Markov and Semi-Markov Processes with Fuzzy States. Part 1. Markov Processes

Demenkov, N.P.; Mirkin, E. A.; Mochalov, I. A.

doi:10.17587/it.26.323-334

Cited by 2 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The error of the results obtained in this case is not discussed. In [11], the fuzzy values of the system transition probabilities are also displayed in intervals. And here the error of the results is not discussed.…”

Section: Methodsmentioning

confidence: 99%

Analysis of semi-Markov systems with fuzzy initial data

et al. 2022

View full text Add to dashboard Cite

In real operating conditions of complex systems, random changes in their possible states occur in the course of their operation. The traditional approach to describing such systems uses Markov models. However, the real non-deterministic mechanism that controls the duration of the system's stay in each of its possible states predetermines the insufficient adequacy of the models obtained in this case. This circumstance makes it expedient to consider models that are more general than Markov ones. In addition, when choosing such models, one should take into account the fundamental often manifested feature of the statistical material actually used in the processing of an array of observations, their small sample. All this, taken together, makes it relevant to study the possibility of developing less demanding, tolerant models of the behavior of complex systems. A method for the analysis of systems described under conditions of initial data uncertainty by semi-Markov models is proposed. The main approaches to the description of this uncertainty are considered: probabilistic, fuzzy, and bi-fuzzy. A procedure has been developed for determining the membership functions of fuzzy numbers based on the results of real data processing. Next, the following tasks are solved sequentially. First, the vector of stationary state probabilities of the Markov chain embedded in the semi-Markov process is found. Then, a set of expected values for the duration of the system's stay in each state before leaving it is determined, after which the required probability distribution of the system states is calculated. The proposed method has been developed to solve the problem in the case when the parameters of the membership functions of fuzzy initial data cannot be clearly estimated under conditions of a small sample

show abstract

Section: Methodsmentioning

confidence: 99%

Analysis of semi-Markov systems with fuzzy initial data

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Let us emphasize the difference between the approach and results of this paper and the studies on continuous-time random processes with discrete fuzzy states. For example, fuzzy queueing systems were discussed in [9][10][11][12]; stochastic fuzzy dynamic automatic control systems were considered in [13,14]. At the same time, stationary fuzzy random processes and their covariance functions were not addressed in the publications cited above.…”

Section: Khatskevichmentioning

confidence: 99%

On the Transformation of a Stationary Fuzzy Random Process by a Linear Dynamic System

Khatskevich

2024

ARC

View full text Add to dashboard Cite

In this paper, stationary random processes with fuzzy states are studied. The properties of their numerical characteristics—fuzzy expectations, expectations, and covariance functions—are established. The spectral representation of the covariance function, the generalized Wiener–Khinchin theorem, is proved. The main attention is paid to the problem of transforming a stationary fuzzy random process (signal) by a linear dynamic system. Explicitform relationships are obtained for the fuzzy expectations (and expectations) of input and output stationary fuzzy random processes. An algorithm is developed and justified to calculate the covariance function of a stationary fuzzy random process at the output of a linear dynamic system from the covariance function of a stationary input fuzzy random process. The results rest on the properties of fuzzy random variables and numerical random processes. Triangular fuzzy random processes are considered as examples.

show abstract

Markov and Semi-Markov Processes with Fuzzy States. Part 1. Markov Processes

Cited by 2 publications

References 0 publications

Analysis of semi-Markov systems with fuzzy initial data

Analysis of semi-Markov systems with fuzzy initial data

On the Transformation of a Stationary Fuzzy Random Process by a Linear Dynamic System

Contact Info

Product

Resources

About