A fuzzy cognitive map (FCM) is made up of factors and direct impacts. In graph
theory, a bipolar weighted digraph is used to model an FCM; its vertices represent the
factors, and the arcs represent the direct impacts. Each direct impact is either positive
or negative, and is assigned a weight; in the model considered in this thesis, each
weight is interpreted as the probability of the impact. A directed walk from factor F
to factor F' is interpreted as an indirect impact of F on F'. The probabilistic transitive
closure (PTC) of an FCM (or bipolar weighted digraph) is a bipolar weighted digraph
with the same set of factors, but with arcs corresponding to the indirect impacts in
the given FCM.
Fuzzy cognitive maps can be used to represent structured knowledge in diverse
fields, which include science, engineering, and the social sciences. In [P. Niesink, K.
Poulin, M. Sajna, Computing transitive closure of bipolar weighted digraphs, Discrete
Appl. Math. 161 (2013), 217-243], it was shown that the transitive closure provides
valuable new information for its corresponding FCM. In particular, it gives the total
impact of each factor on each other factor, which includes both direct and indirect
impacts. Furthermore, several algorithms were developed to compute the transitive
closure of an FCM. Unfortunately, computing the PTC of an FCM is computationally
hard and the implemented algorithms are not successful for large FCMs. Hence, the
Reduction-Recovery Algorithm was proposed to make other (direct) algorithms more
efficient. However, this algorithm has never been implemented before.
In this thesis, we code the Reduction-Recovery Algorithm and compare its running
time with the existing software. Also, we propose a new enhancement on the
existing PTC algorithms, which we call the Separation-Reduction Algorithm. In particular, we state and prove a new theorem that describes how to reduce the input
digraph to smaller components by using a separating vertex. In the application part
of the thesis, we show how the PTC of an FCM can be used to compare different
standpoints on the issue of work-integrated learning.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/41401 |
| Date | 04 November 2020 |
| Creators | Akbari, Masoomeh |
| Contributors | Sajna, Mateja |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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