Search

How to handle an environmental/urban decision problem with many alternatives and the presence of several interdependent criteria? Starting from the 'Futur-e Project' of the main Italian distributor of electricity, the paper proposes an integrated MCDA approach illustrated by the comparison of alternative projects for the reuse of a large abandoned thermoelectric power plant in Italy. We focus on the following aspects: 1) evaluation of the feasible plan performances with respect to criteria; 2) construction of a reliable decision support model requiring the decision-maker parsimonious preference information. We adopted an assessment framework based on the Choquet integral to represent interaction between criteria, parsimonious AHP reducing the number of pairwise comparisons, and SMAA permitting to explore the space of different recommendations supplied by the decision model in case of perturbation of its parameters. We report on the evolution of the procedure and on the aspects of the support provided by the adopted approach.

Supplemental Digital Content is available in the text.

Current Human Reliability Analysis models express error probabilities as a function of task types and operational context, without explicitly modelling the influence of different crew behavioral characteristics on the error probability. The influence of such variability is treated only implicitly, by variability and uncertainty distributions with bounds primarily obtained by expert judgment. This paper presents a methodology to empirically incorporate crew performance variability in error probability quantification, from simulator data. Crew behaviors are represented by a set of “behavioral patterns” that emerge in the observation of operating crews (e.g. in information sharing or in adhering to procedural guidance). The paper demonstrates the use of a Bayesian hierarchical model to explicitly capture the performance variability emerging from data. The methodology is applied to a case study from literature. Numerical demonstrations are performed in order to compare the proposed approach to the existing quantification models used in HRA for treating simulator data.

Confirmation is a useful concept for assessing the impact of the premise on the conclusion of a rule induced from data. Interpretation of probabilistic relationships between premise and conclusion of a rule led to four mathematical formulations of confirmation, called perspectives. The logical equivalence of these perspectives and the resulting general definition of confirmation underline the known qualitative aspect of the concept of confirmation. The quantitative aspect of confirmation is handled by definitions of particular confirmation measures. In this paper, we relate the qualitative and quantitative aspects by introducing a property of monotonicity of measures with respect to left- and right-hand side probabilities defining the perspectives. This new property permits consideration of confirmation measures in association with particular perspectives. We also identify several other properties that valuable confirmation measures should possess. Particular care is devoted to discussion of behavior of confirmation measures monotonic in different perspectives with respect to symmetry properties, taking also into account two new perspectives of Bayesian confirmation. We also prove that confirmation measures monotonic in the six perspectives are exhaustive in the sense that their set is closed under transformations related to symmetry properties. Finally, we verify which confirmation measures enjoy these properties. [ABSTRACT FROM AUTHOR]

We present a new multiple criteria sorting method deriving from Dominance-based Rough Set Approach (DRSA). The preference information supplied by the Decision Maker (DM) is a set of possibly imprecise and inconsistent assignment examples on a subset of reference alternatives relatively well-known to the DM. To structure the data we use DRSA, and subsequently, represent the assignment examples by all minimal sets of rules covering all alternatives from the lower approximations of class unions. Such a set of rules is called minimal-cover set - it is one of the instances of the preference model compatible with DM's preference information. In this way, we implement the principle of Robust Ordinal Regression (ROR) to decision rule preference model. For each alternative, we derive the necessary and possible assignments specifying the range of classes to which the alternative is assigned by all or at least one compatible set of rules, respectively, as well as class acceptability indices. We also introduce the notion of a representative compatible minimal-cover set of rules whose selection builds on the results of ROR, addressing the robustness concern. Application of the approach is demonstrated by classifying 69 land zones in 4 classes representing different risk levels. [ABSTRACT FROM AUTHOR]

