Silvio Giove

Incomplete pairwise comparison and consistency optimization

This paper proposes a new method for calculating the missing elements of an incomplete matrix of pairwise comparison values for a decision problem. The matrix is completed by minimizing a measure of global inconsistency, thus obtaining a matrix which is optimal from the point of view of consistency with respect to the available judgements. The optimal values are obtained by solving a linear system and unicity of the solution is proved under general assumptions. Some other methods proposed in the literature are discussed and a numerical example is presented.

An interval portfolio selection problem based on regret function

Abstract Different approaches, besides the traditional Markowitz’s model, have been proposed in the literature to analyze portfolio selection problems. Among them we can cite the possibilistic portfolio models, which treat the expected return rates of the securities as fuzzy or possibilistic variables, instead of random variables. Such models, which are based on possibilistic mathematical programming, describe the uncertainty of the real world as ambiguity and vagueness, rather than stochasticity. Actually, another way to treat the uncertainty in decision making problems consists of assuming that the data are not well defined, but are able to vary in given intervals. Interval analysis is thus appropriate to handle the imprecise input data. In this paper we consider a portfolio selection problem in which the prices of the securities are treated as interval variables. In order to deal with such an interval portfolio problem, we propose the adoption of a minimax regret approach based on a regret function.

The Choquet integral with respect to a level dependent capacity

We present a generalization of Choquet integral in which the capacity depends also on the value of the aggregated variables. We show that as particular cases of our generalization of Choquet integral there are the Sugeno integral, the Sipos integral and the Cumulative Prospect Theory functional. We also show that many concepts such as Mobius transform, importance index, interaction index, k-order capacities and OWA operators, introduced in the research about Choquet integral, can be generalized in the considered context.

Decision Support Systems and Environment: Role of MCDA

Decision Support Systems (DSS) are computer-based tools designed to support management decisions (Eom, 2001). Many environmental applications of DSS are reported in the current literature, including petroleum contamination detection (Geng et al., 2001), lake remediation (Gallego et al., 2004), soil decontamination (Zhiying et al., 2003), and many others. However, many of these DSS are in fact different models integrated to better visualize data or describe systems; they are not tailored to address specific decision problems or help decision makers in making inevitable trade-offs. Multicriteria Decision Analysis (MCDA), on the other hand, offers the ability to integrate policy preferences with the judgements of technical experts (Figueira et al., 2005; Linkov et al., 2007). MCDA methods enable simultaneous consideration of stakeholder interests and technical evaluations, utilizing rigorous scientific methods to process technical information. MCDA is especially important in situations of significant uncertainty and data scarcity, such as management and restoration of contaminated sites. This Chapter focuses on the conceptual background of MCDA, with particular attention paid to environmental DSS, and it discusses some of the most commonly used approaches, especially for multi-attribute decision problems (i.e. where both criteria and alternatives are finite in number).

Integrated Risk Assessment for WFD Ecological Status classification applied to Llobregat river basin (Spain). Part II - Evaluation process applied to five environmental Lines of Evidence.

Many indicators and indices related to a variety of biological, physico-chemical, chemical, and hydromorphological water conditions have been recently developed or adapted by scientists in order to support water managers in the Water Framework Directive (WFD) implementation. In this context, the achievement of a comprehensive and reliable Ecological Status classification of water bodies across Europe is hampered by the lack of harmonised procedures for selecting an appropriate set of indicators and integrating heterogeneous information in a flexible way. To this purpose, an Integrated Risk Assessment (IRA)(2) methodology was developed based on the Weight of Evidence approach. This method analyses and combines a set of environmental indicators grouped into five Lines of Evidence (LoE), i.e. Biology, Chemistry, Ecotoxicology, Physico-chemistry and Hydromorphology. The whole IRA methodology has been implemented as a specific module into a freeware GIS (Geographic Information System)-based Decision Support System, named MODELKEY DSS. This paper focuses on the evaluation of the four supporting LoE (i.e. Chemistry, Ecotoxicology, Physico-chemistry and Hydromorphology), and includes a procedure for a comparison of each indicator with proper thresholds and a subsequent integration process to combine the obtained output with the LoE Biology results in order to provide a single score expressing the Ecological Status classification. The approach supports the identification of the most prominent stressors, which are responsible for the observed alterations in the river basin under investigation. The results provided by the preliminary testing of the IRA methodology through application of the MODELKEY DSS to the Llobregat case study are finally reported and discussed.

