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  • 1. Anco, S.
    et al.
    Ibragimov, Nail
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Imamutdinova, K.V.
    Karimova, E.N.
    Solutions of gasdynamic equations associated with classical and new conservation laws2015In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 268, p. 52-58Article in journal (Refereed)
    Abstract [en]

    Exact solutions of the one-dimensional gasdynamic equations are constructed by applying the method of conservation laws to all point-wise conserved vectors of the equations under consideration. © 2015 Elsevier Inc.

  • 2. Gazizov, R. K.
    et al.
    Ibragimov, N. H.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Lukashchuk, S. Yu.
    Nonlinear self-adjointness, conservation laws and exact solutions of time-fractional Kompaneets equations2015In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 23, no 1-3, p. 153-163Article in journal (Refereed)
    Abstract [en]

    Four time-fractional generalizations of the Kompaneets equation are considered. Group analysis is performed for physically relevant approximations. It is shown that all approximations have nontrivial symmetries and conservation laws. The symmetries are used for constructing group invariant solutions, whereas the conservation laws allow to find non-invariant exact solutions. (C) 2014 Elsevier B.V. All rights reserved.

  • 3.
    Ibragimov, Nail
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Gandarias, M.L.
    Galiakberova, L.R.
    Bruzon, M.S.
    Avdonina, E.D.
    Group classification and conservation laws of anisotropic wave equations with a source2016In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 57, no 8, article id 083504Article in journal (Refereed)
    Abstract [en]

    Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws.

  • 4.
    Ibragimov, Nail H.
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Kovalev, V. F.
    Meleshko, S. V.
    Bychenkov, V. Yu.
    Group analysis of kinetic equations in a non-linear thermal transport problem2015In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 71, p. 1-7Article in journal (Refereed)
    Abstract [en]

    An application of modern group analysis to electron kinetic equations in non-linear thermal transport problem is discussed. The admitted symmetry group is calculated, and the optimal system of one and two-dimensional subalgebras is constructed. Representations of invariant solutions are presented.

  • 5.
    Ibragimov, Nail
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Ibragimov, Ranis N.
    Univ Wisconsin Parkside, USA.
    Kovalev, Vladimir F.
    Russian Acad Sci, RUS.
    INVARIANT SOLUTIONS AND SHOCK ATMOSPHERIC WAVES IN A THIN CIRCULAR LAYER2018In: Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, E-ISSN 1760-6101, Vol. 13, no 2, article id UNSP 19Article in journal (Refereed)
    Abstract [en]

    The objective of this paper is to investigate the nonlinear mathematical model describing equatorial waves from Lie group analysis point of view in order to understand the nature of shallow water model theory, which is associated to planetary equatorial waves. Such waves correspond to the Cauchy-Poisson free boundary problem on the nonstationary motion of a perfect incompressible fluid circulating around a solid circle of a large radius.

  • 6.
    Ibragimov, Nail
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Karimova, E. N.
    Ufa State Aviat Tech Univ, Lab Grp Anal Math Models Nat & Engn Sci, Ufa 450000, Russia..
    Galiakberova, L. R.
    Ufa State Aviat Tech Univ, Lab Grp Anal Math Models Nat & Engn Sci, Ufa 450000, Russia..
    Chaplygin gas motions associated with nonlocal conservation laws2017In: JOURNAL OF COUPLED SYSTEMS AND MULTISCALE DYNAMICS, ISSN 2330-152X, Vol. 5, no 2-4, p. 63-68Article in journal (Refereed)
    Abstract [en]

    The recent method of conservation laws for constructing exact solutions of partial differential equations is applied to the nonlocal conservation laws of the Chaplygin gas. The nonlocal conservation laws provide twenty different types of exact solutions. They are listed in three tables. Seven types of these solutions describe isentropic flows satisfying Chaplygin's relation between the pressure and density. All solutions are written in the explicit form and contain either arbitrary functions or arbitrary constants.

