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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

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Published on: March 1, 2022

A note on two methods for estimating missing pairwise preference values.

Francisco Chiclana1, Enrique Herrera-Viedma, Sergio Alonso

  • 1Centre for Computational Intelligence, Faculty of Technology, De Montfort University, Leicester LE1 9BH, U.K. chiclana@dmu.ac.uk

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|June 27, 2009
PubMed
Summary
This summary is machine-generated.

This study compares two methods for reconstructing incomplete fuzzy preference relations. A combined approach using both methods offers the most robust reconstruction, with only a chain of missing comparisons preventing success.

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Area of Science:

  • Decision Sciences
  • Fuzzy Logic Systems
  • Operations Research

Background:

  • Analyzes two distinct methods for imputing missing values in incomplete reciprocal fuzzy preference relations.
  • Examines methods proposed by Herrera-Viedma and Fedrizzi-Giove, both leveraging the additive consistency property.

Discussion:

  • Compares the methodologies, highlighting their similarities in independent-missing-comparison scenarios and differences in dependent-missing-comparison cases.
  • Demonstrates that a modification of the Herrera-Viedma method aligns with the Fedrizzi-Giove method.
  • Evaluates the performance in total relation reconstruction, indicating the Herrera-Viedma method's superior capability in certain situations.

Key Insights:

  • Both methods are found to be highly similar, particularly when dealing with independent missing comparisons.
  • The Herrera-Viedma method shows a greater capacity for successful reconstruction when the Fedrizzi-Giove method fails.
  • A complementary application strategy is proposed, integrating both methods for enhanced reconstruction accuracy.

Outlook:

  • Proposes a novel reconstruction policy for incomplete fuzzy preference relations by synergistically employing both analyzed methods.
  • Identifies the sole failure case for the proposed combined policy: a chain of missing pairwise comparisons involving all alternatives.