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

This book offers a comprehensive analysis of the social choice literature and shows, by applying fuzzy sets, how the use of fuzzy preferences, rather than that of strict ones, may affect the social choice theorems. To do this, the book explores the presupposition of rationality within the fuzzy framework and shows that the two conditions for rationality, completeness and transitivity, do exist with fuzzy preferences. Specifically, this book examines: the conditions under which a maximal set exists; the Arrow’s theorem; the Gibbard-Satterthwaite theorem and the median voter theorem. After showing that a non-empty maximal set does exists for fuzzy preference relations, this book goes on to demonstrating the existence of a fuzzy aggregation rule satisfying all five Arrowian conditions, including non-dictatorship. While the Gibbard-Satterthwaite theorem only considers individual fuzzy preferences, this work shows that both individuals and groups can choose alternatives to various degrees, resulting in a social choice that can be both strategy-proof and non-dictatorial. Moreover, the median voter theorem is shown to hold under strict fuzzy preferences but not under weak fuzzy preferences. By providing a standard model of fuzzy social choice and by drawing the necessary connections between the major theorems, this book fills an important gap in the current literature and encourages future empirical research in the field.

The modern origin of fuzzy sets, fuzzy algebra, fuzzy decision making, and “computing with words” is conventionally traced to Lotfi Zadeh’s publication in 1965 of his path-breaking refutation of binary set theory. In a sixteen-page article, modestly titled “Fuzzy Sets” and published in the journal Information and Control, Zadeh launched a multi-disciplinary revolution. The start was relatively slow, but momentum gathered quickly. From 1970 to 1979 there were about 500 journal publications with the word fuzzy in the title; from 2000 to 2009 there were more than 35,000. At present, citations to Zadeh’s publications are running at a rate of about 1,500-2,000 per year, and this rate continues to rise. Almost all applications of Zadeh’s ideas have been in highly technical scientific fields, not in the social sciences. Zadeh was surprised by this development. In a personal note he states: “When I wrote my l965 paper, I expected that fuzzy set theory would be applied primarily in the realm of human sciences. Contrary to my expectation, fuzzy set theory and fuzzy logic are applied in the main in physical and engineering sciences.” In fact, the first comprehensive examination of fuzzy sets by a social scientist did not appear until 1987, a full twenty-two years after the publication of Zadeh’s seminal article, when Michael Smithson, an Australian psychologist, published Fuzzy Set Analysis for Behavioral and Social Sciences.

The book, titled “Linguistic Fuzzy-Logic Methods in Social Sciences,” is a first in its kind. Linguistic fuzzy logic theory deals with sets or categories whose boundaries are blurry or, in other words, “fuzzy,” and which are expressed in a formalism that uses “words” to compute, not numbers, termed in engineering as “soft computing.” This book presents an accessible introduction to this linguistic fuzzy logic methodology, focusing on its applicability to social sciences. Specifically, this is the first book to propose an approach based on linguistic fuzzy-logic and the method of computing with words to the analysis of decision making processes, strategic interactions, causality, and data analysis in social sciences. The project consists of systematic, theoretical and practical discussions and developments of these new methods as well as their applications to various substantive issues of interest to international relations scholars, political scientists, and social scientists in general.

Computational social choice is concerned with the design and analysis of methods for collective decision making. It is a research area that is located at the interface of computer science and economics. The central question studied in computational social choice is that of how best to aggregate the individual points of view of several agents, so as to arrive at a reasonable compromise. Examples include tallying the votes cast in an election, aggregating the professional opinions of several experts, and finding a fair manner of dividing a set of resources amongst the members of a group -- Back cover.

The field of Soft Computing in Humanities and Social Sciences is at a turning point. The strong distinction between “science” and “humanities” has been criticized from many fronts and, at the same time, an increasing cooperation between the so-called “hard sciences” and “soft sciences” is taking place in a wide range of scientific projects dealing with very complex and interdisciplinary topics. In the last fifteen years the area of Soft Computing has also experienced a gradual rapprochement to disciplines in the Humanities and Social Sciences, and also in the field of Medicine, Biology and even the Arts, a phenomenon that did not occur much in the previous years. The collection of this book presents a generous sampling of the new and burgeoning field of Soft Computing in Humanities and Social Sciences, bringing together a wide array of authors and subject matters from different disciplines. Some of the contributors of the book belong to the scientific and technical areas of Soft Computing while others come from various fields in the humanities and social sciences such as Philosophy, History, Sociology or Economics. Rudolf Seising received a Ph.D. degree in philosophy of science and a postdoctoral lecture qualification (PD) in history of science from the Ludwig Maximilians University of Munich. He is an Adjoint Researcher at the European Centre for Soft Computing in Mieres (Asturias), Spain. Veronica Sanz earned a Ph.D. in Philosophy at the University Complutense of Madrid (Spain). At the moment she is a Postdoctoral Researcher at the Science, Technology and Society Center in the University of California at Berkeley. Veronica Sanz earned a Ph.D. in Philosophy at the University Complutense of Madrid (Spain). At the moment she is a Postdoctoral Researcher at the Science, Technology and Society Center in the University of California at Berkeley.

Decision making is certainly a very crucial component of many human activities. It is, therefore, not surprising that models of decisions play a very important role not only in decision theory but also in areas such as operations Research, Management science, social Psychology etc . . The basic model of a decision in classical normative decision theory has very little in common with real decision making: It portrays a decision as a clear-cut act of choice, performed by one individual decision maker and in which states of nature, possible actions, results and preferences are well and crisply defined. The only compo nent in which uncertainty is permitted is the occurence of the different states of nature, for which probabilistic descriptions are allowed. These probabilities are generally assumed to be known numerically, i. e. as single probabili ties or as probability distribution functions. Extensions of this basic model can primarily be conceived in three directions: 1. Rather than a single decision maker there are several decision makers involved. This has lead to the areas of game theory, team theory and group decision theory. 2. The preference or utility function is not single valued but rather vector valued. This extension is considered in multiattribute utility theory and in multicritieria analysis. 3.