Consistency of total fuzzy relations: New algorithms to detect and repair inconsistent judgments

作者：

Highlights：

• New definitions of (in)consistency for fuzzy relations are proposed.

• We consider the link between these concepts and L-cycles in the associated digraph.

• Design of new algorithms to find and eliminate all inconsistent cycles of judgment.

• A new consistency index, called T-consistency, is defined.

• Construction of a consistent judgment based on a total fuzzy T-preorder.

摘要

•New definitions of (in)consistency for fuzzy relations are proposed.•We consider the link between these concepts and L-cycles in the associated digraph.•Design of new algorithms to find and eliminate all inconsistent cycles of judgment.•A new consistency index, called T-consistency, is defined.•Construction of a consistent judgment based on a total fuzzy T-preorder.

论文关键词：Fuzzy T-preordering,T-consistency,α-T-L-cyclic,Directed graph,Ranking problem

论文评审过程：Received 13 March 2022, Revised 27 June 2022, Accepted 17 July 2022, Available online 21 July 2022, Version of Record 30 July 2022.

论文官网地址：https://doi.org/10.1016/j.eswa.2022.118234