On homology groups for pairwise comparisons method

被引：0
作者：
Koczkodaj, Waldemar W. [1 ]
Pedrycz, Witold [2 ]
Pigazzini, Alexander [3 ]
Song, Yingli [1 ]
Szybowski, Jacek [4 ]
机构：
[1] Laurentian Univ, Comp Sci, Sudbury, ON P3E 2C6, Canada
[2] Univ Alberta, Dept Elect & Comp Engn, Edmonton, AB T6R 2G7, Canada
[3] Math & Phys Sci Fdn, DK-4200 Slagelse, Denmark
[4] AGH Univ Krakow, Fac Appl Math, Al A Mickiewicza 30, PL-30059 Krakow, Poland
来源：
INFORMATION SCIENCES | 2024年 / 681卷
关键词：
Inconsistency; First Betti number; Homology group; Pairwise comparisons method; Topological data analysis; INCONSISTENCY INDEXES; CONSISTENT;
D O I：
10.1016/j.ins.2024.121195
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this study, we introduce pairwise comparisons matrix classification based on homology groups of graphs with unique vertices. Algebraic topology transforms a sequence of topological objects (such as graphs associated with pairwise comparison matrices) into algebraic objects such as homology groups. It is the first attempt to use this tool to classify matrices of pairwise comparisons based on the triads in which the inconsistency occurs. The Koczkodaj inconsistency indicator was used in this study.
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页数：10
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