Fabrizio Maturo

Fuzzy Regression Models and Alternative Operations for Economic and Social Sciences

The economic and social research is often based on assumptions that have little to do with reality, because all scientific knowledge of the Western world is based on the Aristotelian binary logic. Often researchers use rigid conventions and treat things as if they were black or white, but the world around us is nuanced, in other words, is fuzzy. In particular, problems inherent the inaccuracy of measurements and the vagueness of linguistic attributes has led many scholars to consider the fuzzy theory during the recent decades. In this paper we face a particular aspect of fuzzy logic, that is, fuzzy regression. After a brief review of the recent studies about this topic, we focus on some limitations of the previous approaches and suggest some possible solutions. Specifically, we propose the use of alternatives operations to solve some problems of addition and multiplication between fuzzy numbers in fuzzy regression models.

Research in Social Sciences: Fuzzy Regression and Causal Complexity

Social science research is now primarily divided into two types: qualitative, or case-oriented research, focused on individual cases, which reviews all aspects of a few case studies and quantitative, or variable-oriented research, which considers only some quantitative aspects (variables) of a large number of cases and is looking for correlations between these variables.

Bell-Shaped Fuzzy Numbers Associated with the Normal Curve

Statisticians often focus on fuzzy numbers with triangular or trapezoidal membership functions because they are very easy to apply. Although they offer a good approximation of a fuzzy variable, several doubts arise about the appropriateness of these kind of shapes. As known, fuzzy sets are useful for interval data when the “degree of truth” of the values varies within this range. In particular, they are desirable for translating human language into numbers. In this paper, we propose an alternative membership function that appears more appropriate to deal with linguistic variables. We refer to this function as “bell-shaped fuzzy number associated with the normal curve”. In particular, we highlight the specific properties of the proposed fuzzy number and illustrate the utility of linking this function with the normal distribution.

Fuzzy Events, Fuzzy Probability and Applications in Economic and Social Sciences

In the subjective approach to the theory of probability, conditional events are always considered as propositions in a three valued logic (De Finetti in Teoria delle probabilita. Einaudi Editore, Torino, 1970; Coletti and Scozzafava in Probabilistic logic in a coherent setting. Kluwer Academic Publishers, London, 2002). Assuming a particular algebraic representation, we propose a definition of fuzzy event that generalizes the concepts of conditional event. Moreover we present some applications of fuzzy events in Social Science, e.g. in Decision Making under uncertainty. Generalizing the subjective approach to conditional probability by De Finetti, we propose some possible subjective definitions of fuzzy probability that are coherent with the axiomatic approach by Dubins to the finitely additive conditional probability. We propose some interpretations of fuzzy probability in Social Sciences, e.g. as an extension of a utility function. Finally, we explore some possible extensions of such concepts, defining fuzzy event and fuzzy probability of type 2 and we look for possible applications in Social Sciences, in particular in fuzzy decision making.

Finite geometric spaces, Steiner systems and cooperative games

Abstract Some relations between finite geometric spaces and cooperative games are considered. The games associated to Steiner systems, in particular projective and affine planes, are considered. The properties of winning and blocking coalitions are investigated.

Do Institutional or Foreign Shareholders Influence National Board Diversity? Assessing Board Diversity Through Functional Data Analysis

This study analyses the external antecedents of board diversity. We use the resource-based view and the agency theory to investigate the impact of institutional and foreign shareholders on national board diversity. Because we highlight that the most used diversity indices neglect the multidimensional aspect of diversity, we refer to diversity profiles and suggest the functional data analysis approach for diversity assessment in corporate governance studies. Specifically, we use the parametric functional analysis of variance in analysing the influence exerted by institutional and foreign shareholders on national board diversity. Focusing on a sample of 1,230 Italian medium-large firms, our results show that institutional shareholders do not influence national board diversity, while foreign shareholders strongly affect it, especially when they hold more than 50% of shares. Thus, we address the research gap on the determinants of national board diversity and enrich comparative European research on this topic.

Consensus in Multiperson Decision Making Using Fuzzy Coalitions

We consider the problem of group decisions, in which decision-makers have different opinions or interests. This study proposes various metric spaces for representing the movements of decision-makers for reaching consensus. We also introduce the concept of fuzzy coalition for developing an algorithm for building a feasible fuzzy coalition, which is defined as the union of winning maximum coalitions which solve the issue of consensus among decision-makers.

Expected Present and Final Value of an Annuity when some Non-Central Moments of the Capitalization Factor are Unknown: Theory and an Application using R

The aim of this chapter is the development of three approaches for obtaining the value of an n-payment annuity, with payments of 1 unit each, when the interest rate is random. To calculate the value of these annuities, we are going to assume that only some non-central moments of the capitalization factor are known. The first technique consists in using a tetraparametric function which depends on the arctangent function. The second expression is derived from the so-called quadratic discounting whereas the third approach is based on the approximation of the mathematical expectation of the ratio of two random variables by Mood et al. (1974). A comparison of these methodologies through an application, using the R statistical software, shows that all of them lead to different results.

Nationality Board Diversity in Organizations: A Brief Review and Future Research Directions

In recent decades, many studies have focused on the issue of diversity in organizations due to the increasing interest on its possible impact on firms’ performance and other organizational aspects. Because of the growing globalized markets, greater mobility, and demographic developments which are bringing more people to work with others who differ in cultural, demographic, informational, and personality attributes, scholars have concentrated on various type of team variety within organizations, e.g. gender, nationality, educational, age, ethnicity, and race. Despite the different goals of these researches, most insiders agree that diversity plays an essential role for the efficacy of management and decisions, long term prosperity, and ability to develop relationships with the external environment. Nevertheless, the findings of many studies are conflicting and suggest a negative role of diversity. For these reasons, this paper, focusing on one aspect of organizational variety, i.e. nationality diversity, aims to propose a brief review of the main existing studies on this topic. The final purpose of this contribution is to discuss and understand what are the results and limits of these studies.

On Consistency and Incoherence in Analytical Hierarchy Process and Intertemporal Choices Models

A rational choice is based on conditions of coherence, that are universally accepted rules to which a decision-maker must comply in expressing his/her preferences. In this paper, we focus on two different approaches in decision-making processes, i.e. the Analytical Hierarchy Process and Intertemporal Choices models, highlighting the consistency conditions usually adopted. After a general discussion on consistence and incoherence in the framework of these two different approaches, we show that sometimes it is preferable to weaken or reinforce coherence conditions according to the specific context.