Advertisement

A Better Group Consensus Ranking via a Min-transitive Fuzzy Linear Ordering

  • Sukhamay KunduEmail author
Conference paper
  • 16 Downloads
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1154)

Abstract

The current fuzzy methods for determining a group consensus ranking (GCR) or, equivalently, a linear order of items of a finite set S from a given set of weighted linear orders \(\mathcal {L}= \{L_1, L_2, \ldots , L_M\}\) on S are ad hoc in nature. This is because the underlying key fuzzy relations used in determining the GCR are not min-transitive. We present here a better method for GCR based on a min-transitive fuzzy linear order on S obtained from \(\mathcal {L}\). We define a collection of probability distributions \(P_x(j), x \in S\), on the rank set \(\{1, 2, \ldots , |S|\}\) based on the linear orders \(\mathcal {L}\). The distributions \(P_x(j)\) give a min-transitive fuzzy partial order \(\mu _{\mathcal {L}}(\cdot , \cdot )\) on S, where \(\mu _{\mathcal {L}}(x, y)\) says how “left” the distribution \(P_x(\cdot )\) is to \(P_y(\cdot )\). We then extend \(\mu _{\mathcal {L}}(\cdot , \cdot )\) to a best possible min-transitive fuzzy linear order \(\mu _{\mathcal {L}}^\star (\cdot , \cdot )\) on S, which gives the desired ranking of items in S.

Keywords

Group ranking Weighted linear orders Fuzzy partial order Fuzzy linear order Min-transitivity 

References

  1. 1.
    Herrera, F., Herrera-Viedma, E.: Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst. 115, 67–82 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Klir, G.J., St. Clair, U., Yuan, B.: Fuzzy Set Theory: Foundations and Applications, 1st ed. Prentice Hall (1997)Google Scholar
  3. 3.
    Kundu, S.: A min-transitive fuzzy left-relationship on finite sets based on distance to left. In: Proceedings of the International Conference on Soft Computing: Theory and Applications (SoCTA-2017), India, Dec. 22–24 (2017)Google Scholar
  4. 4.
    Kundu, S.: The min-transitive fuzzy left-relationship \(\lambda _d(A, B)\) on intervals: a generalization of \(\lambda (A, B)\). In: Proceedings of the International Conference on Soft Computing: Theory and Applications (SoCTA-2018), India, Dec. 21–23 (2018)Google Scholar
  5. 5.
    Orlovsky, S.A.: Decision making with a fuzzy preference relation. Fuzzy Sets Syst. 1, 155–167 (1978)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Xu, Z.: A note on linguistic hybrid arithmetic averaging operator in multiple attribute group decision making with linguistic information. Group Decis. Negot. 15, 593–604 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Computer Science and EngineeringLouisiana State UniversityBaton RougeUSA

Personalised recommendations