A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n-dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the classical Girvan–Newman (GN) modularity for crisp community detection problems and also for crisp overlapping community detection problems. Therefore, it can be used to compare partitions of different nature (i.e. those composed of classical, overlapping and fuzzy communities). Particularly, as is usually done with the GN modularity, the proposed measure may be used to identify the optimal number of communities to be obtained by any network clustering algorithm in a given network. We illustrate this usage by adapting in this way a well-known algorithm for fuzzy community detection problems, extending it to also deal with overlapping community detection problems and produce a ranking of the overlapping nodes. Some computational experiments show the feasibility of the proposed approach to modularity measures through n-dimensional overlap and grouping functions.

South European welfare regime model and the turkish case

The rise of neoliberalism and the experience of several economic crises throughout 1960’s and 70’s have opened the way to question the ability of welfare state to satisfy the basic needs of the societies. Therefore the term “welfare state” left its place to “welfare regime” in which the responsibilities for the well being of the societies are distributed among state, market and families. Following the introduction of this new term, several typologies of welfare regimes are started to be discussed. Esping-Andersen’s (1990) regime typology is considered to be one of the most significant one which covers most of the European countries. On the other hand, it has also led to criticisms for being lack of several aspects. One of them was done by Ferrera (1996), Moreno (2001), Boboli (1997) and Liebfreid (1992), which discusses that the grouping of Mediterranean countries of Europe -Greece, Italy, Spain and Portugal- within the conservative regime type. Those authors affirm that Southern European countries have their peculiar features in terms of structure of welfare provision and they form a fourth type which may be called "Mediterranean/ Southern European Regime". At this point, this doctoral thesis carries the discussion one step further and covers a profound research to answer some fundamental questions. Chiefly, clarifying whether it is possible to talk about a coherent grouping between the Mediterranean countries of Southern Europe in terms of their welfare regimes is our first objective. Then by assuming that it has an affirmative response, it is aimed to reflect the characteristics of this grouping. On the other hand, those group features are not static in time and they are sensible to various economic changes...