Application of fuzzy logic to social choice theory

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Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory. The book explains the concept of a fuzzy max. Fuzzy Choice Functions. Factorization of Fuzzy Preference Relations. Fuzzy NonArrow Results.

Application of Fuzzy Logic to Social Choice Theory

Fuzzy Arrows Theorem. Manipulability of Fuzzy Social Choice Functions. More recently, a research by Nascimento15 registers a total of social scientists in health area activities. Usually, the most used techniques to know who is who in social sciences in health has been the questionnaire and, in case of qualitative studies, the interviews. The use of other secondary sources, such as data bases, especially from CNPq, is less often. In websites of Medicine Universities and Colleges and in Research Institutes, we had access to names of professionals and, after consulting the website, we checked, grounded on inclusion criteria, whether or not they were part of the research universe.

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The other areas of the website are related to Directory of Research Groups and Institutions Directory. This search was carried out as follows: First, we opted by advanced search, individually selecting the words sociology, anthropology, political science and social sciences and selecting the filters according to education everyone should have PhD. As work area, the professionals should have health sciences as great area and collective area as work area.

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The decision to limit the research to professionals with PhD was made as a result of the research objective, attempting to know the professionals profile with full education which worked in areas of teaching, extension, research and were professionally inserted in any type of institution. In order to assure greater validity and reliability to our study, we carried out a search with institutions.

We selected institutions throughout national territory from two sites with different characteristics. One of them www. The other site www. We chose to carry out the search in commercial, unpaid websites, considering that they had the most popular Universities and Colleges among students. In both of them, we decided for a medicine course internal to Medicine Colleges, Collective Health departments or Preventive Medicine and graduation in Collective Health, places where the professionals we seek are in higher number. Such resource allowed us to find and include them in our database.

Most names we found in institutions were already selected by the search on the Lattes Platform, showing, thus, the reliability of our collection. The collected data were part of a bank at SPSS with all information related to the collected variables described above.


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Mapping relationships, building a configuration: The potential of the fuzzy logic. Grounded on collected data at the Lattes Platform, we checked the variability of professional backgrounds. Even if all professionals had in common any education in the area of social sciences, due to their undergraduate and graduate choice, there were proximities and distances related to Collective Health field and social sciences as work areas. As our interest was exactly on the professional intersection configuration between Social Sciences and Collective Health, the fuzzy logic system, which essentially reproduces the human reasoning model, in other words, a relative reasoning, enabled us to reach two objectives of our study: 1 Clarifying relationships between those diverse professional choices; and 2 Mapping those relationships related to the field of Collective Health and social sciences, generating a configuration that embodied the approximation and distance degree of those professionals with both areas.

According to Cox 16 , adopting the fuzzy logic means to carry out three fundamental operations: fuzzification; inference and defuzzification. We adjusted our study to those stages. In this regard, a text by Aguado and Cantanhede 17 , who work with those stages in a didactic way, was important for this research.

The fuzzification corresponds to the stage where data are transformed into linguistic variables. Thus, we had different possibilities related to undergraduate and graduate education of professionals in different knowledge areas, considering all uncertainties or inaccuracies 18 , The possibilities found according to professional backgrounds were described in two typological tables Table 1 and Table 2.

Table 1. Type of professionals and their respective undergraduate and graduate education, starting with social sciences as undergraduate. Caption: Social Sciences: it corresponds to social sciences, anthropology, sociology and political sciences. Collective Health: it corresponds to collective health.

Table 2. Type of professionals and their respective undergraduate and graduate education, starting with undergraduate in different areas of social sciences. Thus, we should relate each type of the Typological Table with regard to proximity or distance with both fields, information that denotes the relevance degree Figure 1. Figure 1. Configuration of a field: Graphic representation of cluster and their relational networks.

The values of those likelihoods are provided by a specialist. Thus, the Social Sciences can value or The variability of values provided to each area corresponds to distance or approximation degree related to the area of social sciences and collective health and corresponds to a process referred to as Inference. According to Von Altrock 19 , mentioned by Aguado and Catanhede 17 , such phase can be referred to as Aggregation and Composition.

