Abstract
Nowadays, to solve a problem, people/systems typically use knowledge from different sources. A binary vector is a useful structure to represent knowledge states, and determining the consensus for a binary vector collective is helpful in many areas. However, determining a consensus that satisfies postulate 2-Optimality is an NP-hard problem; therefore, many heuristic algorithms have been proposed. The basic heuristic algorithm is the fastest in the literature, and most widely used to solve this problem. The computational complexity of the basic heuristic algorithm is O(m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> n). In this study, we propose a quick algorithm (called QADC) to determine the 2-Optimality consensus. The QADC algorithm is developed based on a new approach for calculating the distances from a candidate consensus to the collective members. The computational complexity of the QADC algorithm has been reduced to O(mn), and the consensus quality of QADC algorithm and the basic heuristic algorithm is the same.
Highlights
Using knowledge from different sources for decision-making is getting popular [1]
In Theorem 4, we prove that if initial candidate consensuses xc are the same, the 2-Optimality consensus determined by the QADC algorithm and that by the basic heuristic algorithm are the same
The running time of the QADC algorithm equals to 13.97% that of the basic heuristic algorithm
Summary
Using knowledge from different sources for decision-making is getting popular [1]. For example, to decide on a problem in our life, people typically search for information on the Internet or ask the opinions of experts. A collective consists of knowledge states of different agents, experts, or individuals referring to the same problem [3], [4]. In [15], Nguyen et al presented a general model for conflict and knowledge inconsistency In this model, such factors as conflict representation and consistency measures for conflict collective are considered. Determining the 2-Optimality consensus is an NP-hard problem [6], and heuristic algorithms have been developed for different data structures, such as a complex tree, partition, ontology, and binary vector [6], [18], [19]. Heuristic algorithms have been introduced to determine the consensus for binary vector collectives [19], [30], [31].
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