IDS-EAPD Project: Intelligent decision support based on explanatory analytics of preference data

This project aims at designing, implementing and validating new decision support methods characterized by explanatory preference analytics understood as above. This general objective will guide seven tasks presented in the following research plan:

I.  Interactive evolutionary multiobjective optimization driven by “if…, then…” decision rules representing preferences expressed both in objective and decision space.

This task builds on our positive experience with interactive evolutionary multiobjective optimization guided by a preference elicitation procedure inspired by explainable analytics and designed in line with decision psychology [1]. This interactive method has been called XIMEA-DRSA. During its preference elicitation phase, the DM gets a sample of solutions from the current population and is asked to indicate relatively good solutions. Using the Dominance-based Rough Set Approach (DRSA) [2], “if…, then…” decision rules are induced from this information. They are used in the next optimization phases of the evolutionary algorithm to influence the crossover so as to converge towards the part of the Pareto front containing the best compromise solution. Besides guiding the search process, the decision rules can be read as arguments explaining the DM’s preferences. In this way, the proposed method implements the postulate of transparency and explainability.
The extension planned in this task goes beyond reasoning about preferences in the objective space. While in XIMEA-DRSA, the DM is asked to classify solutions in the objective space, in this task, the DM will also be informed about the inverse image of these solutions in the decision space, i.e., characterized by values of decision variables. Classifications of the same solutions in both spaces may create inconsistencies caused by absence of some non-analytical objectives taken into account when the DM evaluates solutions. This inconsistency has to be represented by the preference model, and DRSA can do it, which is one of its strengths.

II.  Interactive multiobjective optimization reinforced by constraints generated by “if…, then…” decision rules.

This task is related to the previous one by the preference model which is composed of decision rules having the same syntax. The difference is that in this task, the relevant part of the set of non-dominated solutions is generated in each optimization stage with additional constraints on the feasible set generated by decision rules induced from classification of a sample of solutions provided by the DM in the decision stage. This approach has been preliminarily tested in [3], giving promising results. However, in this preliminary study, the classification was binary only (into “good” and “others”) and the DM was allowed to select only one rule that was later translated to new additional constraints of the multiobjective optimization problem. In this task, the classification of solutions would be multi-class, and the DM would be able to select more than one rule.

III.  Construction and explanation of non-compensatory composite indicators using “if…, then…” decision rules.

When approaching multi-attribute decision problems, it is often useful to define a score with a cardinal content permitting to measure the distance between the comprehensive evaluations of considered alternatives. MCDA is more and more often adopted in the construction of composite indicators [4], that are specific scores used for aggregating heterogeneous individual indicators into a synthetic index to describe an overall complex phenomenon such as the industrial competitiveness, the quality of life, the smart cities, and the sustainable development. The composite indicators are commonly constructed by compensatory aggregation procedures,  however, the compensatory effects are often not permitted and then a non-compensatory aggregation procedure has to be applied. The latter takes into account the ordinal nature of elementary indicators only. The challenge related to construction of a non-compensatory composite indicator is to aggregate elementary indicators in terms of ordinal input to obtain a composite indicator in terms of cardinal output. This point of view has been recently adopted in [5]. In this project, we will make substantial alterations to this scoring method substituting the outranking relation preference model with “if…, then…” decision rules obtained by DRSA.

IV.  Interpretation of black-box decision models obtained using neural nets or utility-driven methods in terms of “if…, then…” decision rules.

Utility-driven MCDM methods are often used due to people’s attachment to numerical ratings and the ease of comparing alternatives using numerical scores. In order to improve the explainability aspect of these methods, we will interpret their results by “if…, then…” decision rules. Promising results have been obtained in [6].  Another approach developed within this task would concern the explanatory preference analytics of recommendations presented in terms of predictions induced from data sets using, for example, Neural Nets (NN). To get an explanation of their prediction, we will generate “if…, then…” decision rules that represent well the NN prediction for a given DM. This subtask is meant to make us aware that explanatory preference analytics is not something objective and equal for all users but depends on specific user preferences.

V.  Consensus reaching in group decision-making using compatible instances of decision makers’ preference models.

In case of group decision-making, it is crucial not only for each DM to understand their own preferences but also to comprehend each other’s preferences. This mutual understanding can facilitate mutually beneficial compromises in achieving a consensus. Based on the observation that many previous studies on group decision-making did not pay enough attention to individual participation and satisfaction of DMs, we proposed in [7] a new kind of consensus models for group utility optimization. In the present study, we would represent individual preferences of DMs by “if…, then…” decision rules. The preference information of all DMs provided in terms of pairwise comparisons or classifications of some reference alternatives would be used by DRSA to induce a collective preference model guiding interactively the consensus-reaching process.

VI.  Fuzzy-rough hybridization of granular approximations in view of structuring preference data prior to rule induction.

In all tasks from I to V, the preference model fulfilling the best role in explanatory preference analytics is the set of “if…, then…” decision rules induced from data structured using the rough set concept [8]. 40 years after the concept was proposed, it became clear that fuzzy set theory and rough set theory are not competing theories but, instead, are suited to fruitful hybridization. In reasoning about data, the first handles vagueness due to imprecision, and the second handles ambiguity due to coarseness [9]. Fuzzy-rough hybridization goes together with granular approximation of decision classes [10]. As granules can be interpreted as decision rules, in this project we will refine the multi-class granular approximation in view of rule induction which is a focus of task VII. Another innovative topic related to this task would be a new approach to fuzzy-rough approximation based on a double use of the Choquet integral. This permits to model the effects of synergy and redundancy among both attributes and objects of approximated sets.

VII.  Improved algorithms of rule induction, including hierarchical construction of meta-rules and construction of ensemble classifiers composed of diversified decision rules.

In this task, we will develop granular learning algorithms with a dual focus on accuracy and interpretability of induced decision rules. We will aim to solve the learning problem as an optimisation problem, starting from a nominal classifier and then approaching more complex problems, including ordinal classification, regression, and multi-criteria decision, by using the rich research on different types of granular fuzzy sets. In addition to constructing decision rules associated with granules of granular approximations, we will develop a granular learning model for multi-class classification based on hierarchical rule induction, similar to [11].