engleski

Qualitative Multiple Criteria Models with Cycles: A Preliminary Study with Method DEX

Multiple criteria models, which are aimed at the evaluation of alternatives, usually employ a simple input-output structure: they consist of multiple input criteria (or attributes) that represent some quality measures of the evaluated alternatives, and have one, or rarely more, output attributes that represent the overall assessments of these alternatives. In addition, some methods, such as the AHP (Analytic Hierarch Process), DEX (Decision EXpert), and MCHP (Multi-Criteria Hierarchical Process), internally organize model variables into a tree or hierarchy. In both cases, such a structure corresponds to a directed graph without cycles. Consequently, the evaluation of alternatives boils down to a simple step-by- step aggregation of input values into the overall assessments of alternatives ; there are no loops or cycles involved in the process. However, there is a notable exception to this principle among MCDM methods: the ANP (Analytic Network Process). The ANP is a more general form of the AHP which explicitly addresses the inter-dependence among the criteria and the alternatives. In general, the ANP model has a network structure and does contain cycles. Cycles are also very common in areas other than MCDM and can be found in all kinds of dynamic models, where they represent various aspects of inter-relations and feedback loops between elements of the modelled system. In this study, we investigate possible ways of introducing cycles into DEX models. DEX is a qualitative multicriteria method, in which all criteria are represented by qualitative (symbolic, verbal) attributes. The attributes are structured into a hierarchy, and the evaluation of alternatives is governed by decision rules. The method DEX is implemented in the software DEXi (http://kt.ijs.si/MarkoBohanec/dexi.html). The introduction of cycles to DEX models, and thus turning DEX models into some kind of dynamic models, has been motivated by practical needs observed in some problem areas. For instance, in agriculture, an evaluation of cropping systems may contain strong cyclic elements in cases where some future outcome (e.g., soil quality, weed quantity) depends on today’s decisions and today’s state of that same quality or quantity. Similar cyclic relationships also occur whenever two or more attributes mutually influence each other, requiring a network rather than hierarchical structure. Having a possibility to explicitly model network relationships in DEX would considerably extend the applicability of the method. Furthermore, as we will show in the presentation, DEX models with cycles would be strong enough to simulate the Conway’s Game of Life (CGL), which is in turn known to be Turing complete, i.e., theoretically as powerful as any computer with unlimited memory and no time constraints. In other words, the introduction of cycles to DEX models would substantially boost their computational power. So far, we have conducted a preliminary study aimed at showing that an introduction of cycles to DEX is indeed possible. In the presentation, we will first justify the need to introduce cycles in DEX models. As this introduction comes with a price, for instance, disrupting the natural distinction between inputs and outputs in MCDA models and considerably affecting the evaluation procedure, we will also highlight some problems and obstacles associated with the approach. The theoretical potential of the approach will be demonstrated on the case of CGL, and its practical applicability will be shown on a selected realistic example: evaluation or employees. The DEX and “DEX with Cycles” models will be compared with corresponding models developed by the AHP and ANP, respectively.

DEX ; multi-criteria decision making ; cycles

nije evidentirano