multicriterial Informatica Economică vol. 14, no. 3/2010 205 methods in an expert system used for the preparation stage of an international business negotiation process. Of course, there are also important cultural accents of the negotiators of different countries, which could also be in- troduced into the expert system program [8]. While applying two different methods. the method of additive weight and the TOPSIS method, the results were nearly the same, so the decision-maker could select the most profitable offer among many in the prenegot- iation stage, in order to organize the negotia- tion processes accordingly. The expert sys- tem used the input data as a text file and cal- culated, using Corvid variables, the functions that indicate the proposed order of variants, accordingly to each of the two different me- thods. Acknowledgments This work was supported by ANCS-CNMP, project number PNII–91-049/2007 References [1] B. Pradeep Kumar, J. Selvam, V. S. Mee- nakshi, K. Kanthi, A. L. Suseela and V. Lalith Kumar, Business Decision Mak- ing, Management and Information Tech- nology, Available at: http://www.acm.org/ubiquity/views/pf/v 8i08_lalith.pdf, 2007. [2] C. Muntean and I. Hauer, “Improving the management in organizations by using Expert Systems,” Simpozion Ştiinţific Internaţional „Managementul dezvoltării rurale durabile”, Timişoara, 2010. [3] C. Muntean, A. Butuza and O. Dobrican, Sisteme expert. Elemente de teorie şi aplicaţii, Timisoara: Ed. Mirton, 2007. [4] M. Gheorghiţă, Modelarea şi simularea proceselor economice, Bucureşti: Ed. ASE, 2001. [5] M. Andraşiu, A. Baciu, A. Pascu, E. Puşcaş and A. Taşnadi, Metode de deci- zii multicriteriale, Bucureşti: Ed. Tehnică, 1986. [6] M. Neamţu and D. Opriş, Jocuri econo- mice. Dinamică economică discretă. Aplicaţii, Timişoara: Ed. Mirton, 2008. [7] G. Ionescu, E. Cazan and A.L. Negruţ, Modelarea şi optimizarea deciziilor ma- nageriale, Cluj – Napoca: Ed. Dacia, 2000. [8] C. Vasiliu, Tehnici de negociere şi comunicare în afaceri, Bucureşti: Ed. ASE, 2003. Cornelia L. MUNTEAN has graduated the Faculty of Computer Science at the „Politehnica” University of Timişoara in 1986. She holds a PhD diploma in Engineering and is currently assistant professor at the department of Busi- ness Information Systems and Statistics at the West University of Timişoara. She joined the staff of the Faculty of Economics and Business Administra- tion of the West University of Timisoara in 1991 as a teaching assistant, then graduated in 1997 as a senior lecturer and in 2005 as an assistant professor. She is the author of 7 books and about 50 journal articles in the field of artificial intelligence and intelligent systems. Her work focuses on expert systems and business applications in de- cision support. Mihaela I. MUNTEAN has graduated from the Faculty of Computer Science, „Politehnica” University of Timisoara in 1986. Currently, professor Mihaela I. Muntean is the chair of the Business Information Systems and Sta- tistics Department at the West University of Timişoara and an IT independent consultant. She is interested in information technology and knowledge man- agement, her research activity results are published in over 70 papers in in- dexed reviews and conference proceedings. Now, she is teaching advances in database management systems, business intelligence, decision support systems, bringing im- portant contribution to the foundation of higher education in Economic Informatics within the Faculty of Economics and Business Administration Timişoara. http://www.biblioteca.ase.ro/catalog/detalii.php?c=2&q=curry&st=s&dela=0&ct=108788� http://www.biblioteca.ase.ro/catalog/detalii.php?c=2&q=curry&st=s&dela=0&ct=108788