Over the past few decades, the strategies to perform energy systems analysis have evolved into multiple criteria-based frameworks. However, there still remains a lack of guidance on how to select the most suitable Multiple Criteria Decision Analysis (MCDA) method. These methods provide different decision recommendations for the Decision Makers, including ranking, sorting, choice, and clustering of the alternatives (e.g., technologies or scenarios) under evaluation. They deal with a variety of data typologies and preferences, and lead Decision Makers in shaping the energy systems of the future. Here, we evaluate the MCDA methods used in 56 case studies performing energy systems analysis at different scales. We find that close to 60% of these studies chose an MCDA method that was not the most adequate for the respective decision problem. In particular, this concerned the use of weighting methods (e.g., Analytical Hierarchy Process) in MCDA approaches not suited for this type of weights, sub-optimal selection of MCDA techniques for specific types of problem statements, and lack of handling rather evident interactions in preference models. Our analysis demonstrates that these deficiencies can be overcome by using a recently developed methodology and software that support Decision Makers and analysts in selecting the most suitable MCDA method for a given type of decision-making problem.

Abstract Measuring the level of sustainability taking into account many contributing aspects is a challenge. In this paper, we apply a multiple criteria decision aiding framework, namely, the hierarchical-SMAA-PROMETHEE method, to assess the environmental, social, and economic sustainability of 20 European cities in the period going from 2012 to 2015. The application of the method is innovative for the following reasons: (i) it permits to study the sustainability of the mentioned cities not only comprehensively but also considering separately particular macro-criteria, providing in this way more specific information on their weak and strong points; (ii) the use of PROMETHEE and, in particular, of PROMETHEE II, avoids the compensation between different and heterogeneous criteria, that is arbitrarily assumed in value function aggregation models; finally, (iii) thanks to the application of the Stochastic Multicriteria Acceptability Analysis, the method provides more robust recommendations than a method based on a single instance of the considered preference model compatible with few preference information items provided by the Decision Maker.

We consider a problem of multi-decision sorting subject to multiple criteria. In the newly formulated decision problem, besides performances on multiple criteria, alternatives get evaluations on multiple interrelated decision attributes involving preference-ordered classes. We propose a dedicated method for dealing with such a problem, incorporating a threshold-based value-driven sorting procedure. The Decision Maker (DM) is expected to holistically evaluate a subset of reference alternatives by indicating the quality or risk level on a pre-defined scale of each decision attribute. Based on these evaluations, we construct a set of interrelated preference models, one for each decision attribute, compatible with intra- and inter-decision constraints imposed by such indirect preference information. We also formulate a new way of dealing with potentially non-monotonic criteria by discovering local monotonicity changes in different performance scale regions. The marginal value functions for criteria with unknown monotonicity are represented as a sum of two value functions assuming opposing preference directions, one non-decreasing and the other non-increasing. This permits to obtain an aggregated marginal value function with an arbitrary non-monotonic shape. The practical usefulness of the approach is demonstrated on a case study concerning risk management related to handling (i.e., production, use, manipulation, and processing) nanomaterials in different conditions. We analyze the expert judgments and discuss the inferred preference models, which can be applied to support health and safety managers in reducing the possible risk associated with the respective exposure scenario.

We propose a novel approach to multiple criteria sorting incorporating a threshold-based value-driven procedure. The parameters deciding upon the shape of marginal value functions and separating class thresholds are inferred through preference disaggregation from the Decision Maker's incomplete assignment examples and partial requirements on the type of (non-)monotonicity for each marginal value function. These types include standard monotonic shapes, level-monotonic functions, A- and V-types combining increasing and decreasing value trends, and unknown monotonicity constraints. A representative instance of the sorting model compatible with the preference information is constructed by solving a dedicated Mixed-Integer Linear Programming problem. Its complexity is controlled by minimizing the number of changes in monotonicity between all subsequent sub-intervals of marginal value functions. The assignments derived using the constructed representative model are validated against the outcomes of robustness analysis. The proposed method is applied to a real-world problem of exposure management of engineered nanomaterials. We develop a model for predicting precaution level while handling nanomaterials in certain conditions using a respirator. The model captures interrelations between ten accounted evaluation criteria, including both monotonic and non-monotonic criteria, and the recommended class assignment. This makes it suitable for the management of exposure scenarios, which have not been directly judged by the experts.