  • 7.
    Ibragimov, R. N.
    et al.
    GE Global Res, Niskayuna, NY 12309 USA..
    Ibragimov, Nail
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Galiakberova, L. R.
    Ufa State Aviat Tech Univ, Lab Grp Anal Math Models Nat & Engn Sci, Ufa 450000, Russia..
    Conservation laws and invariant solutions of the non-linear governing equations associated with a thermodynamic model of a rotating detonation engines with Korobeinikov's chemical source term2016In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 78, p. 29-34Article in journal (Refereed)
    Abstract [en]

    The non-linear governing gas dynamics equations that are used as a descriptor of a rotating detonation engine are investigated from the group theoretical standpoint. The equations incorporate approximation of Korobeinikov's chemical reaction model that are used to describe the two-dimensional detonation field on a surface of a two-dimensional cylindrical chamber without thickness. The transformations that leave the equations invariant are found. On the basis of these transformations, the conservation equations were constructed and the invariant solutions were obtained for specific form of the equation of state, for which the equations are non-linearly self-adjoint. The invariant solutions are given in terms of the functions that satisfy non-linear ordinary differential equations. The above reduction simplifies the analysis of the original non-linear system of partial differential equations on a surface of rotating cylinder. (C) 2015 Elsevier Ltd. All rights reserved.

  • 8.
    Nefedov, N. N.
    et al.
    Moscow MV Lomonosov State Univ, RUS.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification2018In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 1, p. 99-103Article in journal (Refereed)
    Abstract [en]

    A singularly perturbed initial-boundary value problem for a parabolic equation known in applications as a Burgers-type or reaction-diffusion-advection equation is considered. An asymptotic approximation of solutions with a moving front is constructed in the case of modular and quadratic nonlinearity and nonlinear amplification. The influence exerted by nonlinear amplification on front propagation and blowing- up is determined. The front localization and the blowing-up time are estimated.

  • 9.
    Nystedt, Patrik
    et al.
    University West, SWE.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Pinedo, Héctor
    Industrial University of Santander, COL.
    Artinian and noetherian partial skew groupoid rings2018In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 503, p. 433-452Article in journal (Refereed)
    Abstract [en]

    Let α={α_g : R_{g^{−1}}→R_g}_{g∈mor(G)} be a partial action of a groupoid G on a (not necessarily associative) ring R and let S=R⋆G be the associated partial skew groupoid ring. We show that if α is global and unital, then S is left (right) artinian if and only if R is left (right) artinian and R_g={0}, for all but finitely many g∈mor(G). We use this result to prove that if α is unital and R is alternative, then S is left (right) artinian if and only if R is left (right) artinian and R_g={0}, for all but finitely many g∈mor(G). This result applies to partial skew group rings, in particular. Both of the above results generalize a theorem by J. K. Park for classical skew group rings, i.e. the case when R is unital and associative, and G is a group which acts globally on R. We provide two additional applications of our main results. Firstly, we generalize I. G. Connell's classical result for group rings by giving a characterization of artinian (not necessarily associative) groupoid rings. This result is in turn applied to partial group algebras. Secondly, we give a characterization of artinian Leavitt path algebras. At the end of the article, we relate noetherian and artinian properties of partial skew groupoid rings to those of global skew groupoid rings, as well as establish two Maschke-type results, thereby generalizing results by M. Ferrero and J. Lazzarin for partial skew group rings to the case of partial skew groupoid rings.

  • 10.
    Rakus-Andersson, Elisabeth
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Fuzzy decision-making model with qualitative states and fuzzified outcomes2018In: Proceedia Computer Science: Knowledge-Based and Intelligent Information & Engineering Systems: Proceedings of the 22nd International Conference, KES-2018 / [ed] Robert J. Howlett, Carlos Toro, Yulia Hicks, Lakhmi C. Jain, Elsevier, 2018, Vol. 126, p. 2030-2039, article id k18is-162Conference paper (Refereed)
    Abstract [en]

    The classical fuzzy decision-making model is now tested for qualitative compound states-symptoms to select the most efficacious medicine, acting on all symptoms. Instead of terminating the decision procedure in the way comparing values of total utilities of decisions-treatments, we test the aggregated utility values in utility levels. This activity lets us assign a verbally verified utility to each medicine.

