Search Results (3)

The Łukasiewicz conjunction (sometimes also considered to be a logic of absolute comparison), which is used in multivalued logic and in fuzzy set theory, is one of the most important t-norms. In combination with the binary operation ‘maximum’, the Łukasiewicz t-norm forms the basis for the so-called max-Łuk algebra, with applications to the investigation of systems working in discrete steps (discrete events systems; DES, in short). Similar algebras describing the work of DES’s are based on other pairs of operations, such as max-min algebra, max-plus algebra, or max-T algebra (with a given t-norm, T). The investigation of the steady states in a DES leads to the study of the eigenvectors of the transition matrix in the corresponding max-algebra. In real systems, the input values are usually taken to be in some interval. Various types of interval eigenvectors of interval matrices in max-min and max-plus algebras have been described. This paper is oriented to the investigation of strong, strongly tolerable, and strongly universal interval eigenvectors in a max-Łuk algebra. The main method used in this paper is based on max-Ł linear combinations of matrices and vectors. Necessary and sufficient conditions for the recognition of strong, strongly tolerable, and strongly universal eigenvectors have been found. The theoretical results are illustrated by numerical examples. Full article

The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. The aim of this study is to describe an algorithm recognizing for which values of the parameter the given bounded parametric max-linear system has a solution—represented by an appropriate state of the fuzzy system in consideration. Necessary and sufficient conditions of the solvability have been found and a polynomial recognition algorithm has been described. The correctness of the algorithm has been verified. The presented polynomial algorithm consists of three parts depending on the entries of the transition matrix and the required state vector. The results are illustrated by numerical examples. The presented results can be also applied in the study of the max-Łukasiewicz systems with interval coefficients. Furthermore, Łukasiewicz arithmetical conjunction can be used in various types of models, for example, in cash-flow system. Full article

The Min–Max control strategy is the most widely used control algorithm for gas turbine engines. This strategy uses minimum and maximum mathematical functions to select the winner of different transient engine control loops at any instantaneous time. This paper examines the potential of using fuzzy T and S norms in Min–Max selection strategy to improve the performance of the controller and the gas turbine engine dynamic behavior. For this purpose, different union and intersection fuzzy norms are used in control strategy instead of using minimum and maximum functions to investigate the impact of this idea in gas turbine engines controller design and optimization. A turbojet engine with an industrial Min–Max control strategy including steady-state and transient control loops is selected as the case study. Different T and S norms including standard, bounded, Einstein, algebraic, and Hamacher norms are considered to be used in control strategy to select the best transient control loop for the engine. Performance indices are defined as pilot command tracking as well as the engine response time. The simulation results confirm that using Einstein and Hamacher norms in the Min–Max selection strategy could enhance the tracking capability and the response time to the pilot command respectively. The limitations of the proposed method are also discussed and potential solutions for dealing with these challenges are proposed. The methodological approach presented in this research could be considered for enhancement of control systems in different types of gas turbine engines from practical point of view. Full article