Aggregating fuzzy subgroups and T-vague groups

Fuzzy subgroups and T-vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T-vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T-indistinguishability operators (fuzzy equivalence relations). In this paper the functions that aggregate fuzzy subgroups and T-vague groups will be studied. The functions aggregating T-indistinguishability operators have been characterized [9] and the main result of this paper is that the functions aggregating T-indistinguishability operators coincide with the ones that aggregate fuzzy subgroups and T-vague groups. In particular, quasi-arithmetic means and some OWA operators aggregate them if the t-norm is continuous Archimedean.Peer ReviewedPostprint (author's final draft

OWA-based fuzzy m-ary adjacency relations in Social Network Analysis.

In this paper we propose an approach to Social Network Analysis (SNA) based on fuzzy m-ary adjacency relations. In particular, we show that the dimension of the analysis can naturally be increased and interesting results can be derived. Therefore, fuzzy m-ary adjacency relations can be computed starting from fuzzy binary relations and introducing OWA-based aggregations. The behavioral assumptions derived from the measure and the exam of individual propensity to connect with other suggest that OWA operators can be considered particularly suitable in characterizing such relationships.reciprocal relation; fuzzy preference relation; priority vector; normalization

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP

On the relationship between fuzzy subgroups and indistinguishability operators

Fuzzy subgroups are revisited considering their close relationship with indistinguishability operators (fuzzy equivalences) invariant under translations. Different ways to obtain new fuzzy subgroups from a given one are provided and different ways to characterize normal fuzzy subgroups are obtained. The idea of double coset of two (crisp) subgroups allow us to relate them via their equivalence classes. This is generalized to the fuzzy framework. The conditions in which a fuzzy relation R on a group G can be considered a fuzzy subgroup of G × G are obtained.Peer ReviewedPostprint (author's final draft

Fifty years of similarity relations: a survey of foundations and applications

On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft

Multidimensional Poverty Comparisons within Europe. Evidence from the European Community Household Panel

This paper is a cross-sectional study on multidimensional poverty comparisons among the European Union countries, based on data provided by the European Community Household Panel (ECHP). In addition to the empirical results and the methodological problems, the study underlines the opportunities and the difficulties met while using the ECHP. The extended concept of poverty is relative and multidimensional and it reflects not only the financial aspects, but also dimensions like family composition, leisure, subjective deprivation, social participation, durable goods, housing conditions, access to education. Hence, it requires comparative assessments through ordinal measures. In order to compare the multidimensional poverty in 1999 and in a time interval (1994-1999), we have applied the Totally Fuzzy and Relative Method (TFR) in two forms: original (Cheli and Lemmi, 1995) and alternative (Cheli, D’Agostino and Filippone, 2001). The research reveals the hierarchy of countries according to different indicators of poverty. Although the rankings given by the two methods are similar in some parts, there are differences establishing the issues which arise when different features of deprivation are aggregated into a collective index. We show that the variables taken into account, the method and its interpretability, the data and the national particularities, they all have a big influence on the relative and comparative measurement of poverty.multidimensional poverty ; fuzzy set theory ; poverty comparisons ; poverty measurement ; well-being assessment

Winning Ideas: Lessons from Free-market Economics

Agency is inescapably plural in both concept and measurement. In Sen’s account of agency, i) agency is exercised with respect to goals the person values; ii) agency includes effective power as well as direct control; iii) agency may advance wellbeing or may address other-regarding goals; iv) to identify agency also entails an assessment of the value of the agent’s goals; v) the agent’s responsibility for a state of affairs should be incorporated into his or her evaluation of it. This chapter refracts the literature on agency measurement through the first four of these characteristics, showing how particular survey-based measures of individual agency elucidate or obscure each distinction. It also observes that existing measures used in development tend to focus on control but not effective freedom, on goals the agent has reason to value rather than goals she values, and on own rather than other-regarding agency. The literature on measurement also raises a number of very relevant issues for the conceptual approach.

A subgroup decomposition of inequality of poverty in Cameroon

This paper studies multi-dimensional aspects of deprivation associated to the living conditions and inequality status in Cameroon. The study employs the fuzzy-set framework to analyze deprivation and inequalities through Dagum sub group decomposition. Results in deprivation analysis and inequalities related reveal some new insights about the poverty situation in the country, which contrasts with the results available from traditional poverty analysis. We observe respectively, high deprivation degrees for household ‘essential’ items such as health, education and housing and a small Gini index for inequalities of deprivation. Decomposition by group reveals that within groups inequalities are as important as the between groups

A subgroup decomposition of inequality of poverty in Cameroon

This paper studies multi-dimensional aspects of deprivation associated to the living conditions and inequality status in Cameroon. The study employs the fuzzy-set framework to analyze deprivation and inequalities through Dagum sub group decomposition. Results in deprivation analysis and inequalities related reveal some new insights about the poverty situation in the country, which contrasts with the results available from traditional poverty analysis. We observe respectively, high deprivation degrees for household ‘essential’ items such as health, education and housing and a small Gini index for inequalities of deprivation. Decomposition by group reveals that within groups inequalities are as important as the between groups

Measuring Poverty as a Fuzzy and Multidimensional Concept: Theory and Evidence from the United Kingdom

Previous research shows that poor people define poverty not only in material terms, but also in psychological and social terms, though it has been consistently characterized by economic resources in social sciences. Using a method based on `fuzzy-set' theory can be uniquely placed to answer the question as it allows us not only to tackle the problem of arbitrary poverty line, but also to integrate multiple dimensions into one index in an intuitive way. It can avoid the problem of poverty line entirely by introducing the concept of `membership function' which represents a degree of inclusion in a fuzzy subgroup poor. I therefore argue that the fuzzy measures of poverty can be a strong multidimensional alternative for the measures centered around income. To support the argument, two crucial points are clarfied. Firstly, the difference between traditional measures and the fuzzy measures needs to be discussed further since the discussions on the new measures so far lean more toward the fresh insights from the measures, so that the distinction in policy-relevant information has not been emphasized enough. From the comparison, I present that the fuzzy measures can provide a richer description of the social phenomenon, enabling a more acceptable distinction between different sub-populations. Secondly, how the measures behave statistically should be considered in depth because one of the most frequent critiques for poverty measurements is that present methods depend too much on arbitrary decisions like setting a poverty line. Utilizing a Monte Carlo simulation, I find that the measures (Totally Fuzzy, Totally Fuzzy and Relative, and Integrated Fuzzy and Relative) acknowledge two points quite well: (i) poverty is a multidimensional concept, and (ii) the `poor' and `non-poor' are not two mutually exclusive sets and the distinction can be `fuzzy'. It also turns out that the sampling distribution of the fuzzy measures is well-behaved, and they are robust to arbitrary choice in the estimation as well as reliable with relatively small sample size. Besides, I show that they are robust to measurement errors. Finally, I investigate the identification performance of each measure and show that the measures have a strong consistency