  • 11.
    Rakus-Andersson, Elisabeth
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    The new approach to the construction of parametric membership functions for fuzzy sets with unequal supports2017In: Knowledge-Based and Intelligent Information & Engineering Systems: Proceedings of the 21st International Conference, KES-20176-8 September 2017, Marseille, France / [ed] Cecilia Zanni-Merk, Claudia Frydman, Carlos Toro, Yulia Hicks, Robert J. Howlett, Lakhmi C. Jain, Elsevier, 2017, Vol. 112, p. 2057-2065, article id kes17-155Conference paper (Refereed)
    Abstract [en]

    The current research is devoted to developing methods of a novel mathematical interpretation of term-sets of linguistic variables. To the term-sets of the linguistic variables fuzzy sets are assigned. We intend to adopt the π-functions and the π-functions to derive formulas of membership functions of these sets. The fuzzy sets are divided in three families in the case of an odd number of the term-sets. To each family, we assign only one parametric formula, which depends on two parameters: the width of a non-fuzzy set, which contains all supports of the fuzzy sets being representatives of the term-sets, and a number of the term-sets. Provided that the supports of fuzzy sets will be unequal, the membership function of the set, belonging to one of the families, is computed by means of a functional modifier, inserted in the common equation typical of this family. Medical examples explain how to use cumulated membership functions practically. The procedure can be easily computerized.

  • 12.
    Rakus-Andersson, Elisabeth
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Frey, Janusz
    Blekinge Sjukhus, Karlskrona.
    Finite Fuzzy Sets in the Medication Decision Concerning the Retreat of Symptoms in Radiation Cystitis2015In: The Proceedings of the International Conference eHEALTH 2015 / [ed] Mario Macedo, Claire Genzenta, Guo Chao Peng, Miguel Baptista Nunes, IADIS PRESS , 2015, p. 55-62Conference paper (Refereed)
    Abstract [en]

    Radiation cystitis is a rare disease, appearing as the result of radiation of pelvic tumors. We support mathematically the recognition of the most efficacious treatments, which reduce the impact of symptoms typical of the illness. To permute the therapies in the ordering, commencing with the optimal therapy, we apply the fuzzy decision making model furnished with finite fuzzy sets. These act as measures of the treatment effectiveness-utility. In the solution, we adopt the older operations on fuzzy sets of type 1, which make the model simple to be easily converted into a computer program.

  • 13.
    Rakus-Andersson, Elisabeth
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Frey, Janusz
    Blekinge Sjukhuset, Blekinge County Hospital.
    Fuzzy One-Decision Making Model with Fuzzified Outcomes in the Treatment of Necrotizing Fasciitis2016In: Proceedings of eTELEMED 2016 : The Eighth International Conference on eHealth, Telemedicine, and Social Medicine / [ed] Marike Hettinga et al., International Academy, Research and Industry Association (IARIA), 2016, p. 145-152Conference paper (Refereed)
    Abstract [en]

    By proposing a new approach to fuzzy decision making, we try to support the medical decision, concerning recommendations for the treatment with hyperbaric oxygen (HBO). This treatment can be used for patients, suffering from necrotizing fasciitis. Due to the disease rarity, it sometimes is difficult for a physician to determine, if a single patient needs the treatment with HBO. We thus identify the decision with a linguistic variable, equipped with treatment recommendation levels. The choice of the appropriate level is based on values of clinical symptoms, found in the patient. To extract the optimal recommendation level for the treatment with HBO, we involve fuzzy set techniques in the decision model. In the paper, we mainly concentrate on designs of fuzzy sets, standing for clinical symptoms and recommendation levels. The levels act as the outcomes, dependent on the cumulative input of the patient’s clinical markers. Since the focus is laid on a parametric structure of the outcomes, then we can categorize the model as robust approach to algorithmic modeling of outcomes, being part of eHealth data records.

  • 14.
    Rakus-Andersson, Elisabeth
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Frey, Janusz
    Blekinge County Hospital, Karlskrona, Sweden.
    Rutkowska, Danuta
    Czestochowa Uniwersity of Technology, Czestochowa, Poland.
    The Fuzzified Quasi-perceptron in Decision Making Concerning Treatments in Necrotizing Fasciitis2015In: Artificial Intelligence and Soft Computing LNAI 9120: Proceedings of the 14th International Conference ICAISC 2015 / [ed] L. Rutkowski, M. Korytkowski, R. Scherer, R. Tadeusiewicz, L.A. Zadeh, J.M. Zurada, Cham Heidelberg New York Dortrecht London: Springer, 2015, Vol. II, p. 130-141Conference paper (Refereed)
    Abstract [en]

    In the current paper we mathematically try to support the decision concerning the treatment with hyperbaric oxygen for patients, suffering from necrotizing fasciitis. To accomplish the task, we involve the fuzzified model of a quasi-perceptron, which is our modification of the classical artificial simple neuron. By means of the fuzzification of input signals and output decision levels, we wish to distinguish between decisions “treatment without recommended hyperbaric oxygen” versus “treatment with hyperbaric oxygen”. The number of decision levels can be arbitrary in order to extend the decision scale.

