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.

È da molto tempo che gli studiosi di scienze sociali segnalano la necessità di un indicatore economico che vada oltre il concetto di PIL. Da più parti si propone di pensare questo indicatore come frutto dell’aggregazione di più indicatori che non tengano conto solo di aspetti economici, ma anche di altri, al fine di valutare la piena sostenibilità di un sistema economico. Lo studio di cui presentiamo la fase iniziale, prende lo spunto dal lavoro promosso ed avviato nel 2009: il Progetto “Oltre il PIL” che ha come obiettivo la revisione della misurazione tradizionale del benessere individuando nuovi indicatori al fine di fornire un supporto analitico alle scelte strategiche degli attori economici e delle istituzioni, per formulare politiche sostenibili in tema sociale, economico, fiscale e ambientale.

The “Solvency II” directive will be enforced starting from 2016. The insurance and reassurance companies have asked to reflect upon ways of adapting to the new rules and to consider value creation strategies under the new constraints. An Observatory was started for understanding how open Italian insurance companies are to change and how the announced rules influence the current operations. In order to monitor the behaviour of the companies over the years and evaluate the responsiveness to the new regulatory requirements of the Italian insurance Companies, a Fuzzy Expert System (FES) was developed. The objective of this work is to show the evaluation / monitoring tool created for the observatory. The special feature of the FES is to be created exclusively on judgments and not on objective data

The new impulse from European Commission’s “Beyond GDP” and the Stiglitz, Sen and Fitoussi’s report renewed the necessity to define new indicators of wellbeing that go beyond GDP, and increased the need of measuring complex dimensions of living not measurable with classical techniques. Concepts as quality of life, child well being, health are mediated by human perception and intangible evaluation. A fuzzy logic approach gives the opportunity to face these problems thanks to its capability to work in a framework of uncertainty, ambiguity and vague information, situations that are typical of social and human problems. This paper provides the results based on different socioeconomic surveys with the use of fuzzy logic.

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.

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 deal of the method to evaluate the health level in Italy. This method SF12 has been proposed by US administration for his population and the major part of the world now, use the same method. This paper deals with the problem this approach may present and proposes a new method based on fuzzy logic.

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.

A significant threat to the natural and cultural heritage of Mediterranean natural protected areas (NPAs) is related to uncontrolled fires that can cause potential damages related to the loss or a reduction of ecosystems. The assessment and mapping of the vulnerability to fire can be useful to reduce landscape damages and to establish priority areas where it is necessary to plan measures to reduce the fire vulnerability. To this aim, a methodology based on an interactive computer-based system has been proposed in order to support NPA's management authority for the identification of vulnerable hotspots to fire through the selection of suitable indicators that allow discriminating different levels of sensitivity (e.g. Habitat relevance, Fragmentation, Fire behavior, Ecosystem Services, Vegetation recovery after fire) and stresses (agriculture, tourism, urbanization). In particular, a multi-criteria analysis based on Fuzzy Expert System (FES) integrated in a GIS environment has been developed in order to identify and map potential “hotspots” of fire vulnerability, where fire protection measures can be undertaken in advance. In order to test the effectiveness of this approach, this approach has been applied to the NPA of Torre Guaceto (Apulia Region, southern Italy). The most fire vulnerable areas are the patch of century-old forest characterized by high sensitivity and stress, and the wetlands and century-old olive groves due to their high sensitivity. The GIS fuzzy expert system provides evidence of its potential usefulness for the effective management of natural protected areas and can help conservation managers to plan and intervene in order to mitigate the fire vulnerability in accordance with conservation goals.

This paper wants to provoke the people showing a new research field of application of Soft Computing Techniques. In this case we propose Fuzzy Inference Systems. This type of approach has never been applied to problems of International affairs or to Intelligence and Security. This research is proposed by a research Centre on Fuzzy Logic born at Link Campus University in Rome*. The problem we face is connected with what happened in Mediterranean sea under the denomination of "Arab Spring". Our idea is to build a Fuzzy Inference System, which not only describe but is also able to monitor what it is happening in an area that is complex for the connection among many countries which are different for cultures, religions and economic factors. This new instrument can help either International Organizations and local authorities to have a more clear idea of what is really happening. The final goal is always the maintain peace and to work for a well-timed diplomatic intervention to avoid that the situation crashes in a war. We have started with Lybian situation to get to a more general painting of any country in the same area.