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The Aggregation stage corresponds to use of the term If , production of terms that start the inference process. The second stage corresponds to the use of the term So , which defines the result after carrying out the inference. Focusing on our study, both terms translate exactly the relational aspect of choices of undergraduate and graduate courses with the fields of SS and CH.

The third and last stage corresponds to translation of two previous stages in a numerical value, in other words, the translation of a fuzzy value in a real number, according to Cox.

Thus, it was created two new variables, numerical, deterministic Not fuzzy , that represent the co-relation of each professional with the SS and CH areas. To define the relevance degree of each area, it was added, in a balanced way, the values of each of three education stages, making the defuzzification function a triple entry function Equations 1 and 2. From the created ESS and ECH variables, and with the objective of making data operational and representing the "cartography" of social scientists who work in the health area, according to the logic of relational networks of Norbert Elias, we used the cluster package of statistical software R.

Through such software, it is possible to calculate the Fanny function that defines vectorial distances between professionals related to two axes represented by Ess and Ech variables and classify them in clusters. The amount of clusters used 6 was set out according to typology empirically observed. The graphic representation of clusters was obtained through clusplot function, required as tool to analyze the co-relation between clusters and their composition and the areas of Social Sciences and Collective Health.

We submit the results obtained in this study, which allow us to visualize the configuration.

Application of Fuzzy Logic to Social Choice Theory by John N. Mordeson -

The figure composition brings the different groups, formed with undergraduate and graduate education and their relationships with other groups. Each group or cluster has its own specificities which makes it unique and represents a group of professionals and their co-relations with the area of social sciences and collective health Figure 2. Figure 2. Configuration of a field: Numerical clusters composition. Cluster 1 is located near the corresponding vector red arrows of social sciences and represents the group with greater linearity in its education, with 42 undergraduates in social sciences and most of them have both undergraduate and graduate education in social sciences.

As a result of its homogeneity, the space occupied by such cluster is very small, related to other ones, although having a greater concentration of professionals Such cluster is mostly formed by women 45 , denoting a gender specificity in professional education choice, related with studies that affirm the relationship between choices of professional areas and gender 20 , Such fact highlights the concentration of resources of state and federal governments in South and Southeastern regions, in addition to be defined as the main places that produce knowledge.

According to the National Plan for Graduate Studies 23 , up to the distribution of graduate programs in different Brazilian regions was unequal. The Southeastern region concentrated The Southern region totalized The Northern region totalized Midwest had 6.

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We have experienced nowadays a considerable increase in graduate programs specifically in collective health, and In our research, of the total of 58 professionals, 27 of them identify themselves as working in anthropology area and 14 in sociology, only 10 mention collective health as their work area, even if institutionalized in School of health area or Collective Health Departments, Preventive and Social Medicine or Research Institutes of health area.

Such fact emphasizes the importance of professional education background as the bases of professional identity that often exceeds the professional institutionalization. Cluster 2 concentrates a total of 38 subjects, 26 of them are female and 12 are male, including professionals with education in social sciences and collective health. Such professionals represent exactly the intersection between both areas in professional education choices.

Located near the end of the vector of collective health, as a result of greater number of professionals with two educations in collective health other than with one education in collective health and two in social sciences, this group is places closer to collective health, in addition to have a greater space comprehension, exactly due to variance of combinations. Because they are greater to the collective health vector, the importance of education related to work area is reinforced, as 25 professionals mention collective health as their work area.

Cluster 3 is formed by 57 subjects, 36 of them are female and 21 are male, mostly formed by professionals with education in areas of human sciences and social sciences and, in smaller number, with education in social sciences and collective health. As a result of its composition, cluster 3 has an elliptical form to comprehend the human sciences area, which is closer to social sciences than to collective health, but with some professionals with education in collective health, which justifies its form, its approximation of SS component vector and relative approximation of collective health.

His research interests include fuzzy math spatial modeling, comparative politics, international relations, social network analysis, and intelligence analysis. Du kanske gillar. Inbunden Engelska, Spara som favorit. Skickas inom vardagar. Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.

The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the "union" conorm of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow's theorem, and Black's median voter theorem for fuzzy preferences.