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

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


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.


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


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Computer Science and EngineeringLouisiana State UniversityBaton RougeUSA

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