A new approach to blood pressure and blood volume modulation during hemodialysis: an adaptive fuzzy control module

The paper proposes a fuzzy logic based procedure able to control as far as possible the behaviour of the blood pressure of a patient during a dialysis session, allowing him to reach the foreseen dry weight. A PI discrete-time fuzzy control is used in order to compare the controlled variables concerning the (blood pressure and blood volume) to the reference values. Two different reference tables, concerning the pressure and volume errors and rates are introduced, then the proposed control actions are mixed in order to obtain the final value (net ultrafiltration rate). A smooth function of volemia acts on the second control variable, Na concentration in the dialysate. The adaptive control system was simulated on an IBM-PC, rules and terms were expressed by linguistic judgements like: IF “situation”, THEN “action”. A pre-processor converts the rules into the numerical values of the reference tables. The obtained simulation results are satisfactory, the introduction of the Na control allows reaching the target dry weight of the patient with a stable blood pressure.

Variable Consistency Monotonic Decision Trees

We introduce the concept of variable-consistency monotonic decision tree induced from preference-ordered data concerning a multicriteria sorting (classification) problem. Given the data in form of an information table including some sorting examples, we propose to induce a decision tree using an inductive learning algorithm. The decision tree can be considered as a preference model of a decision maker who supplied the sorting examples. Moreover, a partial violation of the dominance principle is admitted and controlled by an index called consistency level. The monotonic decision trees with variable consistency can be applied to a wide range of possible applications, for instance, financial rating, bank creditworthiness, medical diagnosis, and the like.

Interval TOPSIS for Multicriteria Decision Making

In this paper, an interval version of the classical multicriteria TOPSIS method is proposed. In particular, the so-called Bag-Based TOPSIS proposed by Rebai will be considered, and suitably modified to treat with interval number, using the acceptability index suggested by Sengupta. Interval analysis can be a powerful tool to deal with complex decision problems where the values of the criteria for each alternatives can be characterized by uncertainty.

The FEEM Sustainability Index: An Integrated Tool for Sustainability Assessment

The FEEM Sustainability Index (FEEM SI) proposes an integrated methodological approach to quantitatively assess sustainability performance across countries and over time. Three are the main features of this approach: (1) the index considers sustainability based on economic, environmental and social indicators simultaneously; (2) the framework used to compute the indicators, i.e. a Computable General Equilibrium (CGE) model, allows to generate projections on the future evolution of sustainability; and (3) the methodology used for the normalisation and aggregation of the indicators delivers a unique and comprehensive measure of sustainability. These features along with the multi-regional nature of the CGE model consent to perform policy evaluations and sustainability assessments for different countries or regions in the world. This chapter offers a methodological overview of the FEEM SI approach. To illustrate the potential of the methodology for the measurement of sustainability, the chapter also illustrates results from a climate policy scenario. In the mitigation scenario considered Annex I and Non-Annex I countries taking action towards climate change achieve the lower end of the pledges proposed at the 15th UNFCCC Conference of the Parties in Copenhagen. For countries putting into practice the policy, the environmental sphere more than offsets the related costs (economic pillar), leading to an overall improvement in sustainability. At world level, the outcome is positive even though carbon leakage in countries that are not acting reduces the effectiveness of the policy and the sustainability performance.

An Adaptive Fuzzy Control Module for Automatic Dialysis

This paper presents a fuzzy adaptive control technique to automate the dialysis procedure. The main points of this research are: use of a data base of fuzzy inference rules to formalize the medical experience, use of pre-processed lookup tables to speed up the computation and to allow for run-time changes of the inference rules, implementation of adaptive concept by means a set of performance tables, and — finally — the smooth blending of different control actions to obtain a single output action.