An Approach to Distributed Systems from Orderings and Representability

In the present paper, we propose a new approach on ‘distributed systems’: the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations met in various fields (such as computer science, economics and decision theory). We investigate questions associated to the numerical representability of order structures, relating concepts of economics and computing to each other. The concept of ‘quasi-finite partial orders’ is introduced as a finite family of chains with a communication between them. The representability of this kind of structure is studied, achieving a construction method for a finite (continuous) Richter–Peleg multi-utility representation.

• Publication year

  2024

• Venue

  Bulletin of the Iranian Mathematical Society

• Publication date

  2024-04-08

• Fields of study

  Not labeled

• Identifiers
  DOI 10.1007/s41980-024-00865-0
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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  2017influential reference
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  2011cited by this paper
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  2011influential reference
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  2008cited by this paper
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  2008influential reference
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  2007cited by this paper
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  2003cited by this paper
• Real interval representations

  2002influential reference
• Virtual Time and Global States of Distributed Systems

  2002influential reference
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  1995cited by this paper
• Combinatorics and Partially Ordered Sets: Dimension Theory

  1992cited by this paper
• Logical time in distributed computing systems

  1991cited by this paper
• Continuous representation of a preference relation on a connected topological space

  1987influential reference
• Biorder families, valued relations and preference modelling

  1986cited by this paper
• On realizable biorders and the biorder dimension of a relation

  1984influential reference
• Time, clocks, and the ordering of events in a distributed system

  1978influential reference
• Intransitive Indifference in Preference Theory: A Survey

  1970cited by this paper
• UTILITY FUNCTIONS FOR PARTIALLY ORDERED TOPOLOGICAL SPACES.

  1970influential reference
• Intransitivity of preferences.

  1969cited by this paper
• On the structure of causal spaces

  1967cited by this paper
• Revealed Preference Theory

  1966cited by this paper
• Foundational aspects of theories of measurement

  1958cited by this paper
• Semiorders and a Theory of Utility Discrimination

  1956cited by this paper
• A basis for scaling qualitative data.

  1944cited by this paper

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