Search Results (6)

Similarity between two fuzzy values, sets, etc., may be defined in various ways. The authors here attempt introducing a general similarity measure based on the direct extension of the Boolean minimal form of equivalence operation. It is further extended to hierarchically structured multicomponent fuzzy signatures. Two versions of this measure, one based on the classic min–max operations and one based on the strictly monotonic algebraic norms, are proposed for practical application. A real example from management science is chosen, namely the comparison of employee attitudes in two different populations. This example has application possibilities in the evaluation and analysis of employee behaviour in companies as, due to the complex aspects in analysing multifaceted behavioural paradigms in organizational management, it is difficult for companies to make reliable decisions in creating processes for better social interactions between employees. In the paper, the authors go through the steps of building a model for exploring a set of different features, where a statistical pre-processing step enables the identification of the interdependency and thus the setup of the fuzzy signature structure suitable to describe the partially redundant answers given to a standard questionnaire and the comparison of them with help of the (pair of the) new similarity measures. As a side result in management science, by using an internationally applied standard questionnaire for exploring the factors of employee engagement and using a sample of data obtained from Hungarian and Lithuanian firms, it was found that responses in Hungary and Lithuania were partially different, and the employee attitude was thus in general different although in some questions an unambiguous similarity could be also discovered. Full article

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

Systems working in discrete time (discrete event systems, in short: DES)—based on binary operations: the maximum and the minimum—are studied in so-called max–min (fuzzy) algebra. The steady states of a DES correspond to eigenvectors of its transition matrix. In reality, the matrix (vector) entries are usually not exact numbers and they can instead be considered as values in some intervals. The aim of this paper is to investigate the eigenvectors for max–min matrices (vectors) with interval coefficients. This topic is closely related to the research of fuzzy DES in which the entries of state vectors and transition matrices are kept between 0 and 1, in order to describe uncertain and vague values. Such approach has many various applications, especially for decision-making support in biomedical research. On the other side, the interval data obtained as a result of impreciseness, or data errors, play important role in practise, and allow to model similar concepts. The interval approach in this paper is applied in combination with forall–exists quantification of the values. It is assumed that the set of indices is divided into two disjoint subsets: the E-indices correspond to those components of a DES, in which the existence of one entry in the assigned interval is only required, while the A-indices correspond to the universal quantifier, where all entries in the corresponding interval must be considered. In this paper, the properties of EA/AE-interval eigenvectors have been studied and characterized by equivalent conditions. Furthermore, numerical recognition algorithms working in polynomial time have been described. Finally, the results are illustrated by numerical examples. Full article

Max–min algebra (called also fuzzy algebra) is an extremal algebra with operations maximum and minimum. In this paper, we study the robustness of Monge matrices with inexact data over max–min algebra. A matrix with inexact data (also called interval matrix) is a set of matrices given by a lower bound matrix and an upper bound matrix. An interval Monge matrix is the set of all Monge matrices from an interval matrix with Monge lower and upper bound matrices. There are two possibilities to define the robustness of an interval matrix. First, the possible robustness, if there is at least one robust matrix. Second, universal robustness, if all matrices are robust in the considered set of matrices. We found necessary and sufficient conditions for universal robustness in cases when the lower bound matrix is trivial. Moreover, we proved necessary conditions for possible robustness and equivalent conditions for universal robustness in cases where the lower bound matrix is non-trivial. 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