MATEUSZ PIWOWARSKI Wydział Informatyki Politechnika Szczeciska
Summary
The article presents a method for the selection of didactic personnel for the re-alization of the individual subjects in institutions of higher education. The proposed procedure can represent a decisive mechanism possible to implement in an informa-tion system (DSS) for the support of the planning of didactic processes.
Keywords: institutions of higher education, planning didactic process, decision support system 1. Introduction
The elaboration of an attractive profile of a graduate from an institution of higher education is connected with the necessity to conduct a series of analyses with regard to the selection of contents of education programmers, the choice of didactic personnel as well as other conditions for the realization of the didactic process. Due to the complexity of this process, the heuristic approaches do not supply the “best” solutions and decisions should be sought for in formalized optimizing methods [1,2]. The tool to improve the planning of didactic processes is undoubtedly an informa-tion system of the DSS class, in which an appropriate computainforma-tional mechanism can be imple-mented in a database of models and methods [3]. One of the most important criteria that appears in the aspect of procedures for the optimizing of didactic processes is the criterion of the quality of education. An essential component in the assessment of this quality surely is the didactic person-nel, which has a considerable impact on the quality of the realization of the whole didactic process. The problem, which has to be solved, is therefore the proper selection of the personnel for the realization of the individual subjects, in order to achieve the best qualitative effects. The objective of the article is to present the methodical basis for the solution of this issue in the context of the DSS system.
2. The issue of the selection of didactic personnel
When considering the problem of the assessment of the quality of education in the context of the selection of didactic personnel the following information pools have to be taken into account: the personnel pool, the opinion pool (depending on the pool of participants in the decision process) and the character of the problem (definition of the objective of the assessment). For each decision problem l the decision situation is considered, where the final pool of decision variants (actions) A is submitted to an assessment according to n criteria g1,g2,…,gn, creating the family G={1,2, ...,n}. It can be assumed, without loss of generality, that the bigger the value of the function of the criterion gi(a), creating the family G={1,2, ...,n}. It can be assumed, without loss of generality, that the bigger the value of the function of the criterion gi, for all i∈G. In this situation, the
decision-maker, or the systems analyst, wants to isolate a minimal pool of decision variants, or construct their ranking from the best to the worst, in accordance with the established preferences.
The basis for the construction of a ranking of didactic personnel with a division into subjects is the collection of appropriate input data. The procedure, the result of which is supposed to be such a ranking, can be presented in a few steps: analysis of the realized processes, determination of the criteria for the assessment of the individual variants and formulation of the variants based on the established assessment criteria.
After the completion of the first step in this procedure, a bundle of assessment criteria has to be defined. For the purpose of the present example, a bundle of 7 criteria was defined, which make it possible to describe the process of determining quality from different points of view. In the as-sessment of the individual variants also the cost aspect has to be taken into account, as well as the assessment of the quality of the offer, for example in connection with the scientific output, the opinion of the superior or the didactic experience.
The bundle of objectives thus defined includes the following criteria: The general scientific output (points) g1 (maximization of the criterion). The scientific output within the subject taught (points) g2 (maximization). The didactic experience (points) Kg3 (maximization).
The opinion of the superior (points) g4– linguistic variable (maximization). The employment costs of the employee (zloty) g5 (minimization).
The practical experience in the subject (years) g6 (maximization).
The average monthly costs for the scientific and didactic development (zloty) g7 (minimiza-tion).
Based on an expert assessment, a collection of 15 variants was established (marked A1-A15), representing competitive possibilities for the selection of didactic personnel for the realization of individual subjects.
3. The NAIADE method in the assessment of decision variants
In essence the NAIADE method represents the possibility not to specify preferential informa-tion with a simultaneous considerainforma-tion of uncertainty and risk. The value of the alternatives with regard to the given criteria can be expressed in form of numbers, variable stochastic as well as fuzzy and linguistic numbers [4,5]. NAIADE is a discrete MCDA method (the pool of alternatives is of a final form), in which no assessment of the importance of the criteria is applied [6]. The applied technique of comparison in pairs makes it possible to achieve a final ranking of decision variants (model issue γ). The method offers two types of assessment:
an assessment of the decision variants with regard to all the criteria,
- an analysis of the conflicts between the different groups of interests [7].
The comparison of the values of the criteria occurs through the determination of the distance be-tween them.
