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Simulations and bisimulations are well-established notions in crisp/fuzzy automata theory and are widely used to compare the behaviors of automata. Their main drawback is that they compare the behaviors of fuzzy automata in a crisp manner.…
Simulations and bisimulations between two fuzzy automata over a complete residuated lattice were defined by \'Ciri\'c et al. (2012) as fuzzy relations between the sets of states of the automata. However, they act as a crisp relationship…
Bisimulations have been widely used in many areas of computer science to model equivalence between various systems, and to reduce the number of states of these systems, whereas uniform fuzzy relations have recently been introduced as a…
In this paper we study the equivalence of nondeterministic automata pairing the concept of a bisimulation with the recently introduced concept of a uniform relation. In this symbiosis, uniform relations serve as equivalence relations which…
Fuzzy structures such as fuzzy automata, fuzzy transition systems, weighted social networks and fuzzy interpretations in fuzzy description logics have been widely studied. For such structures, bisimulation is a natural notion for…
Like bisimulations, simulations and directed simulations are used for analyzing graph-based structures such as automata, labeled transition systems, linked data networks, Kripke models and interpretations in description logic. Simulations…
There has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems, but the comparison at this level is too coarse. Recently, a finer behavioral measure, bisimulation, has been introduced to fuzzy…
Fuzzy graph-based structures such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models, fuzzy social networks and fuzzy interpretations in fuzzy description logics are useful in various applications. Given two states,…
Fuzzy transition systems offer a robust framework for modeling and analyzing systems with inherent uncertainties and imprecision, which are prevalent in real-world scenarios. As their extension, nondeterministic fuzzy transition systems…
In a recent paper, we have introduced two types of fuzzy simulations (forward and backward) and five types of fuzzy bisimulations (forward, backward, forward-backward, backward-forward and regular) between Kripke models for the fuzzy…
New types of systems of fuzzy relation inequalities and equations, called weakly linear, have been recently introduced in [J. Ignjatovi\'c, M. \'Ciri\'c, S. Bogdanovi\'c, On the greatest solutions to weakly linear systems of fuzzy relation…
There are two kinds of bisimulation, namely crisp and fuzzy, between fuzzy structures such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models and fuzzy interpretations in description logics. Fuzzy bisimulations between…
Fuzzy relational identification builds a relational model describing systems behaviour by a nonlinear mapping between its variables. In this paper, we propose a new fuzzy relational algorithm based on simplified max-min relational equation.…
The limited version of bisimulation, called limited approximate bisimulation, has recently been introduced to fuzzy transition systems (NFTSs). This article extends limited approximate bisimulation to NFTSs, which are more general…
We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and…
In this paper we adapt the well-known Brzozowski determinization method to fuzzy automata. This method gives better results than all previously known methods for determinization of fuzzy automata developed by B\v{e}lohl\'avek [Inform…
This paper compares various optimization methods for fuzzy inference system optimization. The optimization methods compared are genetic algorithm, particle swarm optimization and simulated annealing. When these techniques were implemented…
Adjusting the control actions of a wheeled robot to eliminate oscillations and ensure smoother motion is critical in applications requiring accurate and soft movements. Fuzzy controllers enable a robot to operate smoothly while accounting…
Bisimulation relation has been successfully applied to computer science and control theory. In our previous work, simulation-based controllability and simulation-based observability are proposed, under which the existence of bisimilarity…
Efficient methods for the simulation of quantum circuits on classic computers are crucial for their analysis due to the exponential growth of the problem size with the number of qubits. Here we study lumping methods based on bisimulation,…