Multicriteria decision-making

In pharmaceutical technology research is, among other things, directed to the design of formulations. Considering a tablet system, the physical properties of the formulation depend on the nature and levels of the compounding substances and of the process variables used in manufacturing such as for instance compression force. 

The first group consists of the model dependent approach in which mathematical models are generated for every formulation property of interest as a function of the composition of the mixture of the compounding substances and possibly process variables [23]. This method is called the simultaneous approach. The settings of all the variables (mixture components and/or process variables) in the employed model have to be 

The second approach to optimisation is a model independent one. One of these model independent methods is the sequential simplex [24,25] used by Shek et al. [26], The method is claimed to be ideally suited for the optimisation of formulations [27] because of the relatively low number of experiments to be performed. 

Disadvantages of the simplex method are the number of experiments to reach an optimum is not known beforehand, this can lead to better but also to worse results compared to a simultaneous approach. If an optimum is reached nothing is known about that part of the response surface that has not been investigated, e.g. other, even higher optima can be present and, which is more important, the stability of the reached optimum against small variations of a criterion, is not known. 

In this particular situation two criteria are optimised. The overall responses of the vertices of the present simplex are compared and the simplex moves away from low responses. The optimisation route depends on the measured values of R and i 2 the values of a and b, which have to be chosen before the start of the optimisation procedure. Suppose in the progress of the optimisation procedure the following results are obtained  

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Horn, J. (1997) Multicriteria Decision Making. In Back, T., Fogel, D.B., Ichalewicz, Z. (eds) Handbook of Evolutionary Computation. Institute of Physics Publishing, Bristol, UK. 

Notice that in comparisons such as these sometimes slight inconsistencies in the results can be obtained. In two cases A was considered better than B, and B better than C, yet C was judged superior to A This inconsistency or non-transitivity is known as Simpson s or de Condorcet s paradox. In this particular case it can perfectly well be attributed to random variation. Assessors who are not sure about their conclusion are forced to make a choice, which then can only be a random guess. It is possible, however, to obtain results which are conflicting and statistically significant at the same time A < B and B < C, but C < A. This situation may occur when the attribute to be assessed in the comparisons is open to different interpretations. Actually, this is a case of multicriteria decision making (see Chapter 26) and it may be impossible to rank the three products unambiguously... 

Several, but not all, of these mathematical methods (e.g. multicriteria decision making. Chapter 26) or problems (the non-hierarchical clustering methods of Chapter 30, which can be treated as allocation models) have been treated earlier. In this chapter, we will briefly discuss the methods that are relevant to chemo-metricians and have not been treated in earlier chapters yet. 

The optimisation of the robustness will be combined with the optimisation of the mixture property itself using a Multicriteria Decision Making strategy, which will be explained there. 

The Multicriteria Decision Making (MCDM) method that is proposed here [28] is based on the Pareto Optimality (PO) concept, does not make preliminary assumptions about the weighting factors, the various responses are considered explicitly. 

Brugha CM (1998) Structuring and Weighting Criteria in Multi Criteria Decision Making (MCDM). In Stewart TJ, van den Honert RC (eds) Trends in Multicriteria Decision Making. Springer, Berlin et al., pp 229-242... 

Roy B (1999) Decision-Aiding Today What Should we Expect. In Gal T, Stewart TJ, Hanne T (eds) Multicriteria Decision Making Advances in MCDM Models, Algorithms, Theory, and Applications. Kluwer Academic Publishers, Boston et al., pp 1.1-1.35 Roy B (1996) Multicriteria Methodology for Decision Aiding. Kluwer Academic Publishers, Boston et al. 

Papadaki M, Andonidakis E, Tsoutsos T, Maria E (2003). A multicriteria decision making methodology for sustainable energy development. Fresenius Environmental Bulletin 12(5) 426 130... 

The multicriteria decision making (MCDM) approach is based on methods to rank the studied objects (events, molecules, cases, etc.) on the basis of multiple criteria [Hendriks et al, 1992 Carlson, 1992], In particular, desirability functions and utility functions are multicriteria decision functions able to assign a score to each object on a user-defined tuning. 

Mulliken electronegativity - quantum-chemical descriptors Mulliken population analysis charge descriptors (O atomic charge) multicriteria decision making - chemometrics multigraph -> graph... 

Santana-Quinter, L. V., Serrano-Hernandez, V. A., Coello Coello, C. A., Hemandez-Diaz, A. G. and Mohna, J. (2007). Use of radial basis functions and rough sets for evolutionary multi-objective optimization, in Proceedings of the 2007 IEEE Symposium on Computational Intelligence in Multicriteria Decision Making (MCDM 2007) (IEEE Press, Honolulu, Hawaii, USA), pp. 107-114. 

Brans, J.P., Mareschal, B., and Vincke, Ph. (1984). PROMETHEE A new family of outranking methods in multicriteria decision making. Operations Research, 84, 477-498. 

Triantaphyllou, E. (2000). Multicriteria decision making methods A comparative study. Applied Optimization Series, Kluwer Academic Publishers. 

Roberto Todeschini is full professor of chemometrics at the Department of Environmental Sciences of the University of Milano-Bicocca (Milano, Italy), where he constituted the Milano Chemometrics and QSAR Research Group. His main research activities concern chemometrics in all its aspects, QSAR, molecular descriptors, multicriteria decision making, and software development. President of the International Academy of Mathematical Chemistry, president of the Italian Chemometric Society, and ad honorem professor of the University of Azuay (Cuenca, Ecuador), he is author of more than 170 publications in international journals and of the books The Data Analysis Handbook, by I.E. Frank and R. Todeschini, 1994, and Handbook of Molecular Descriptors, by R. Todeschini and V. Consonni, 2000. 

HYPERCHEM Rel 4 for Windows (1995) Autodesk Inc Sausalito CA. USA Keller RH, Massart DL (1991) Multicriteria decision making a case study, Chemomlntell Lab Syst 175-189... 

Multicriteria decision making is feasible in two ways. First, the different performance characteristics are aggregated to an objective function, most easily by a weighted sum. The objective function, Z, is obtained from the p individual objective criteria, z,-, by... 

Wang et al. (1986) postulate that if the relative contribution of the different cognitive skills towards the performance of a human-machine system can be either known or inferred, then the corresponding subjective assessment of these skills can help in the designing cognitive aids for the human. They developed a fuzzy set approach to formulate a multicriteria decision-making problem to determine whether individuals can prioritize cognitive skills considered important for inspection performance. 

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