In case of assessments of a stochastic or fuzzy character, a semantic distance is applied. For-mally, for two fuzzy numbers ( )
1 x
A
µ
and ( )2 x
A
µ
and for two defined functions ( ) ( )1 1 x k x f = µA and ( ) ( ) 2 2 y k y
g = µA , the semantic distance Sd(f(x),g(y))between the fuzzy numbers is defined as [8]:
³ ³
− =X Y
d f x g y x y f x g ydxdy
S ( ( ), ( )) | | ( ) ( ) (1)
In case of measures, the stochastics f(x) and g(y) represent the function of probability density. The expression of preferences by the decision-maker (in form of the distance between the al-ternatives) occurs through the use of six preferential relations (much better >>, better >, almost equal ≅, equal =, worse <<, much worse <). The hypotheticla form of the binary relation – much better (
µ
>>(d)) is the following [6]:° ° ¯ °° ® − + = >> >> 2 ) ) 1 2 ( 1 ( 1 0 ) ( 2 2 d c d
µ
(2)The values 0 and 1 are assumed in turn for d<0 and d≥0, whereas c>>represents the crossing point of the values (the value of the function is 0,5).
The algorithm for the aggregation is based on the determination of an intensity index of the preferences between the alternatives. The purpose of the use of the parameter α is to define the possibility to fulfil minimal requirements. The intensity index
µ
χ( ba, )of the relation χ has the form [7,9]:¦
¦
= = − − = M m m M m m b a b a b a 1 1 | ) , ( | ) 0 , ) , ( max( ) , (α
µ
α
µ
µ
χ χ χ (3) where:χ={>>, >, ≅, =,<<,<}, whereas the intensity index
µ
χ( ba, ) assumes the value1 ) , (
0≤
µ
χ ab < . The thus defined intensity index, and the entropy Hχ( ba, ) connected with it, form the basis for the determination of the degree of truth τ. In a formal solution of the case, a is better than b with regard to the majority of the criteria [8]:) , ( ) , ( ) , ( )^ , ( ) , ( )^ , ( ) , ( b a C b a C b a C b a b a C b a b a better > >> > > >> >> + + =µ µ ω (4) ) , ( 1 ) , (a b H ab Cχ = − χ (5) where: χ
C - connected level of entropy (above the index of preferences),
^ - operator (dependent on the means of modelling the effect of linear compensation) can be replaced by a minimum operator or a Zimmermana-Zynso operator.
The next stage of the method consists in the elaboration of the final ranking of alternatives, which represents an intersection of two separate rankings. The first, +(a)
Φ , is based on the rela-tion {>>, >} and assumes the values <0÷1> and determines how much “better” alternative a is compared to the others. The second, −(a)
Φ , based on the relation {<<,<} indicates how much „worse” alternative a is compared to the others. Formally, for alternative n +(a)
Φ and −(a) Φ are marked as follows [7]:
¦
¦
¦
− = > − = >> − = > > >> >> + + + = 1 1 1 1 1 1 ) , ( ) , ( )) , ( )^ , ( ) , ( )^ , ( ( ) ( N n N n N n n a C n a C n a C n a n a C n a aµ
µ
φ
(6)¦
¦
¦
− = < − = << − = < < << << − + + = 1 1 1 1 1 1 ) , ( ) , ( )) , ( )^ , ( ) , ( )^ , ( ( ) ( N n N n N n n a C n a C n a C n a n a C n a aµ
µ
φ
(7) where:N – total number of alternatives.
An analysis of the conflicts between the different groups of interests can be carried out through the construction of a similarity matrix [10]. The use of distance operators (e.g. the Min-kowski distance) is the basis for the determination of the distance between the groups [7].
4. Computation experiment
The procedure of computation is based on a matrix of criterial assessments, taking into con-sideration the bundle of 7 assessment criteria and the pool of 15 competitive variants.
The applied assessment values of the criteria for the analyzed decision variants were presented in table 1.
