This paper presents the development of two of the eight indicators to evaluate the Country Wellbeing. We start from the Stiglitz document (2009) that for the first time puts a fixed point on what are the indicators that, aggregated, produces a multidimensional description of wellbeing that goes beyond GDP. Following the document indications, we present a fuzzy approach for this measure as a proposal that overcome the deficiencies that the usual statistical methods produce. The country we have in mind is Italy, but the instrument we propose is not calibrate on this country, but may be useful for every country that share the Stiglitz document indications. The fuzzy instrument we propose is a fuzzy inference system that, by its rule-blocks, let the possibility to use verbal judgement about the importance of one input respect the others.

In this paper we propose a general procedure to represent a fuzzy set that may be non-normal and/or non-convex. This representation will be offered by an interval and a crisp value. This idea is useful either in optimization and decision making problems or in defuzzification step of a fuzzy inference system. This proposal, depending on some parameters, either offers new methods or contains previous ones present in literature.

In this paper, we associate a probability distribution to a fuzzy variable represented by a continuous fuzzy quantity, where a fuzzy quantity is a fuzzy set that may be nonnormal and/or nonconvex. Our proposal is quite general and contains as particular cases other transformations presented in the literature. Furthermore, we define the variance of a fuzzy quantity as the variance of the probability distribution associated with it. The proposed variance agrees in the case of fuzzy numbers with the possibilistic one introduced by Irina Georgescu. We also apply our transformation to the evaluation of fuzzy quantities. The expected value of such probability distribution agrees with those introduced for fuzzy numbers by other authors; moreover, it matches the defuzzification value of a fuzzy quantity proposed by the same authors in other papers. To capture more information contained in a fuzzy quantity, or for ranking problems, we suggest to evaluate it by means of the pair mean variance, using the probability distribution associated with it. To illustrate how our method works, we apply it to evaluate the financial risk tolerance of a bank client using a fuzzy inference system.

In this paper we propose a new evaluation/defuzzification formula for an Interval Type-2 Fuzzy Quantity (IT2 FQ), that is an Interval Type-2 Fuzzy Set (IT2 FS) defined by two Type-1 Fuzzy Quantities (T1 FQs) having membership functions that may be neither convex nor normal. We start from a parametric formula to evaluate them and we propose to call the IT2 FQ value their average. To compare the results we obtain changing the parameters, we use the final output of an example of Interval Type-2 Fuzzy Logic System (IT2 FLS).

In this paper we propose a method to defuzzify an intuitionistic fuzzy quantity that, depending on two parameters, recover previous methods and leaves freedom to the user

In this paper we present a new general framework to face the problem of evaluating fuzzy quantities. A fuzzy quantity is a fuzzy set that may be non-normal and/or non-convex. It is based on the idea of “interval approximation of a fuzzy number”. The classical approach followed for fuzzy numbers is not pursuable in a fuzzy quantity context but anyway our proposal produces an interesting general formulation that offers the opportunity to create many different types of evaluations as it depends on several parameters.

In this paperwepresent a parametric formulation of interval approximation of fuzzy numbers. It is based on a more complex version of generalized Trutschnig et al. distance. General conclusions are showed and particular cases are studied in details.

The concept of possibilistic mean value and variance of fuzzy numbers has been applied to investment decisions by using a nonlinear type of fuzzy numbers called adaptive fuzzy numbers. In this paper, by extending the notion of adaptive fuzzy number, we propose a more flexible methodology. Our aim is to allow decision maker more flexibility in dealing with ambiguity and uncertainty. To illustrate the use of our approach and its ability in dealing with ambiguity and imprecision we analyze, as an application, the fuzzy net present value of future cash flows and give some numerical results.

We deal with the problem of evaluating and ranking fuzzy quantities. We call fuzzy quantity any non-normal and non-convex fuzzy set, defined as the union of two, or more, generalized fuzzy numbers. For this purpose we suggest an evaluation defined by a pair index based on “value” & “ambiguity”. Either value or ambiguity depend on two parameters connected the first with the optimistic/pessimistic point of view of the decision maker and the second on an additive measure that can be used to express the decision maker's preferences.

In this paper we propose a cardiovascular risk diagnosis model based on non additive measures (fuzzy measures) and the Choquet integral. To this purpose, an ad hoc questionnaire was submitted to a set of doctors, from which a set of measures was elicited. The answers were then aggregated together in the spirit of consensus and an unique fuzzy measure was obtained. Again, the criteria used for the diagnosis were transformed using suitable membership functions. A cardiovascular disease risk index was then introduced as the Choquet integral of membership functions with respect to the fuzzy measure. A sensitivity analysis was performed too.

In this paper we propose a parametric way to associate to an interval-valued fuzzy set its evaluation useful for its ranking. The novelty of this paper is connected with the fact that we follow a line based on its alpha-cuts and the parametric formulation we obtain, leaves to the decision maker a wide freedom. For particular values of these parameters we obtain Nie and Tan defuzzification method that, in its classical definition, shows only the evaluation, but looking at it in this new version we obtain further information. The proposed methodology is then applied to risk profiling of a bank client using an interval type-2 fuzzy logic system.

