annals of the university of petroÅani â¼ economics â¼ vol. xi - part i ...

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156 Muntean, C.; Hauer, I.; Butuza, A. The hierarchy of variants is given by the descending values of the aggregation function (Aggr). 2.5. 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=(r ij ), i=1,...,m, j=1,...,n; - Step 2. We build the weighted normalized matrix V=(v ij ), i=1,...,m, j=1,...,n, where v ij = p n ∑ j j = 1 r ij p j (8) Step 3. We calculate the ideal solution A and the ideal negative solution B, defined as: A= (a 1 , a 2 , ..., a n ), B= (b 1 , b 2 , ..., b n ) where: ⎪⎧ max vij , if the criterion C j is max a j = 1≤i≤m ⎨ (9) min vij , if the criterion C j is min ⎪⎩ 1≤i≤m ⎪⎧ max vij , if the criterionC j is min b j = 1≤i≤m ⎨ (10) min vij , if the criterionC j is max ⎪⎩ 1≤i≤m Step 4. We calculate the distance between the solutions: n S i = ∑ ( v ij − aj ) j = 1 2 , i = 1, 2, … ,m; (11) n T i = 2 ∑ ( v ij − b j ) , i = 1, 2, ... , m; (12) j = 1 Step 5. We calculate the relative nearness from the ideal solution: Ci = S i T i + T i (13) Step 6. We make a classification on the assemblage V according to the descending values of C i obtained in step 5.
3. CASE STUDY Decisions in Negotiations Using Expert Systems and … 157 The case study in this paper wants to mark out the role of mathematical methods implemented in an expert system for the stage of preparation in an international negotiation process. An Expert System (Andone I., Mockler R., 2001) 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 structures, 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. Exsys Corvid (www.exsys.com) provides an object-oriented structure that makes it easy to build expert systems using methods and properties of variables, while not requiring the developer to change the way they think and describe their decisionmaking steps and logic (Muntean, Butuza, Dobrican 2002). The result is a very flexible and powerful development environment that can easily be learned. We used Corvid for implementing our application. We considered the Romanian textile company IASITEX S.A. and used the three multi-attribute methods presented in paragraph 2 (the method of simple additive weight, the diameter method, the TOPSIS method) for selecting, in the stage of prenegotiation, of the best offer and for organizing the negotiation processes thereafter. After an initial stage of commercial tender, Iasitex S.A. will have to decide between two offers of two foreign companies, taking into account six selection criterions: • C 1 : the account of the good that has to be purchased (million Euro); • C 2 : requested advance money (%); • C 3 : time period allowed for the payments (years); • C 4 : payment staggering (month); • C 5 : guarantee period (years); • C 6 : offer validity (month). The following two offers of two foreign companies will be approached further as potential variants of the Romanian company Iasitex S.A: • the offer of VAKONA GmbH, from Germany – variant 1 (V 1 ); • the offer of Hashima Co., Ltd., from Japan – variant 2 (V 2 ) In following table are presented the offers of the two companies according to the criteria invoked by Iasitex S.A. Table 2. The characteristics of the variants according to the criteria C 1 Mil.Euro C 2 % C 3 years C 4 month C 5 years C 6 month V 1 10 10 3 12 2 1 V 2 8 15 2 6 3 2
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