FuzzyStatProb: An R Package for the Estimation of Fuzzy Stationary Probabilities from a Sequence of Observations of an Unknown Markov Chain

Markov chains are well-established probabilistic models of a wide variety of real systems that evolve along time. Countless examples of applications of Markov chains that successfully capture the probabilistic nature of real problems include areas as diverse as biology, medicine, social science, and engineering. One interesting feature which characterizes certain kinds of Markov chains is their stationary distribution, which stands for the global fraction of time the system spends in each state. The computation of the stationary distribution requires precise knowledge of the transition probabilities. When the only information available is a sequence of observations drawn from the system, such probabilities have to be estimated. Here we review an existing method to estimate fuzzy transition probabilities from observations and, with them, obtain the fuzzy stationary distribution of the resulting fuzzy Markov chain. The method also works when the user directly provides fuzzy transition probabilities. We provide an implementation in the R environment that is the first available to the community and serves as a proof of concept. We demonstrate the usefulness of our proposal with computational experiments on a toy problem, namely a time-homogeneous Markov chain that guides the randomized movement of an autonomous robot that patrols a small area

Optimal Design of a Sustainable Hydrogen Supply Chain Network: Application in an Airport Ecosystem

Hydrogen and fuel cell technologies are one solution foraddressing the challenges that major airports are facing today, such asupward price trends of liquid hydrocarbon fuels, greenhouse gasemission regulations, and stricter noise and air pollutant emissionregulations, especially for on-ground pollution. An airport can also beviewed as the center of a hydrogen ecosystem, around which multiplehydrogen users could be clustered, with cost sharing of hydrogenproduction and storage occurring among users. The main novelty of thepresent work is the design of a hydrogen infrastructure irrigated by theairport ecosystem that satisfies the airport ecosystem energy needs. Forthis purpose, the model development is based on a multiobjectiveoptimization framework designed to consider four echelons: energysources, hydrogen production, transportation, and storage. Themultiperiod problem is then solved using theε-constraint method.Two objective functions are involved, that is, the total daily cost (TDC) of the network and an environmental indicator basedon the global warming potential. The second innovative contribution is to model the demand uncertainty using fuzzy conceptsfor a hydrogen supply chain design. Because hydrogen demand is one the most significant parameters, the uncertainty of thedemand has been considered using a proposed fuzzy linear programming strategy. The solutions are compared with the originalcrisp model, giving more robustness to the proposed approach. This work has been performed in the framework of the Hyportmeta-project and, in particular, within the“H2modeling”project. This paper focuses on a hydrogen airport ecosystem located inthe department of Hautes-Pyrénées (France). However, the developed methodology could be extended to other hydrogenecosystems for which deployment involves a multiperiod multi-objective formulation under an uncertain deman

A Learning Process for Fuzzy Control Rules using Genetic Algorithms

The purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples. It is developed in three stages: the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach, the second one combines two kinds of rules, experts rules if there are and the previously generated fuzzy control rules, removing the redundant fuzzy rules, and the third one is a tuning process for adjusting the membership functions of the fuzzy rules. The three components of the learning process are developed formulating suitable Genetic Algorithms. Keywords: Fuzzy logic control systems, learning, genetic algorithms. 1 Introduction Fuzzy rule based systems have been shown to be an important tool for modelling complex systems, in which due to the complexity or the imprecision, classical tools are unsuccessful. Fuzzy Logic Controllers (FLCs) are now considered as one of the most important applications of the fuzzy rule based systems. The e..

FuzzyStatProb

Markov chains are well-established probabilistic models of a wide variety of real systems that evolve along time. Countless examples of applications of Markov chains that successfully capture the probabilistic nature of real problems include areas as diverse as biology, medicine, social science, and engineering. One interesting feature which characterizes certain kinds of Markov chains is their stationary distribution, which stands for the global fraction of time the system spends in each state. The computation of the stationary distribution requires precise knowledge of the transition probabilities. When the only information available is a sequence of observations drawn from the system, such probabilities have to be estimated. Here we review an existing method to estimate fuzzy transition probabilities from observations and, with them, obtain the fuzzy stationary distribution of the resulting fuzzy Markov chain. The method also works when the user directly provides fuzzy transition probabilities. We provide an implementation in the R environment that is the first available to the community and serves as a proof of concept. We demonstrate the usefulness of our proposal with computational experiments on a toy problem, namely a time-homogeneous Markov chain that guides the randomized movement of an autonomous robot that patrols a small area