  • 15.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Exact solutions of an integro-differential equation with quadratically cubic nonlinearity2016In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 94, no 1, p. 468-471Article in journal (Refereed)
    Abstract [en]

    Exact solutions of a nonlinear integro-differential equation with quadratically cubic nonlinear term are found. The equation governs, in particular, stationary shock wave propagation in relaxing media. For the exponential kernel the shapes of both compression and rarefaction shocks having a finite width of the front are calculated. For media with limited "memorizing time" the difference relation permitting the construction of wave profile by the mapping method is derived. The initial equation is rather general. It governs the evolution of nonlinear waves in real distributed systems, for example, in biological tissues, structurally inhomogeneous media and in some meta-materials.

  • 16.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Nonlinear Oscillators with "Modulus" Potentials: Dynamic and Stochastic Solutions2015In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 92, no 2, p. 268-271Article in journal (Refereed)
    Abstract [en]

    Two models of an anharmonic oscillator that have exact solutions are considered. The equationsdescribe motion in a “modulus” potential well with a singularity at the minimum and in a double symmetricwell with a singularity at the vertex of the potential barrier. The forms and spectra of the oscillations are computed. Forced oscillations caused by a random force are analyzed on the basis of equations with Langevinsources. Nonstationary solutions of the corresponding Fokker–Planck equations are constructed. Thesesolutions describe

  • 17.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Moscow MV Lomonosov State Univ, Phys Fac, Moscow 119991, Russia.;Nizhnii Novgorod State Univ, Radiophys Fac, Nizhn Novgorod, Russia.;Russian Acad Sci, Prokhorov Gen Phys Inst, Moscow, Russia.;Russian Acad Sci, Schmidt Inst Phys Earth, Moscow, Russia.;Blekinge Inst Technol, Karlskrona, Sweden..
    Gurbatov, S. N.
    Nizhnii Novgorod State Univ, RUS.
    Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems2018In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 1, p. 95-98Article in journal (Refereed)
    Abstract [en]

    A one-dimensional equation is presented that generalizes the Burgers equation known in the theory of waves and in turbulence models. It describes the nonlinear evolution of waves in pipes of variable cross section filled with a dissipative medium, as well as in ray tubes, if the approximation of geometric acoustics of an inhomogeneous medium is used. The generalized equation is reduced to the common Burgers equation with a dissipative parameter-the "Reynolds-Goldberg number," depending on the coordinate. The method for solving statistical problems corresponding to specified characteristics of a noise signal at the input of the system is described. Integral expressions for exact solutions are given for the correlation function and the noise intensity spectrum experiencing nonlinear distortions during propagation in a waveguide. For waves in a dissipative medium, an approximate method of calculating statistical characteristics is given, consisting in finding an auxiliary correlation function and the subsequent nonlinear functional transformation. Solutions have a complicated form, so physical analysis of phenomena requires the numerical methods. For some correlation functions of stationary noise with initial Gaussian statistics and some waveguide systems, it is possible to obtain simple results.

  • 18.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Gurbatov, Sergey N.
    Lobachevsky State University of Nizhni Novgorod, RUS.
    Tyurina, A. V.
    Lobachevsky State University of Nizhni Novgorod, RUS.
    Evolution of weak noise and regular waves on dissipative shock fronts described by the Burgers model2018In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 82, p. 20-29Article in journal (Refereed)
    Abstract [en]

    The interaction of weak noise and regular signals with a shock wave having a finite width is studied in the framework of the Burgers equation model. The temporal realization of the random process located behind the front approaches it at supersonic speed. In the process of moving to the front, the intensity of noise decreases and the correlation time increases. In the central region of the shock front, noise reveals non-trivial behaviour. For large acoustic Reynolds numbers the average intensity can increase and reach a maximum value at a definite distance. The behaviour of statistical characteristics is studied using linearized Burgers equation with variable coefficients reducible to an autonomous equation. This model allows one to take into account not only the finite width of the front, but the attenuation and diverse character of initial profiles and spectra as well. Analytical solutions of this equation are derived. Interaction of regular signals of complex shape with the front is studied by numerical methods. Some illustrative examples of ongoing processes are given. Among possible applications, the controlling the spectra of signals, in particular, noise suppression by irradiating it with shocks or sawtooth waves can be mentioned. © 2018 Elsevier B.V.

