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  Volume: 02, October 2013, Pages: 167-176 International Journal of Computing Algorithm Integrated Intelligent Research (IIR) 167 FUZZY SET THEORY APPROACH TO SOCIO-ECONOMIC STATUS OF MIGRATED STUDENTS STUDYING IN CHENNAI, USING AMARTYA SEN’S FUNCTIONING MULTIDIMENSIONAL PARADIGM Raj Kumar, T. Pathinathan Department of Mathematics, Loyola College, Chennai, Tamil Nadu, India.  Abstract  Migration of any kind creates social exclusion in society, leading to inability to participate in economic, social, and cultural life, and in some characteristics, alienation and distance from mainstream society. Migration of students is one the burning social issues today, which finally affects the academic progress and level of performance of the students.The main purpose of this paper is to suggest practical implementation of Sen’s capability approach that is able to preserve its interpretative reality and methodological problems that couldn’t find an operative solution in more standard approaches to migrated students and their socio-economic well-being analysis. A strategy based on fuzzy sets theory has been suggested to analyze why this kind of approach could be useful  for dealing with the complexity of a multidimensional assessment of well-being. Finally, the analysis depicts that the student community and their well-beings in terms of safe living, educations, social and  psychological well-being is affected very badly. Key words:   Capability approach, Functioning’s, Multidimensional analysis of well-being, Fuzzy Set.   1. Introduction India is a country having within itself a multi-cultural and multi-ethnic society. ‘Unity in Diversity’ is the jargon that is repeated often on stage. Migrated Students, all over the world, face certain difficulties and challenges yet there are certain specific regional flavors to their new demands. The issue analyzed through this paper is on the well-being of migrated students living mainly in Chennai city. A study has been conducted with college students migrated from Tibet, South Africa, Bangaladesh, Sri Lanka, East Timor, Bihar, Jharkhand, Udisha, West Bengal, Assam, Chhatisgarh, Andaman-Nikobar, Meghalaya, Tripura, Nagaland, Manipur, Mizoram, Delhi and Uthrapradesh. Majority of the migrated students think of themselves or feel treated by others as ‘different’. Why do the majority of migrated students made to think or feel ‘different’? Spoken language, physical appearance, dress habits, food habits, cultural traits and level of social security and economic independence are some of the attributes that differentiates migrated students from other students. 2. The Well-Being Concept The well-being is defined in association with one’s current standard of life and it is not an easy concept to express it in clear cut terms and definitions. Initially it has been measured through the income per capita, but this showed itself to be insufficient to explain such a complex concept. The capability approach, introduced by A. Sen, looks at freedom, human rights and defines human well-being in terms of functioning and capabilities, where functioning are achievements of human well- being and capabilities the ability to achieve them. Well-being refers to being able to live a long, healthy and educated lifestyle that is locked within a decent social security system that one is allowed to and capable to use. A vast variety of measurements, such as average life expectancy, school enrollment and literacy rates for example, can be used in this discussion. However, the question of how to  Volume: 02, October 2013, Pages: 167-176 International Journal of Computing Algorithm Integrated Intelligent Research (IIR) 168 measure the happiness of student or children is not easily resolved. The dimensions depend on the availability of data and the distinction  between doing well and being well has to be emphasized throughout the research. The following dimensions of well-being were established by UNICEF to examine “child well-being”    Material well-being    Health and Safety    Educational well-being    Relationships    Behaviors and Risks    Subjective well-being Those are neat categories, but it is not always clear whether a particular characteristic is a  problem or only correlated with one. Thus, very different outcomes can be found throughout the report. Well-being can be explained as the following function: Well-being of migrant children = f (H, B, C, D)  where  H   is the vector of human capital variables, for example age, health care access, educational opportunities,  B  stands for demographic and economic characteristics such as gender and race. C can  be the vector of the country of srcin and  D  captures the effects that are particular to immigrant groups. 2.1 Social Responsibility as well-being:  Some quotes on Social responsibility: "Social responsibility-that is, a personal investment in the well-being of others and of the planet-doesn't just happen. It takes intention, attention, and time."   -- Sheldon Berman, "Educating for Social Responsibility," Educational Leadership,  November 1990. "Students can and should be given opportunities to take part in the significant events in their world. As teachers, we can create very powerful opportunities for our students, both in the classroom and extending into the larger world….We can help them understand processes of group decision making and the political process. And, we can structure ways for them to participate in the empowering experience of acting to make a real difference in the world." --ESR's Making History. Some may question Berman's definition of social responsibility. What constitutes "well- being"? Exactly who are the "others"? Will the well-being of others be promoted by free trade agreements? By immigration reform? Thus, Well-being means different things to different  people. 2.2 Sen’s Functioning Multidimensional Approach to Well-being Sen frequently uses the well-being of someone with ability of someone who can achieve  with a given amount of wealth, depends on certain conditions, and any measure of inequality has to take these “conversion factors” into account, focusing on outcomes rather than means. 