Purpose – This study aims to build and test an International Market Selection (IMS) decision process method that is able to capture, within a small firm’s risk-averse setting, the entrepreneur's experience, reduce cognitive biases, and preserve the flexibility of the decision, by combining the advantages of systematic and behavioural-based international market selection approaches. Design/methodology/approach – The unit of analysis is the IMS decision process of a small firm venturing abroad. We adopt a ranking approach based on three-step screening. We assess the markets through a multi-criteria approach with a wider set of variables aggregated within a tree-shaped model. To obtain the ranking, we use a Fuzzy Expert System (FES) as an evaluative tool. Findings – The results show that the proposed decision method is consistent with the entrepreneur’s strategic orientation and experience, while preserving the flexibility requested for decision-making in small firms. Unlike traditional behavioural IMS approaches, the method demonstrates an ability to reduce the cognitive biases associated with the use of a limited set of variables and unreliable evaluation models. Research limitations/implications – The single-case-study approach limits generalization of the findings. Practical implications – The proposed methodology helps the decision-maker to improve the quality of the IMS decision by reducing the effect of cognitive biases that usually affect traditional behavioural models. Originality/value – For the first time, a decision-process methodology based on an FES is applied to a small firm’s IMS problem.

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.

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.

The capability of living a healthy life can be considered a key dimension in the construction of individual well-being. It is itself the outcome of a complex sets of indicators including also subjective indicators. This paper measures health at individual level by using fuzzy logic to keep the complexity of its definition while providing a crisp indicators of the level of health that can be disaggregated in relevant intermediate variables. The system has been implemented on Italian Istat survey on health conditions and the results show a higher gender inequality in the level of health than it can be obtained by using traditional techniques to measure health. We do find that controlling for age, still women are characterized by poorer health conditions. Data disaggregated by regional area show variability in the outcome that can be connected to the different policies enacted across regions.

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.

This paper focuses on the definition and measurement of quality of work (QoW) using a multidimensional approach, based on fuzzy logic. The multidimensional nature of quality of work has been widely acknowledged in economic and sociological literature and attempts at measuring its different dimensions can be found at European level in the work carried out by the European Foundation for the Improvement of living and working conditions. The European Commission and the International Labour Office have also identified different dimensions for quality of work and proposed new indicators to measure them. In this paper an attempt is made to maintain the complexity of the quality of work concept by using a technique that allows measurement without introducing too strong assumptions and makes the rules for judging the different dimensions of QoW and their interactions explicit.

The aim of this paper is to present a brief sketch of what has been a wide project funded by the Puglia region with a group of researchers at the University of Salento. The purpose of the project was to provide three indexes that are based on the principle of sustainability and gender equality as a new tool to address public policies. Here we will focus our attention on one particular index definition and evaluation in a fuzzy way. This index we named Life would offer, in an aggregated way, an evaluation of the connection between quality of daily work and life.

This paper follows in the study of the building of children' social interaction with parents using the capability approach. Parents' role in child well being is well documented by evolutionary psychology and psychoanalysis, here we will try to put in relation and to come to a measure of different factors that can affect its development. We propose a fuzzy expert system to measure this capability both at a theoretical and empirical level. The applied part of the paper use a data set based on a matched data source of ISTAT (Italian National Statistical Office 2008) multipurpose survey on family and on children condition in Italy to recover information on children’s education, the socio-demographic structure of their families, child care provided by relatives and parents according to the type of activities in which the children are involved, and Bank of Italy Survey on household income and wealth year 2008 (SHIW08) to control how family income may enter in the final evaluation This is one step of a more complex system allowing for a richer set of indicators and of dimension of child well being as well as for their interaction.

This paper follows in the study of the building of children' social interaction with parents using the capability approach. Parents' role in child well being is well documented by evolutionary psychology and psychoanalysis, here we will try to put in relation and to come to a measure of different factors that can affect its development. We propose a fuzzy expert system to measure this capability both at a theoretical and empirical level. The applied part of the paper use a data set based on a matched data source of ISTAT (Italian National Statistical Office 2008) multipurpose survey on family and on children condition in Italy to recover information on children’s education, the socio-demographic structure of their families, child care provided by relatives and parents according to the type of activities in which the children are involved, and Bank of Italy Survey on household income and wealth year 2008 (SHIW08) to control how family income may enter in the final evaluation This is one step of a more complex system allowing for a richer set of indicators and of dimension of child well being as well as for their interaction.

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.