  • 19.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Hedberg, Claes
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Blekinge Inst Technol, S-37179 Karlskrona, Sweden..
    SINGLE SHOCK AND PERIODIC SAWTOOTH-SHAPED WAVES IN MEDIA WITH NON-ANALYTIC NONLINEARITIES2018In: Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, E-ISSN 1760-6101, Vol. 13, no 2, article id UNSP 18Article in journal (Refereed)
    Abstract [en]

    The review of new mathematical models containing non-analytic nonlinearities is given. These equations have been proposed recently, over the past few years. The models describe strongly nonlinear waves of the first type, according to the classification introduced earlier by the authors. These models are interesting because of two reasons: (i) equations admit exact analytic solutions, and (ii) solutions describe the real physical phenomena. Among these models are modular and quadratically cubic equations of Hopf, Burgers, Korteveg-de Vries, Khokhlov-Zabolotskaya and Ostrovsky-Vakhnenko type. Media with non-analytic nonlinearities exist among composites, meta-materials, inhomogeneous and multiphase systems. Some physical phenomena manifested in the propagation of waves in such media are described on the qualitative level of severity.

  • 20.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Hedberg, Claes
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Wave Resonance in Media with Modular, Quadratic and Quadratically-Cubic Nonlinearities Described by Inhomogeneous Burgers-Type Equations2018In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 64, no 4, p. 422-431Article in journal (Refereed)
    Abstract [en]

    The phenomenon of “wave resonance” which occurs at excitation of traveling waves in dissipative media possessing modular, quadratic and quadratically-cubic nonlinearities is studied. The mathematical model of this phenomenon is the inhomogeneous (or “forced”) equation of Burgers type. Such nonlinearities are of interest because the corresponding equations admit exact linearization and describe real physical objects. The presence of “accompanying sources” (traveling with the wave) on the right-hand side of the inhomogeneous equations ensures the inflow of energy into the wave, which thereafter spreads throughout the wave profile, flows to emerging shock fronts, and then dissipates due to linear and nonlinear losses. As an introduction, the phenomenon of wave resonance in ideal and dissipative media is described and physical examples are given. Exact expressions for nonlinear steady-state wave profiles are derived. Non-stationary processes of wave generation, spatial “beating” of amplitudes with different relationship between the speed of motion of the sources and the natural wave velocity in the medium are studied. Resonance curves are constructed that contain a nonlinear shift of the absolute maxima to the “supersonic” region. The features of the resonance in each of the three types of nonlinearity are discussed. © 2018, Pleiades Publishing, Ltd.

  • 21.
    Wiaderek, Krzysztof
    et al.
    Politechnika Czestochowska, POL.
    Rutkowska, Danuta
    Politechnika Czestochowska, POL.
    Rakus-Andersson, Elisabeth
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Linguistic description of color images generated by a granular recognition system2017In: ARTIFICIAL INTELLIGENCE AND SOFT COMPUTING, ICAISC 2017, PT I / [ed] Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M., Springer Verlag , 2017, Vol. 10245, p. 603-615Conference paper (Refereed)
    Abstract [en]

    The paper proposes a new method employed in an intelligent pattern recognition system that generates linguistic description of color digital images. The linguistic description is produced based on fuzzy rules and information granules concerning colors as most important among image attributes. With regard to the color, the CIE chromaticity color model is applied, with the concept of fuzzy color areas. The linguistic description uses information about location of color granules in input images. © Springer International Publishing AG 2017.

  • 22.
    Wiaderek, Krzysztof
    et al.
    Czestochowa University of Technology, POL.
    Rutkowska, Danuta
    Czestochowa University of Technology.
    Rakus-Andersson, Elisabeth
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    New Algorithms for a Granular Image Recognition System2016In: Artificial Intelligence and Soft Computing LNAI 9693: Proceedings of the 15th International Conference, ICAISC 2016 / [ed] Leszek Rutkowski et al., Berlin Heidelberg: Springer, 2016, Vol. II, p. 755-766Conference paper (Refereed)
    Abstract [en]

    The paper describes new algorithms proposed for the granular pattern recognition system that retrieves an image from a collection of color digital pictures based on the knowledge contained in the object information granule (OIG). The algorithms use the granulation approach that employs fuzzy and rough granules. The information granules present knowledge concerning attributes of the object to be recognized. Different problems are considered depending on the full or partial knowledge where attributes are "color", "location", "size", and  "shape".

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