scholarly journals Logika preferencija na grubim i rasplinutim skupovima

2004 ◽  
Vol 44 (160) ◽  
pp. 131-146
Author(s):  
Branislav Boricic ◽  
Snezana Konjikusic
Keyword(s):  
Social Choice ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Rough Sets ◽  
Classical Logic ◽  
Choice Theory ◽  
Preference Relation ◽  
Social Choice Theory ◽  
The Social

Theories of fuzzy sets and rough sets, as alternatives to the usual set theory founded on the two valued classical logic, present an appropriate context for developing the basic notions of the logic of preference and consequently, of the social choice theory. In this paper we present an introductory survey of two non-classical concepts of set: fuzzy set and rough set, as originally introduced by L. A. Zadeh and Z. Pawlak respectively, and then we prove that a preference relation defined by means of rough sets has the same basic properties as the classical or the fuzzy one. Moreover, we prove that The Liberal Paradox, as originally formulated by A. Sen, holds in the framework of theory of rough sets as well.

Precursors to Public Choice

2019 ◽  
pp. 796-816
Author(s):  
Iain McLean
Keyword(s):  
Public Choice ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Ancient Greek ◽  
The Social ◽  
Mathematical Skill ◽  
The Many ◽  
Selection Of

This chapter reviews the many appearances, disappearances, and reappearances of axiomatic thought about social choice and elections since the era of ancient Greek democracy. Social choice is linked to the wider public-choice movement because both are theories of agency. Thus, just as the first public-choice theorists include Hobbes, Hume, and Madison, so the first social-choice theorists include Pliny, Llull, and Cusanus. The social-choice theory of agency appears in many strands. The most important of these are binary vs. nonbinary choice; aggregation of judgement vs. aggregation of opinion; and selection of one person vs. selection of many people. The development of social choice required both a public-choice mindset and mathematical skill.

Rough Sets

2011 ◽  
pp. 129-151
Author(s):  
Theresa Beaubouef ◽  
Frederick E Petry
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Object Oriented ◽  
Uncertainty Management ◽  
Database Model ◽  
Management Of Uncertainty ◽  
Object Oriented Database

This chapter discusses ways in which rough set theory can enhance databases by allowing for the management of uncertainty. Rough sets can be integrated into an underlying database model, relational or object oriented, and also used in design and querying of databases. Because rough sets are a versatile theory, they can also be combined with other theories. The authors discuss the rough relational database model, the rough object oriented database model, and fuzzy set and intuitionistic set extensions to each of these models. Comparisons and benefits of the various approaches are discussed, illustrating the usefulness and versatility of rough sets for uncertainty management in databases.

scholarly journals Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 432 ◽  
Author(s):  
Vilém Novák
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Sets ◽  
Type Theory ◽  
Rough Set Theory ◽  
Basic Concepts ◽  
Alternative Set

In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they are universally valid.

Bargaining in Legislatures

1989 ◽  
Vol 83 (4) ◽  
pp. 1181-1206 ◽  
Author(s):  
David P. Baron ◽  
John A. Ferejohn
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Institutional Structure ◽  
The Social ◽  
Free Model ◽  
Sequential Nature ◽  
Choice Literature ◽  
Formal Rules

Bargaining in legislatures is conducted according to formal rules specifying who may make proposals and how they will be decided. Legislative outcomes depend on those rules and on the structure of the legislature. Although the social choice literature provides theories about voting equilibria, it does not endogenize the formation of the agenda on which the voting is based and rarely takes into account the institutional structure found in legislatures. In our theory members of the legislature act noncooperatively in choosing strategies to serve their own districts, explicitly taking into account the strategies members adopt in response to the sequential nature of proposal making and voting. The model permits the characterization of a legislative equilibrium reflecting the structure of the legislature and also allows consideration of the choice of elements of that structure in a context in which the standard, institution-free model of social choice theory yields no equilibrium.

scholarly journals Negotiating Socially Optimal Allocations of Resources

2006 ◽  
Vol 25 ◽  
pp. 315-348 ◽  
Author(s):  
U. Endriss ◽  
N. Maudet ◽  
F. Sadri ◽  
F. Toni
Keyword(s):  
Social Welfare ◽  
Social Choice ◽  
Multiagent System ◽  
Optimal Allocation ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Allocation Of Resources ◽  
Artificial Society ◽  
The Social ◽  
Optimal Allocations

A multiagent system may be thought of as an artificial society of autonomous software agents and we can apply concepts borrowed from welfare economics and social choice theory to assess the social welfare of such an agent society. In this paper, we study an abstract negotiation framework where agents can agree on multilateral deals to exchange bundles of indivisible resources. We then analyse how these deals affect social welfare for different instances of the basic framework and different interpretations of the concept of social welfare itself. In particular, we show how certain classes of deals are both sufficient and necessary to guarantee that a socially optimal allocation of resources will be reached eventually.