2.2.1   Sen’s Capability Theory  The capability approach was initially conceived in the 1980s as an approach to welfare economics. In this approach, Amartya Sen brought together a range of ideas that were hitherto excluded from (or inadequately formulated in) traditional approaches to the economics of welfare. The core focus of the capability approach is on what individuals are able to do Capabilities refer to things a person can achieve or could have achieved in life. The notion of capability is essentially one of freedom. This theory helps us to be a part of society that is having friends, freedom to  pursue education, freedom to pursue career, freedom to be mobile, freedom to have job of one’s liking, ability to marry, ability to raise a family, and ability to pursue spiritual goals. It would be useful research to examine the extent of role of the capabilities in predicting the well  being of persons with migrants. Interventions can also be designed to modify capabilities in the lives of persons with migration.   Initially Sen argued for five components in assessing capability: 1.   The importance of real freedoms in the assessment of a person's advantage.  Volume: 02, October 2013, Pages: 167-176 International Journal of Computing Algorithm Integrated Intelligent Research (IIR) 169 2.   Individual differences in the ability to transform resources into valuable activities. 3.   The multi-variate nature of activities giving rise to happiness. 4.   A balance of materialistic and non-materialistic factors in evaluating human welfare. 5.   Concern for the distribution of opportunities within society. Formulations of capability have two parts: functionings and opportunity freedom – the substantive freedom to pursue different functioning combinations. Ultimately, capabilities denote a person’s opportunity and ability to generate valuable outcomes, taking into account relevant personal characteristics and external factors. The important part of this definition is the “freedom to achieve”; the reason being, if freedom had only instrumental value – valuable as a means to achieve an end  – and no intrinsic value – valuable in and of itself – to a person’s well being, then the value of the capability set as a whole would simply  be defined by the value of a person’s actual combination of functionings. Consequently, the capability set outlined by this approach is not merely concerned with achievements; rather, freedom of choice, in and of itself, is of direct importance to a person’s quality of life. Take the example of fasting as a functioning; there is an important difference between fasting and starving because, in examining a starving person’s achieved well being, it is critical to consider whether the individual is  personally choosing not to eat or whether the  person cannot eat because they lack the means to acquire an adequate amount of food. In this example, therefore, the functioning is starving  but the capability to obtain an adequate amount of food is the key element to be considered in evaluating well being between individuals in the two states. In sum, choosing a lifestyle is not exactly the same as having that lifestyle no matter how chosen, and a  person’s well being does depend on how that lifestyle came to be. For this reason, while the combination of a person’s functionings represents their actual achievements, their capability set represents their opportunity freedom – their freedom to choose between alternative functioning combinations. 2.2.2 Functionings  Functionings refer to a mixture of “doings and  beings” or the various options or actions we  perform in everyday life to achieve things in life. Functioning ranges from achieving basic things such as obtaining food and maintaining health, to more complex tasks such as achieving inner peace or performing leadership role in the community. Sen, in his theory promotes an equality of capabilities and not necessarily an equality of functionings that makes it interesting and different from many other theorists some of the functioinings that can be measured are: performing activities of daily living, obtaining food, procuring clothing, living in own home, using transportation or driving, having enough friends, having enough family support,doing work, raising a family, pursuing a career,  being active in the neighborhood, being active in town, being active in the state, being active nationally and internationally. In the most basic sense, functionings consist of “beings and doings”. As a result, living may be seen as a set of interrelated functionings. Essentially, functionings are the states and activities constitutive of a person’s  being. Examples of functionings can vary from elementary things, such as being healthy, having a good job, and being safe, to more complex states, such as being happy, having self-respect, and being calm. Moreover, Amartya Sen contends that functionings are crucial to an adequate understanding of the capability approach; capability is conceptualized as a reflection of the freedom to achieve valuable functionings. In other words, functionings are the subjects of the capabilities referred to in the approach: what we are capable, want to be capable, or should  be capable to be and/or do. Therefore, a  person’s chosen combination of functionings, what they are and do, is part of their overall capability set – the functionings they were able to do. Yet, functionings can also be  Volume: 02, October 2013, Pages: 167-176 International Journal of Computing Algorithm Integrated Intelligent Research (IIR) 170 conceptualized in a way that signifies an individual’s capabilities. Eating, starving, and fasting would all be considered functionings,  but the functioning of fasting differs significantly from that of starving because fasting, unlike starving, involves a choice and is understood as choosing to starve despite the  presence of other options. Consequently, an understanding of what constitutes functionings is inherently tied together with an understanding of capabilities, as defined by this approach. 2.2.3 Well-being:  Well-being refers to one’s own welfare. Besides preference fulfillment (which is commonly the only interpretation in utilitarian  paradigms), well being also includes a feeling of satisfaction and other features of a person’s life, such as their attained state of health. In the context of migrated students this construct can be measured by measuring the extent of ability to get good education and services one wants, feeling of satisfaction, and self  perceived healthy living. Thus, the real measure of well-being had to be not the actual functioning which a person exercised, but capability  — the set of functionings from which one can choose. So for example, the university graduate who is serving tables has an unmistakable advantage over their uneducated colleague, for they have a choice , just as the adventurer who suffers exposure while mountain climbing is obviously more advantaged than the slum-dweller who freezes out of necessity. 