In this paper we present a new approach to rough set approximations that permits to distinguish between two kinds of “imperfect” knowledge in a joint framework: on one hand, vagueness, due to imprecise knowledge and uncertainty typical of fuzzy sets, and on the other hand, ambiguity, due to granularity of knowledge originating from the coarseness typical of rough sets. The basic idea of our approach is that each concept is represented by an orthopair, that is, a pair of disjoint sets in the universe of knowledge. The first set in the pair contains all the objects that are considered as surely belonging to the concept, while the second set contains all the objects that surely do not belong to the concept. In this context, following some previous research conducted by us on the algebra of rough sets, we propose to define as rough approximation of the orthopair representing the considered concept another orthopair composed of lower approximations of the two sets in the first orthopair. We shall apply this idea to the classical rough set approach based on indiscernibility, as well as to the dominance-based rough set approach. We discuss also a variable precision rough approximation, and a fuzzy rough approximation of the orthopairs. Some didactic examples illustrate the proposed methodology.

Providing partial preference information for multiple criteria ranking or sorting problems results in the indetermination of the preference model. Investigating the influence of this indetermination on the suggested recommendation, we may obtain the necessary, possible and extreme results confirmed by, respectively, all, at least one, or the most and least advantageous preference model instances compatible with the input preference information. We propose a framework for answering questions regarding stability of these results. In particular, we are investigating the minimal improvement that warrants feasibility of some currently impossible outcome as well as the maximal deterioration by which some already attainable result still holds. Taking into account the setting of multiple criteria ranking and sorting problems, we consider such questions in view of pairwise preference relations, or attaining some rank, or assignment. The improvement or deterioration of the sort of an alternative is quantified with the change of its performances on particular criteria and/or its comprehensive score. The proposed framework is useful in terms of design, planning, formulating the guidelines, or defining the future performance targets. It is also important for robustness concern because it finds which parts of the recommendation are robust or sensitive with respect to the modification of the alternatives’ performance values or scores. Application of the proposed approach is demonstrated on the problem of assessing environmental impact of main European cities.

This paper proposes an interactive multiobjective evolutionary algorithm (MOEA) that attempts to learn a value function capturing the users' true preferences. At regular intervals, the user is asked to rank a single pair of solutions. This information is used to update the algorithm's internal value function model, and the model is used in subsequent generations to rank solutions incomparable according to dominance. This speeds up evolution toward the region of the Pareto front that is most desirable to the user. We take into account the most general additive value function as a preference model and we empirically compare different ways to identify the value function that seems to be the most representative with respect to the given preference information, different types of user preferences, and different ways to use the learned value function in the MOEA. Results on a number of different scenarios suggest that the proposed algorithm works well over a range of benchmark problems and types of user preferences.

The paper investigates relationships between chemical structure, surface active properties and antibacterial activity of 70 bis-quaternary imidazolium chlorides. Chemical structure and properties of imidazolium chlorides were described by 7 condition

In order to handle inconsistencies in ordinal and monotonic information systems, several relaxed versions of the Dominance-based Rough Set Approach (DRSA) have been proposed, e.g., VC-DRSA. These versions use special consistency measures to admit some inconsistent objects in the lower approximations. The minimal consistency level that has to be attained by objects included in the lower approximations is defined using a prior knowledge or a trial-and-error procedure. In order to avoid dependence on prior knowledge, an alternative way of handling inconsistencies is to iteratively eliminate the most inconsistent objects (according to some measure) until the information system becomes consistent. This idea is a base of a new method of handling inconsistencies presented in this paper and called TIPStoC. The TIPStoC algorithm is illustrated by an example from the area of telecommunication and the efficiency of the new method is proved by a computational experiment.

The paper focuses on Bayesian confirmation measures used for evaluation of rules induced from data. To distinguish between many confirmation measures, their properties are analyzed. The article considers a group of symmetry properties. We demonstrate that the symmetry properties proposed in the literature focus on extreme cases corresponding to entailment or refutation of the rule's conclusion by its premise, forgetting intermediate cases. We conduct a thorough analysis of the symmetries regarding that the confirmation should express how much more probable the rule's hypothesis is when the premise is present rather than when the negation of the premise is present. As a result we point out which symmetries are desired for Bayesian confirmation measures. Next, we analyze a set of popular confirmation measures with respect to the symmetry properties and other valuable properties, being monotonicity M, Ex 1 and weak Ex 1 , logicality L and weak L. Our work points out two measures to be the most meaningful ones regarding the considered properties.

In this paper, we present a new preference disaggregation method for multiple criteria sorting problems, called DIS-CARD. Real-life experience indicates the need of considering decision making situations in which a decision maker (DM) specifies a desired number of alternatives to be assigned to single classes or to unions of some classes. These situations require special methods for multiple criteria sorting subject to desired cardinalities of classes. DIS-CARD deals with such a problem, using the ordinal regression approach to construct a model of DM’s preferences from preference information provided in terms of exemplary assignments of some reference alternatives, together with the above desired cardinalities. We develop a mathematical model for incorporating such preference information via mixed integer linear programming (MILP). Then, we adapt the MILP model to two types of preference models: an additive value function and an outranking relation. Illustrative example is solved to illustrate the methodology.

