University of Twente Student Theses


Fuzzy Markov chains

Socha, Konrad (2023) Fuzzy Markov chains.

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Abstract:This paper presents novel methods to enhance the analysis of Markov chains in situations where event probabilities are uncertain, a scenario encountered when information about a system is incomplete or when planning a new system. Fuzzy numbers, which represent imprecise or vague quantities through the use of a membership function, are utilized to model these uncertain probabilities. A genetic algorithm, an optimization technique inspired by natural selection and genetic processes, is utilized to calculate the values of fuzzy transition matrix powers, streamlining the analysis of reachability and stationary distribution for fuzzy Markov chains. Reachability investigates whether a state is accessible within a certain number of steps from another state, while stationary distribution refers to a stable probability distribution that remains unaltered over time. The proposed algorithm is integrated into a probabilistic model checker STORM. Its performance is evaluated through convergence towards optimal solutions and scalability. The evaluation results indicate that although input size significantly impacts the algorithm's performance, it effectively handles uncertainty and offers reliable solutions for fuzzy Markov chain analysis in complex decision-making. This highlights the effectiveness and promise of the proposed method and makes it a valuable contribution to the analysis of fuzzy Markov chains.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics, 54 computer science
Programme:Computer Science MSc (60300)
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