Inconsistency in classification and regression problems occurs when instances that relate in a certain way on the condition attributes, do not follow the same relation on the decision attribute. It typically appears as a result of perturbation in data caused by incomplete knowledge (missing attributes) or by random effects that occur during data generation (instability in the assessment of decision attribute values). Inconsistencies with respect to a crisp preorder relation (expressing either dominance or indiscernibility between instances) can be handled with set-theoretic approaches like rough sets and by using statistical/machine learning approaches that involve optimization methods. In particular, the Kotłowski-Słowiński (KS) approach relabels the objects from a dataset such that inconsistencies are removed, and such that the new class labels are as close as possible to the original ones in terms of a given loss function. In this paper, we generalize the KS approach to handle inconsistency determined by a fuzzy preorder relation rather than a crisp one. The method produces a consistent fuzzy relabeling of the instances and may be used as a preprocessing tool with algorithms for binary classification and regression. As the obtained fuzzy sets can be represented as unions of meaningful simple fuzzy sets or granules, we call them granular approximations. We provide statistical foundations for our method, develop appropriate optimization procedures, provide didactic examples, and prove several important properties. • Proposing the definition of granular approximations; a novel way of integrating machine learning, fuzzy sets, and rough sets. • Inconsistencies in data, defined according to the rough set framework, are removed with optimization methods. • The new method generalizes Kotłowski and Słowiński's approach defined for crisp relations. • The fuzzy rough set lower and upper approximations are extreme cases of the granular approximation. [ABSTRACT FROM AUTHOR]

Highlights: [•] We present a methodology for preference learning in multicriteria ranking. [•] We apply variable consistency dominance-based rough set approach. [•] Pairwise comparisons of reference objects are used to learn a rule preference model. [•] Application of rules on a set of objects induces a preference relation on this set. [•] Net flow rule exploiting this relation is identified as the best ranking method. [Copyright &y& Elsevier]

Highlights: [•] The concept of universal integral, has been recently proposed and axiomatized. [•] This encompasses several integrals, including the Choquet, Shilkret and Sugeno integrals. [•] In this paper we present two new axiomatizations of the universal integral. [ABSTRACT FROM AUTHOR]

The paper shows the contribution that two different multiple criteria decision aiding (MCDA) methods could provide in the field of strategic decisions and urban and territorial planning. In particular, the analytic network process and the dominance-based rough set approach have been considered and discussed in the work with reference to their role in supporting such decision-making processes, trying to compare the different contributions given by the two approaches in this specific domain of application.

Abstract: We are considering properties of interestingness measures of rules induced from data. These are: Bayesian confirmation property, two properties related to the case of entailment or refutation, called and logicality L, and a group of symmetry properties. We propose a modification of properties and L, called weak , and weak L, that deploy the concept of confirmation in its larger sense. We demonstrate that properties and L do not fully reflect such understanding of the confirmation concept, and thus, we propose to substitute by weak and L by weak L. Moreover, we introduce four new approaches to normalization of confirmation measures in order to transform measures so that they would obtain desired properties. The analysis of the results of the normalizations of the confirmation measures takes into account all considered properties. We advocate for two normalized confirmation measures: measure Z considered in the literature, and newly proposed measure A. Finally, we provide some ideas for combining them in a single measure keeping all desirable properties. [Copyright &y& Elsevier]

Abstract: We consider probabilistic rough set approaches based on different versions of the definition of rough approximation of a set. In these versions, consistency measures are used to control assignment of objects to lower and upper approximations. Inspired by some basic properties of rough sets, we find it reasonable to require from these measures several properties of monotonicity. We consider three types of monotonicity properties: monotonicity with respect to the set of attributes, monotonicity with respect to the set of objects, and monotonicity with respect to the dominance relation. We show that consistency measures used so far in the definition of rough approximation lack some of these monotonicity properties. This observation led us to propose new measures within two kinds of rough set approaches: Variable Consistency Indiscernibility-based Rough Set Approaches (VC-IRSA) and Variable Consistency Dominance-based Rough Set Approaches (VC-DRSA). We investigate properties of these approaches and compare them to previously proposed Variable Precision Rough Set (VPRS) model, Rough Bayesian (RB) model, and previous versions of VC-DRSA. [Copyright &y& Elsevier]