Table 1. Matrix of criteria for the analyzed decision variants
Criteria Variants g1 g2 g3 g4 g5 g6 g7 A1 68 29 71 good 10285 36 2332 A2 65 38 61 exceptional 6795 36 2449 A3 63 42 64 average 5060 12 2682 A4 64 39 56 very good 6000 12 2947 A5 65 37 55 exceptional 10145 36 2688 A6 63 35 56 almost good 4330 24 2666 A7 56 60 44 almost good 4250 36 3176 A8 63 33 47 good 5050 24 2828 A9 56 55 40 almost good 3120 24 2910
Criteria Variants g1 g2 g3 g4 g5 g6 g7 A10 53 53 47 almost good 4200 24 2667 A11 51 36 53 good 7965 36 2875 A12 53 37 51 almost good 5515 12 2505 A13 54 49 44 average 7410 24 2950 A14 52 50 37 good 2880 24 2763 A15 57 39 36 good 3850 12 2749
Source: own investigations
Thanks to the computations according to the procedure ot the NAIADE method, a final rank-ing of the alternatives could be achieved. Rankrank-ing +
(a
)
Φ
provided information about how much better the given alternative is than the others (table 2).Table 2. Ranking
Φ
+(a
)
Variants A1 A2 A3 A4 A5 A6 A7 A8
Value 0,7213 0,779 0,6073 0,4279 0,6046 0,5701 0,5636 0,4 Variants A9 A10 A11 A12 A13 A14 A15
Value 0,5058 0,5401 0,3583 0,3744 0,2816 0,4861 0,384 Source: own investigations
Ranking Φ−(a) showed how much worse the given alternative is than the others (table 3). Table 3. Ranking −(a) Φ Variants A1 A2 A3 A4 A5 A6 A7 A8 Value 0,3808 0,2525 0,4911 0,5472 0,3846 0,3532 0,4857 0,6 Variants A9 A10 A11 A12 A13 A14 A15 Value 0,5173 0,558 0,6071 0,6046 0,7529 0,5163 0,6314 Source: own investigations
On the basis of the ranking +(a)
Φ of 15 competitive variants it is possible to confirm, that the best variant, from the point of view of the established criteria and the proposed model of prefer-ences, is variant A2, characterized a.o. by an “exceptional” opinion of the superior, an extensive practical experience measured in years, as well as by low costs for the further professional devel-opment. At the other end of the ranking was the variant marked as A13. The final ranking of alter-natives is represents an intersection of two separate rankings ( +(a)
Φ and −(a)
5. Conclusion
The presented article illustrates the practical application of the multicriteria NAIADE method for decision support in the selection of didactic personnel for the realization of the individual sub-jects in institutions of higher education. The advantages of this method undoubtedly include the possibility not to specify preferential information (taking into consideration uncertainty and risk), as well as the interactive modelling of the degree of linear compensation. Potential faults of the method are the omission of a postulate concerning the relative importance of the criteria in the realization of an overriding aim, as well as the missing possibility to structure complex hierarchi-cal decision problems. A practihierarchi-cal verification of the application of the NAIADE method with regard to the quality of education has confirmed, that it can be used as a mechanism to support decision-making in information systems of the DSS class. The choice of assessment criteria, their value or other decision variables can be different for each case.
Bibliography
1. Grzywaczewski M., Jastriebow A., Optymalizacja wielokryterialna modeli mate-matycznych struktur edukacyjnych. XV Ogólnopolska Konferencja Polioptymalizacja I CAD, Mielno, 1997.
2. Piwowarski M., Metoda modelowania procesów dydaktycznych szkoły wyszej z wykorzystaniem optymalizacji wielokryterialnej, Szczecin, 2004.
3. Turban E., Aronson E. J., Decision Support Systems and intelligent systems, Prentice-Hall, Upper Saddle River, 1998.
4. Funtowicz S.O., Ravetz J.R., Uncertainty, Complexity and Post-normal Science, Envi-ronmental Toxicology 13, 1994.
5. Martinez-Alier J., Munda G., O’Neill J., Weak comparability of values as foundation for ecological economies, Ecological Economies 26, 1998.
6. Munda G., Cost-benefit analysis in integrated environmental assessment: some methodo-logical issues, Ecomethodo-logical Economies 19, 1996.
7. Munda G., Social multi-criteria evaluation: methodological foundations and operational consequences, European Journal of Operational Research, Forthcoming, 2002.
8. Munda G., Matarazzo B., New approaches for the comparison of L-R fuzzy numbers: a theoretical and operational analysis, Fuzzy Sets and Systems 118, 2001.
9. Munda G., Multicriteria evaluation in fuzzy environment, Theory and applications in ecological economies, Physica-Verlag, 1995.
10. Jansen R., Munda G., Multicriteria methods for Quantitative, qualitive and fuzzy evalua-tion problems, Springer-Verlag, 2001.
JAROSŁAW W TRÓBSKI e-mail: jwatrobski@wi.ps.pl MATEUSZ PIWOWARSKI e-mail: mpiwowarski@wi.ps.pl Wydział Informatyki
Instytut Systemów Informatycznych Politechnika Szczeciska