Multiple Criteria Decision Aiding (MCDA) offers a diversity of approaches designed for providing the decision maker (DM) with a recommendation concerning a set of alternatives (items, actions) evaluated from multiple points of view, called criteria. This paper aims at drawing attention of the Machine Learning (ML) community upon recent advances in a representative MCDA methodology, called Robust Ordinal Regression (ROR). ROR learns by examples in order to rank a set of alternatives, thus considering a similar problem as Preference Learning (ML-PL) does. However, ROR implements the interactive preference construction paradigm, which should be perceived as a mutual learning of the model and the DM. The paper clarifies the specific interpretation of the concept of preference learning adopted in ROR and MCDA, comparing it to the usual concept of preference learning considered within ML. This comparison concerns a structure of the considered problem, types of admitted preference information, a character of the employed preference models, ways of exploiting them, and techniques to arrive at a final ranking.

We consider the problem of ordinal classification with monotonicity constraints. It differs from usual classification by handling background knowledge about ordered classes, ordered domains of attributes, and about a monotonic relationship between an evaluation of an object on the attributes and its class assignment. In other words, the class label (output variable) should not decrease when attribute values (input variables) increase. Although this problem is of great practical importance, it has received relatively low attention in machine learning. Among existing approaches to learning with monotonicity constraints, the most general is the nonparametric approach, where no other assumption is made apart from the monotonicity constraints assumption. The main contribution of this paper is the analysis of the nonparametric approach from statistical point of view. To this end, we first provide a statistical framework for classification with monotonicity constraints. Then, we focus on learning in the nonparametric setting, and we consider two approaches: the "plug-in" method (classification by estimating first the class conditional distribution) and the direct method (classification by minimization of the empirical risk). We show that these two methods are very closely related. We also perform a thorough theoretical analysis of their statistical and computational properties, confirmed in a computational experiment.

We introduce the bipolar complemented de Morgan Brouwer-Zadeh distributive lattice in order to give an algebraic model the to Dominance-based Rough Set Approach. We present also the concept of bipolar approximation space and we show how it can be ind

We present basic ideas related to application of Dominance-based Rough Set Approach (DRSA) in interactive Evolutionary Multiobjective Optimization (EMO). In the proposed methodology, the preference information elicited by the decision maker in successive iterations consists in sorting some solutions in the current population into “relatively good” and “others”, or in comparing some pairs of solutions with respect to preference. The “if ..., then ...” decision rules are then induced from this preference information using Dominance-based Rough Set Approach (DRSA). These rules are used within EMO in order to focus on populations of solutions satisfying the preferences of the decision maker, speeding up convergence to the most preferred region of the Pareto-front. The resulting interactive schemes, corresponding to the two types of preference information, are called DRSA-EMO and DRSA-EMO-PCT, respectively. The proposed methodology permits also to take into account robust concerns in multiobjective optimization.

In classification with monotonicity constraints, it is assumed that the class label should increase with increasing values on the attributes. In this paper we aim at formalizing the approach to learning with monotonicity constraints from statistical point of view. Motivated by the statistical analysis, we present an algorithm for learning rule ensembles. The algorithm first "monotonizes" the data using a nonparametric classification procedure and then generates a rule ensemble consistent with the training set. The procedure is justified by a theoretical analysis and verified in a computational experiment.

Ordinal classification problems with monotonicity constraints (also referred to as multicriteria classification problems) often appear in real-life applications, however, they are considered relatively less frequently in theoretical studies than regular classification problems. We introduce a rule induction algorithm based on the statistical learning approach that is tailored for this type of problems. The algorithm first monotonizes the dataset (excludes strongly inconsistent objects), using Stochastic Dominance-based Rough Set Approach, and then uses forward stagewise additive modeling framework for generating a monotone rule ensemble. Experimental results indicate that taking into account knowledge about order andmonotonicity constraints in the classifier can improve the prediction accuracy.

We propose a new rule induction algorithm for solving classification problems via probability estimation. The main advantage of decision rules is their simplicity and good interpretability. While the early approaches to rule induction were based on sequential covering, we follow an approach in which a single decision rule is treated as a base classifier in an ensemble. The ensemble is built by greedily minimizing the negative loglikelihood which results in estimating the class conditional probability distribution. The introduced approach is compared with other decision rule induction algorithms such as SLIPPER, LRI and RuleFit.

