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A Consideration Of Different Definitions Of Fuzzy Covering Relations

Author

Listed:
  • JOHN N. MORDESON

    (Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA)

  • TERRY D. CLARK

    (Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA)

  • MICHAEL B. GIBILISCO

    (Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA)

  • PETER C. CASEY

    (Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA)

Abstract

Fuzzy spatial models map a substantial degree of preference indifference. It has been shown that different definitions of covering result in different elements in the uncovered set when preference indifference is present. We consider several of the most frequently used definitions of covering relations found in the literature. The first definition that we examine yields an uncovered set, some of the elements of which are not Pareto efficient. Given that there is no reason to expect a set of players comprising a majority to settle for a Pareto deficient outcome, the remainder of the paper considers the ability of alternative definitions to avoid such a result.

Suggested Citation

  • John N. Mordeson & Terry D. Clark & Michael B. Gibilisco & Peter C. Casey, 2010. "A Consideration Of Different Definitions Of Fuzzy Covering Relations," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 247-259.
    • Handle: RePEc:wsi:nmncxx:v:06:y:2010:i:03:n:s1793005710001736
    DOI: 10.1142/S1793005710001736
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