scholarly journals Automated Search for Impossibility Theorems in Social Choice Theory: Ranking Sets of Objects

2011 ◽  
Vol 40 ◽  
pp. 143-174 ◽  
Author(s):  
C. Geist ◽  
U. Endriss
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Preference Relation ◽  
Social Choice Theory ◽  
Domain Size ◽  
Wide Range ◽  
Sat Solver ◽  
Ranking Sets ◽  
General Impossibility ◽  
Standard Techniques

We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important applications in social choice theory and decision making under uncertainty, is how to extend an agent's preferences over a number of objects to a preference relation over nonempty sets of such objects. Certain combinations of seemingly natural principles for this kind of preference extension can result in logical inconsistencies, which has led to a number of important impossibility theorems. We first prove a general result that shows that for a wide range of such principles, characterised by their syntactic form when expressed in a many-sorted first-order logic, any impossibility exhibited at a fixed (small) domain size will necessarily extend to the general case. We then show how to formulate candidates for impossibility theorems at a fixed domain size in propositional logic, which in turn enables us to automatically search for (general) impossibility theorems using a SAT solver. When applied to a space of 20 principles for preference extension familiar from the literature, this method yields a total of 84 impossibility theorems, including both known and nontrivial new results.

John Roemer’s Economic Philosophy and the Perils of Formalism

1989 ◽  
Vol 15 ◽  
pp. 267-279
Author(s):  
Drew Christie
Keyword(s):  
Social Choice ◽  
Recent Work ◽  
Choice Theory ◽  
Social Choice Theory ◽  
The Social ◽  
Economic Philosophy ◽  
Means Of Production

John Roemer’s recent work uses the mathematics of Social Choice Theory to examine the structure of socialist ideals. One striking conclusion is that the social ownership of the means of production entails the strict equalization of ‘utility.’1 The conclusion is surprising. While of course opposing many existing inequalities, socialists (as opposed to their critics) have not traditionally understood socialism to require strict equalization. Marx, for example, is scathing in his criticism of levelling, which he sees as a form of ‘crude’ communism.2This paper is both exposition and critique. By way of exposition, I show with less than full mathematical rigor what several of Roemer’s axioms of social ownership mean and why they entail the equality of utility.

The Possibility of Self-Government

2000 ◽  
Vol 94 (3) ◽  
pp. 563-577 ◽  
Author(s):  
Colin Bird
Keyword(s):  
Social Choice ◽  
Common Good ◽  
Choice Theory ◽  
Social Choice Theory ◽  
The Common Good ◽  
The People ◽  
The Social ◽  
Cast Doubt ◽  
Intuitive Concept ◽  
The Common

Many have suggested that the findings of social choice theory demonstrate that there can be no “will of the people.” This has subversive implications for our intuitive concept of self-government. I explore the relation between the notion of a “social will,” that of self-government, and the impossibility theorems of social choice theory. I conclude that although the concept of the social will is essential to that of self-government, the findings of social choice theory do not cast doubt upon the possibility of either. Unlike many attempts to respond to the threat posed by social choice theory, my argument does not require any appeal to the problematic notion of the common good.

scholarly journals Multicriteria ABC Inventory Classification Using the Social Choice Theory

2019 ◽  
Vol 12 (1) ◽  
pp. 182
Author(s):  
Fan Liu ◽  
Ning Ma
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Correlation Method ◽  
Classification Problem ◽  
Inventory Cost ◽  
The Social ◽  
Criteria Importance ◽  
The Individual ◽  
Substantial Degree

The multicriteria ABC inventory classification has been widely adopted by organizations for the purpose of specifying, monitoring, and controlling inventory efficiently. It categorizes the items into three groups based on some certain criteria, such as inventory cost, part criticality, lead time, and commonality. There has been extensive research on such a problem, but few have considered that the judgments about criteria’s importance order usually exhibit a substantial degree of variability. In light of this, we propose a new methodology for handling the multicriteria ABC inventory classification problem using the social choice theory. Specifically, the pessimistic and optimistic results for all possible individual judgments are obtained in a closed-form manner, which are then balanced by the Hurwicz criterion with a “coefficient of optimism”. The CRITIC (Criteria Importance Through Intercriteria Correlation) method is used to aggregate the individual judgments into a collective choice, according to which the items are classified into Groups A, B, and C. Through a numerical experiment, we show that the proposed methodology not only considers all possible preferences among the criteria, but also generates flexible classification schemes.

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