Decision rules induced from a data set represent knowledge patterns relating premises and decisions in ‘if … , then …’ statements. Premise is a conjunction of elementary conditions relative to independent variables and decision is a conclusion relative to dependent variables. Given a set of decision rules induced from a data set, it is useful to estimate possible effects on the dependent variables caused by an intervention on some independent variables. The authors introduce a methodology for quantifying the impact of a strategy of intervention based on a decision rule induced from data. While the usual interestingness measures of decision rules are taking into account only characteristics of universe U where they come from, the measures of efficiency of intervention depend also on characteristics of universe U′ where intervention takes place. The authors are considering the intervention on a single independent variable and on a combination of these variables.

Given a ranking of actions evaluated by a set of evaluation criteria, we construct a rough approximation of the preference relation known from this ranking. The rough approximation of the preference relation is a starting point for mining " if... then" decision rules constituting a symbolic preference model. The set of rules is induced such as to be compatible with a concordance-discordance preference model used in well-known multicriteria decision aiding methods. An application of the set of decision rules to a new set of actions gives a fuzzy outranking graph. Positive and negative flows are calculated for each action in the graph, giving arguments about its strength and weakness. Aggregation of both arguments leads to a final ranking, either partial or complete. The approach can be applied to support a multicriteria choice and ranking of actions when the input information is a ranking of some reference actions.

In this article we are considering a multicriteria classification that differs from usual classification problems since it takes into account preference orders in the description of objects by condition and decision attributes. To deal with multicriteria classification we propose to use a dominance-based rough set approach (DRSA). This approach is different from the classic rough set approach (CRSA) because it takes into account preference orders in the domains of attributes and in the set of decision classes. Given a set of objects partitioned into pre-defined and preference-ordered classes, the new rough set approach is able to approximate this partition by means of dominance relations (instead of indiscernibility relations used in the CRSA). The rough approximation of this partition is a starting point for induction of if-then decision rules. The syntax of these rules is adapted to represent preference orders. The DRSA keeps the best properties of the CRSA: it analyses only facts present in data, and possible inconsistencies are not corrected. Moreover, the new approach does not need any prior discretization of continuous-valued attributes. In this article we characterize the DRSA as well as decision rules induced from these approximations. The usefulness of the DRSA and its advantages over the CRSA are presented in a real study of evaluation of the risk of business failure. © 2002 John Wiley & Sons, Inc.

This paper proposes new definitions of lower and upper approximations, which are basic concepts of the rough set theory. These definitions follow naturally from the concept of ambiguity introduced in this paper. The new definitions are compared to the classical definitions and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.

Rough set theory refers to classification of objects described by well-defined values of qualitative and quantitative attributes. The values of attributes defined for each pair [object, attribute], called descriptors, are assumed to be unique and pre

This paper presents an empirical study of the use of the rough set approach to reduction of data for a neural network classifying objects described by quantitative and qualitative attributes. Two kinds of reduction are considered: reduction of the set of attributes and reduction of the domains of attributes. Computational tests were performed with five data sets having different character, for original and two reduced representations of data. The learning time acceleration due to data reduction is up to 4.72 times. The resulting increase of misclassification error does not exceed 11.06%. These promising results let us claim that the rough set approach is a useful tool for preprocessing of data for neural networks.

PurposeSubroutine A R S M E solves a resource constrained, network scheduling problem for the case in which activities may be arbitrarily interrupted and restarted later with no increase in activity duration.The number of resource types is not a limiting factor in our procedure.The amount of any one resource available at any moment is constant.We shall use the "activity-on-arc" network representation, under the commonly imposed assumption that the network contains no directed cycles and has only one "beginning" and only one "terminal" node (event).I t is further assumed that the network nodes (events) are ordered in such a way t h a t node i precedes node j, if i < j.Such an ordering is always possible and it induces an ordering among the arcs (activities).Optimal approaches to resource constrained, network scheduling problems where activities can require more than one resource type are presented in [1,4].Both methods assume integer durations of activities, and the method presented in [1] divides activity durations into unit intervals.Both methods can handle networks with up to about 30 activities and 3 resource types.Subroutine A R S M E is constructed in such a way that its storage requirements are minimal, a fact which permits the solution of problems for very large networks with many resource types.Moreover, an optimal solution can be obtained in a shorter time when relatively smaller amounts of the resources are available than when resources are less limited.Let the number of activities be equal to M and the number of resource types be equal to RT.For activityj (j = 1, 2 , . . ., M) and resource k (k = 1, 2 , . . ., RT)