Abstract: A generalization of the original definition of rough sets and variable precision rough sets is introduced. This generalization is based on the concept of absolute and relative rough membership. Similarly to variable precision rough set model, the generalization called parameterized rough set model, is aimed at modeling data relationships expressed in terms of frequency distribution rather than in terms of a full inclusion relation used in the classical definition of rough sets. However, differently from the variable precision rough set model, one or more parameters modeling the degree to which the condition attribute values confirm the decision attribute value, are considered. The properties of this extended model are investigated and compared to the classical rough set model and to the variable precision rough set model. [Copyright &y& Elsevier]

Abstract: We propose a new fuzzy rough set approach which, differently from most known fuzzy set extensions of rough set theory, does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication). As there is no rationale for a particular choice of these connectives, avoiding this choice permits to reduce the part of arbitrary in the fuzzy rough approximation. Another advantage of the new approach is that it is based on the ordinal properties of fuzzy membership degrees only. The concepts of fuzzy lower and upper approximations are thus proposed, creating a base for induction of fuzzy decision rules having syntax and semantics of gradual rules. The proposed approach to rule induction is also interesting from the viewpoint of philosophy supporting data mining and knowledge discovery, because it is concordant with the method of concomitant variations by John Stuart Mill. The decision rules are induced from lower and upper approximations defined for positive and negative relationships between credibility degrees of multiple premises, on one hand, and conclusion, on the other hand. [Copyright &y& Elsevier]

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.

Aim:To assess the usefulness of ambulatory blood pressure monitoring (ABPM) in the prognostic stratification of patients with a recent myocardial infarction.

Inflammatory bowel diseases IBDs are associated with pathologic findings in the liver and biliary tract. Ultrasonography US represents a noninvasive means to study hepatobiliary abnormalities. This study evaluated the prevalence of US hepatobiliary changes and their relationship to clinical variables in a large IBD patient population followed in a single center.

Abstract: The results of a study conducted to determine the usefulness of carcinoembryonic antigen (CEA) monitoring in the follow-up of patients with resected colorectal cancer are reported herein. The subjects of this study were 125 patients in whom CEA had been determined preoperatively and 239 patients in whom CEA had been monitored postoperatively. The results revealed increased preoperative CEA in only 24% of the subjects, and that this increment was correlated with subsequent more advanced tumor stage and a higher recurrence rate (P<0.01). The postoperative CEA level exceeded the threshold in 71% of the patients affected by recurrence, 94.4% of whom developed liver metastases and 50%, nonhepatic recurrence. This marker showed elevated sensitivity for liver metastases (99%), whereas the sensitivity was lower for nonhepatic recurrence of the disease (94%). Thus, we concluded that CEA monitoring can be useful for preoperative colorectal tumor grading, even if its validity in the early diagnosis of recurrence is problematic, especially in terms of radical repeated surgery and survival.

In this paper, we first review existing fuzzy extensions of the dominance-based rough set approach (DRSA), and advance the theory considering additional properties. Moreover, we examine the application of Ordered Weighted Average (OWA) operators to fuzzy DRSA. OWA operators have shown a lot of potential in handling outliers and noisy data in decision tables, when they are combined with the indiscernibility-based rough set approach (IRSA). We examine theoretical properties of the proposed hybridisation of OWA operators with fuzzy DRSA. At the end, we experimentally compare the robustness of the standard fuzzy DRSA approach with the OWA one. [ABSTRACT FROM AUTHOR]