3. A multidimensional assessment of well-being Well-being has been evaluated on the basis of a list of achieved functionings instead of capabilities. Attention has been confined to a set of five functionings - housing, health, education and knowledge, social interactions and psychological conditions - to which corresponds a large spectrum of elementary indicators, mainly qualitative and on an in ordinal scale, sometimes dichotomous. The functionings selected and the correlated indicators are, therefore, the following 1) Housing (safer living/campus security) is the result of two main indicators : i) a crowding index, defined as the number of rooms available for each student “corrected”  by equivalence coefficients to take into account the economies of scale ; ii) a basic housing utilities measure that includes telephone, regular water availability and heating. 2) Health conditions are described by the  presence/absence of chronic illnesses. Information available is related to a list of fifteen chronic illnesses with different degrees of seriousness. Three homogenous clusters have been determined : a first group includes chronic illnesses with not very serious disability consequences , the second group refers to severe chronic illnesses that generates a partial disability, while the last group includes the more serious or incurable illnesses. 3) Education and knowledge are measured by means of three ordinal indicators: the higher educational attainment and two variables that refer to personal knowledge in a wider sense that is the number of books read during the last twelve months and the frequency of reading newspapers during a week. 4) Social interactions are depicted by two subsets of indicators that respectively refer to the social relationships during the leisure time (frequency of contact and meeting with friends) and to the participation in the social life. 5) Psychological conditions are described by a  plurality of indicators that express a subjective  perception on one’s own situation or a  personal judgment about the level of satisfaction regarding some relevant aspects of one’s own life. Nine variables measured on ordinal scales have been included in our analysis and re-arranged in five homogenous groups that refer to : i) economic conditions; ii) personal and social relations; iii) health conditions; iv) working conditions ;v) leisure time.  Volume: 02, October 2013, Pages: 167-176 International Journal of Computing Algorithm Integrated Intelligent Research (IIR) 171 However, the decision to consider also the subjective dimension of well-being is justified  by the fact that it doesn’t substitute but just complements our assessment and permits us to compare the results derived from the use of objective and subjective evaluation criteria. At the same time, the concept of “being well” in the sense of being happy, having self respect, and satisfying one’s own desires assumes an important role in determining the personal well-being achievement (see Sen, 1992,1993) . Of course, these aspects are only partially reflected in our available data. 4. The use of fuzzy sets theory for a fuzzy assessment of well-being In the capability approach, well-being can be seen as a broad and fuzzy concept that is intrinsically complex and vague in the sense that it is not possible to express a clear cut  boundaries and definitions. Deprivation too is not an “all-or-nothing condition” that identifies a certain class of people, but rather a vague predicate that manifests itself in different degrees. When we refer to a given functioning, such as healthy living or education and knowledge, we can think that it could be fully achieved by a person or not achieved at all, but more often it will be only  partially fulfilled. At the same time, when we make an attempt to measure the well-being of the migrated individual’s well-being, we presumably work with a wide set of indicators that can assume quantitative or qualitative values or linguistic attributes such as good, bad, low, high living and so on. A useful tool for the treatment of “inexact knowledge” and approximate reasoning is represented by the fuzzy set theory. First introduced by Lotfi A. Zadeh (1965) and extensively applied in many areas of research, this theory has also recently gained considerable attention in inequality and well- being analysis and in poverty measurement. In a nutshell, fuzzy set theory substitutes the characteristic function of a crisp set that traditionally assigns a value of either 1 or 0 to each element in the universal set (Discriminating between members and non-members of the crisp set), with a generalized characteristic function (called membership function) which varies between 0 and 1. Larger values denote higher degrees of membership. In formal terms, if X denotes a universal set, then the membership function   , by which a fuzzy set A is usually defined, has the form    : X →[0, 1] [1]  Where [0, 1] is the interval of real numbers from 0 to 1. Hence,   (x) = 0 if the element x ∈  X does not belong to A,    (x) = 1 if x completely belongs to A and 0 <   (x) < 1 if x  partially belongs to A. Let us assume that the subset A defines the  position of each individual according to the degree of achievement of a given attainment or refers to one of the indicators considered for the functioning assessment. When we consider quantitative variables or qualitative variables measured on an ordinal scale or expressed with linguistic attributes (as in the case of health and physical condition or subjective opinions or perception on one’s own conditions), intermediate values between 0 and 1 describe gradual positions within the arrangement. In this case, it will be necessary: i) to define an appropriate arrangement of modalities (or values) on the basis of the different degrees of hardship/well-being; ii) to identify the two extreme conditions such that   (x) = 1 (full membership) and     (x) = 0 (non-membership); iii) to specify the membership functions for all the other intermediate positions. 1.   Traditional approach μ(x) =1 if 0 ≤  ≤    μ(x) = 0 if  ≤  ≤    
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