In this paper we present a general framework to face the problem of evaluate fuzzy quantities. A fuzzy quantity is a fuzzy set that may be non normal and/or non convex. This new formulation contains as particular cases the ones proposed by Fortemps and Roubens (1996), Yager and Filev (1981,1999) and follows a completely different approach. It starts with idea of “interval approximation of a fuzzy number” proposed, e.g., in Chanas (2001), Grzegorzewski (2002,2012).

We deal with the problem of evaluating and ranking intuitionistic fuzzy quantitities (IFQs). We call IFQ an intuitionistic fuzzy set (IFS) described by a pair of fuzzy quantities, where a fuzzy quantity is defined as the union of two, or more, convex fuzzy sets that may be non-normal. We suggest an evaluation defined by a pair index based on “value” & “ambiguity” and a ranking method based on them. This new formulation contains as particular cases the ones proposed by Fortemps and Roubens, Yager and Filev and follows a completely different approach.

In regard to the LEADER program (European Union initiative for rural development), in the paper the authors propose a model for assessing the governance system of Local Action Groups (LAGs) in terms of structure, decision making processes and principles that ensure a clear and transparent activity thus creating significant value for the community. Governance, in particular, is a highly important theme when it evaluates the impacts of LEADER measures: if the quality of their governance is high, they could contribute to make the rural development process more efficient in each region of EU. The empirical literature on this subject is not well developed and the authors hope and expect that this new assessment model will produce important ideas for making governance of the LAGs more effective. It is based on a Fuzzy Expert System and here are presented results for Puglia (Italy) LAGs.

Negli ultimi dieci anni gli Enti locali italiani hanno usato i derivati finanziari per la gestione delle loro passività. Il presente lavoro illustra i risultati di una recente ricerca avente per oggetto lo studio della diffusione dei derivati finanziari nei comuni del Nord Salento e del loro effetto sui bilanci delle amministrazioni interessate. Si presentano inizialmente le definizioni di liability management e di derivati finanziari, con particolare attenzione ai contratti IRS, quindi se ne illustrano le caratteristiche principali e le logiche di funzionamento. Per la realizzazione del progetto sono stati reperiti tutti i contratti sottoscritti dai dieci comuni del Consorzio Valle della Cupa – Nord Salento. Tali contratti sono stati analizzati e per ciascuno di essi è stata valutata la convenienza economica. Ai fini della valutazione finanziaria è stata utilizzata la metodologia dei tassi forward impliciti, impiegando la tecnica del bootstrap per la stima dei tassi futuri. I dati utilizzati in ingresso nel metodo del bootstrap sono stati i tassi Euribor per il breve termine ed i tassi Eurirs per il lungo termine. Il presente studio si propone come un valido ausilio alle amministrazioni locali per le scelte strategiche nelle politiche di liability-management.

We propose a definition of mean value and variance for fuzzy numbers whose membership functions are upper-semicontinuous but are not necessarily continuous. Our proposal uses the total variation of bounded variation functions.

We propose a new definition of mean value and variance for fuzzy numbers whose membership functions are upper-semicontinuous but are not necessarily continuous. Our proposal uses the total variation of bounded variation functions. The proposed concepts are used for the evaluation of insurance contracts and real options in a fuzzy framework.

We propose a model for the pricing of the minimum guarantee option embedded in equity-linked life insurance policies under uncertainty of randomness and fuzziness. The future lifetime of the insured is modelled as a random variable and the asset price evolu- tion is described using a fuzzy binomial-tree model. In order to deal with both randomness and fuzziness, we model the present value of liabilities as a fuzzy random variable. Our re- sults can be used by the actuary to understand the incidence of the minimum guarantee on the premium and to define the appropriate coverage strategies. A numerical example illustrates how our methodology works.

In this paper we present an innovative procedure to reduce the number of rules in a Mamdani rule-based fuzzy systems. First of all, we extend the similarity measure or degree between antecedent and consequent of two rules. Subsequently, we use the similarity degree to compute two new measures of conflicting and reinforcement between fuzzy rules. We apply these conflicting and reinforcement measures to suitably reduce the number of rules. Namely, we merge two rules together if they are redundant, i.e. if both antecedent and consequence are similar together, repeating this operation until no similar rules exist, obtaining a reduced set of rules. Again, we remove from the reduced set the rule with conflict with other, i.e. if antecedent are similar and consequence not; among the two, we remove the one characterized by higher average conflict with all the rules in the reduced set.

Formulazione ed implementazione di un modello stocastico per l'analisi e la previsione dei flussi turistici nella provincia di Lecce

In this paper, we present a different approach to introduce evaluation and ranking of fuzzy quantities. These general fuzzy sets are obtained by the union of several fuzzy sets. They are neither normal nor convex. The idea we have followed is to use the total variation and the bounded variation function definitions applied to the membership function of a fuzzy set to introduce its evaluation. This approach has produced that the well-known method of area compensation, introduced by Fortemps and Roubens only in a geometrical framework, is now presented in a general contest and useful for any fuzzy set. Moreover, this new representation formula provides an α-cut view. This aspect, absent in Fortemps and Roubens paper, offers an evaluation by a weighted average of alfa-cuts values, where the weights are connected with the number of subintervals that produce every α-cut. Following the same idea, we have introduced the ambiguity definition of a general fuzzy set. By this new definition of evaluation and the consequent ambiguity, we present a way to rank fuzzy quantities.