Rationalizability has been a main topic in individual choice theory since the seminal paper of Samuelson (1938). The rationalization of a multi-valued choice is classically obtained by maximizing the binary relation of revealed preference, which is fully informative of the primitive choice as long as suitable axioms of choice consistency hold. In line with this tradition, we give a purely axiomatic treatment of the topic of choice rationalization. In fact, we introduce a new class of properties of choice coherence, called axioms of replacement consistency, which examine how the addition of an item to a menu may cause a substitution in the selected set. These axioms are used to uniformly characterize rationalizable choices such that their revealed preferences are quasi-transitive, Ferrers, semitransitive, and transitive. Further, regardless of rationalizability, we study the relationship of these new axioms with some classical properties of choice consistency, such as standard contraction, standard expansion, and WARP . To complete our analysis of the transitive structure of rationalizable choices, we examine the case of revealed preferences satisfying weak ( m , n ) -Ferrers properties in the sense of Giarlotta and Watson (2014). Originally introduced with the purpose of extending the notions of interval orders and semiorders, these Ferrers properties give a descriptive taxonomy of binary relations displaying a transitive strict preference but an intransitive indifference. Here we suggest a possible economic interpretation of weak ( m , n ) -Ferrers properties, showing that, in a suitable model of transactions, they provide a way of controlling phenomena of money-pump due to the presence of mixed cycles of preference/indifference. Finally, we define ( m , n ) -rationalizable choices as those having a weakly ( m , n ) -Ferrers revealed preference, and characterize these choices by means of additional axioms of replacement consistency. [ABSTRACT FROM AUTHOR]

We consider decision under uncertainty as a multi-attribute classification problem where a set of acts is described by outcomes gained with given probabilities. The Decision Maker (DM) provides desired classification for a small subset of reference acts. Such preference information is structured using Dominance-based Rough Set Approach (DRSA), and the resulting lower approximations of the quality class unions are used as an input for construction of an aggregate preference model. We induce all minimal-cover sets of rules being compatible with the non-ambiguous assignment examples, and satisfying some additional requirements that may be imposed by the DM. Applying such compatible instances of the preference model on a set of all acts, we draw conclusions about the certainty of recommendation assured by different minimal-cover sets of rules. In particular, we analyze the diversity of class assignments, assignment-based preference relations, and class cardinalities. Then, we solve an optimization problem to get a univocal (precise) classification for all acts, taking into account the robustness concern. This optimization problem admits incorporation of additional indirect and imprecise preferences in form of desired class cardinalities and assignment-based pairwise comparisons. Finally, we extend the proposed approach to group decision under uncertainty. We present a set of indicators and outcomes giving an insight into the spaces of consensus and disagreement between the DMs. [ABSTRACT FROM AUTHOR]

Interpretability is the next frontier in machine learning research. In the search for white box models — as opposed to black box models, like random forests or neural networks — rule induction algorithms are a logical and promising option, since the rules can easily be understood by humans. Fuzzy and rough set theory have been successfully applied to this archetype, almost always separately. As both approaches offer different ways to deal with imprecise and uncertain information, often with the use of an indiscernibility relation, it is natural to combine them. The QuickRules [20] algorithm was a first attempt at using fuzzy rough set theory for rule induction. It is based on QuickReduct, a greedy algorithm for building decision superreducts. QuickRules already showed an improvement over other rule induction methods. However, to evaluate the full potential of a fuzzy rough rule induction algorithm, one needs to start from the foundations. Accordingly, the novel rule induction algorithm, Fuzzy Rough Rule Induction (FRRI), we introduce in this paper, uses an approach that has not yet been utilised in this setting. We provide background and explain the workings of our algorithm. Furthermore, we perform a computational experiment to evaluate the performance of our algorithm and compare it to other state-of-the-art rule induction approaches. We find that our algorithm is more accurate while creating small rulesets consisting of relatively short rules. [ABSTRACT FROM AUTHOR]

Abstract: In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, dominance-based rough set approach (DRSA) has been introduced to deal with the problem of ordinal classification with monotonicity constraints (also referred to as multicriteria classification in decision analysis). However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive. In this paper, we introduce a probabilistic model for ordinal classification problems with monotonicity constraints. Then, we generalize the notion of lower approximations to the stochastic case. We estimate the probabilities with the maximum likelihood method which leads to the isotonic regression problem for a two-class (binary) case. The approach is easily generalized to a multi-class case. Finally, we show the equivalence of the variable consistency rough sets to the specific empirical risk-minimizing decision rule in the statistical decision theory. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications. [ABSTRACT FROM AUTHOR]