Browsing by Author "Amrahov, Sahin Emrah"

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A New Curve Fitting Based Rating Prediction Algorithm For Recommender Systems
(2022) Yilmaz, A. R.; Amrahov, Sahin Emrah; Gasilov, Nizami A.; Yigit-Sert, Sevgi
The most algorithms for Recommender Systems (RSs) are based on a Collaborative Filtering (CF) approach, in particular on the Probabilistic Matrix Factorization (PMF) method. It is known that the PMF method is quite successful for the rating prediction. In this study, we consider the problem of rating prediction in RSs. We propose a new algorithm which is also in the CF framework; however, it is completely different from the PMF-based algorithms. There are studies in the literature that can increase the accuracy of rating prediction by using additional information. However, we seek the answer to the question that if the input data does not contain additional information, how we can increase the accuracy of rating prediction. In the proposed algorithm, we construct a curve (a low-degree polynomial) for each user using the sparse input data and by this curve, we predict the unknown ratings of items. The proposed algorithm is easy to implement. The main advantage of the algorithm is that the running time is polynomial, namely it is theta(n2), for sparse matrices. Moreover, in the experiments we get slightly more accurate results compared to the known rating prediction algorithms.
Numerical solution of linear inhomogeneous fuzzy delay differential equations
(2019) Fatullayev, A.G.; Gasilov, Nizami A.; Amrahov, Sahin Emrah; AAN-9386-2020
We investigate inhomogeneous fuzzy delay differential equation (FDDE) in which initial function and source function are fuzzy. We assume these functions be in a special form, which we call triangular fuzzy function. We define solution as a fuzzy bunch of real functions such that each real function satisfies the equation with certain membership degree. We develop an algorithm to find the solution, and we provide the existence and uniqueness results for the considered FDDE. We also present an example to show the applicability of the proposed algorithm.
On differential equations with interval coefficients
(2019) Gasilov, Nizami A.; Amrahov, Sahin Emrah; AAN-9386-2020
In this study, a new approach is developed to solve the initial value problem for interval linear differential equations. In the considered problem, the coefficients and the initial values are constant intervals. In the developed approach, there is no need to define a derivative for interval-valued functions. All derivatives used in the approach are classical derivatives of real functions. The reason for this is that the solution of the problem is defined as a bunch of real functions. Such a solution concept is compatible also with the robust stability concept. Sufficient conditions are provided for the solution to be expressed analytically. In addition, on a numerical example, the solution obtained by the proposed approach is compared with the solution obtained by the generalized Hukuhara differentiability. It is shown that the proposed approach gives a new type of solution. The main advantage of the proposed approach is that the solution to the considered interval initial value problem exists and is unique, as in the real case.
Relationship Between Bede-Gal Differentiable Set-Valued Functions and Their Associated Support Functions
(2016) Amrahov, Sahin Emrah; Khastan, Alireza; Gasilov, Nizami; Fatullayev, Afet Golayoglu; AEN-1756-2022
In this study, we adapt the concept of the Bede-Gal derivative, which was initially suggested for fuzzy number-valued functions, to set-valued functions. We use an example to demonstrate that this concept overcomes some of the shortcomings of the Hukuhara derivative. We prove some properties of Bede-Gal differentiable set-valued functions. We also study the relationship between a Bede-Gal differentiable set-valued function and its value's support function, which we call the associated support function. We provide examples of set-valued functions that are not Bede-Gal differentiable whereas their associated support functions are differentiable. We also present some applications of the Bede-Gal derivative to solving set-valued differential equations. (C) 2015 Elsevier B.V. All rights reserved.
Solution Method For A Non-Homogeneous Fuzzy Linear System Of Differential Equations
(2018) Gasilov, Nizami A.; Fatullayev, Afet Golayoglu; Amrahov, Sahin Emrah; AAN-9386-2020; 0000-0001-7747-5467; AAF-3339-2020
In this paper, we propose a new solution method to non-homogeneous fuzzy linear system of differential equations. The coefficients of the considered system are crisp while forcing functions and initial values are fuzzy. We assume each forcing function be in a special form, which we call as triangular fuzzy function and which represents a fuzzy bunch (set) of real functions. We construct a solution as a fuzzy set of real vector-functions, not as a vector of fuzzy-valued functions, as usual. We interpret the given fuzzy initial value problem (fuzzy IVP) as a set of crisp (classical) IVPs. Such a crisp IVP is obtained if we take a forcing function from each of fuzzy bunches and an initial value from each of fuzzy intervals. The solution of the crisp IVP is a vector-function. We define it to be an element of the fuzzy solution set and assign a membership degree which is the lowest value among membership degrees of taken forcing functions and initial values in the corresponding fuzzy sets. We explain our approach and solution method with the help of several illustrative examples. We show the advantage of our method over the differential inclusions method and its applicability to real-world problems. (C) 2018 Elsevier B.V. All rights reserved.
Solution of Linear Differential Equations with Fuzzy Boundary Values
(2014) Gasilov, Nizami; Amrahov, Sahin Emrah; Fatullayev, Afet Golayoglu; https://orcid.org/0000-0002-9955-8439; AEN-1756-2022
We investigate linear differential equations with boundary values expressed by fuzzy numbers. In contrast to most approaches, which search for a fuzzy-valued function as the solution, we search for a fuzzy set of real functions as the solution. We define a real function as an element of the solution set if it satisfies the differential equation and its boundary values are in intervals determined by the corresponding fuzzy numbers. The membership degree of the real function is defined as the lowest value among membership degrees of its boundary values in the corresponding fuzzy sets. To find the fuzzy solution, we use a method based on the properties of linear transformations. We show that the fuzzy problem has a unique solution if the corresponding crisp problem has a unique solution. We prove that if the boundary values are triangular fuzzy numbers, then the value of the solution at a given time is also a triangular fuzzy number. The defined solution is the same as one of the solutions obtained by Zadeh's extension principle. For a second-order differential equation with constant coefficients, the solution is expressed in analytical form. Examples are given to describe the proposed approach and to compare it to a method that uses the generalized Hukuhara derivative, which demonstrates the advantages of our method. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.
Solving A Nonhomogeneous Linear System of Interval Differential Equations
(2018) Gasilov, Nizami A.; Amrahov, Sahin Emrah; AAN-9386-2020
In most application problems, the exact values of the input parameters are unknown, but the intervals in which these values lie can be determined. In such problems, the dynamics of the system are described by an interval-valued differential equation. In this study, we present a new approach to nonhomogeneous systems of interval differential equations. We consider linear differential equations with real coefficients, but with interval initial values and forcing terms that are sets of real functions. For each forcing term, we assume these real functions to be linearly distributed between two given real functions. We seek solutions not as a vector of interval-valued functions, as usual, but as a set of real vector functions. We develop a method to find the solution and establish an existence and uniqueness theorem. We explain our approach and solution method through an illustrative example. Further, we demonstrate the advantages of the proposed approach over the differential inclusion approach and the generalized differentiability approach.