Browsing by Author "Temelcan, G.T."

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Determining the Type of a Solution to the Fully Pythagorean Fuzzy Linear Equations System: Exact, Restricted, or Relaxed Approximate Solution
(Springer Nature, 2025) Temelcan, G.T.
In engineering and social research, linear systems are commonly used to address real-life problems of various dimensions. Therefore, many studies start by developing linear systems and then finding their solutions. Recent studies have demonstrated the effectiveness of Pythagorean fuzzy sets in capturing and representing complex forms of uncertainty, particularly when understanding the distinctions between membership and non-membership is crucial. This paper pioneers the finding a solution for a general (square or nonsquare) Fully Pythagorean Fuzzy Linear Equations System (FPFLES) with arbitrary triangular Pythagorean fuzzy numbers and fills a critical gap in the existing literature. Since an FPFLES consists of the sum of the multiplications of each arbitrary parameter and variable, and the fuzzy multiplication operation includes the min and max operators, a nonlinearity situation is observed in each equation. To overcome this situation, a transformation from fuzzy multiplication to inequalities is applied, and thus, a mixed integer programming (MIP) problem is formed. Depending on whether the MIP problems created by changing the constraints have an optimal solution, FPFLES has an exact solution or an approximate solution. The types of solutions are examined using a distance measure definition available in the literature. This paper also defines restricted and relaxed approximate solutions for FPFLES by determining whether the left-hand sides obtained from the substitution of solutions are completely covered by the right-hand sides of the equations. The approach is illustrated with some numerical examples, and the numerical results are analyzed within the distance measure to determine the closeness between the left-hand and right-hand sides of the system. © The Author(s) 2025.
Fuzzy Complex System of Linear Equations
(IGI Global, 2022) Temelcan, G.T.; Gonce Kocken, H.; Albayrak, I.
The complex system of linear equations (CSLE) has a wide range of applications in engineering, optimization, operational research, such as circuit analysis and wave equations in quantum mechanics. Since variables and/or parameters of the CSLE are generally unknown, uncertain, or imprecise in real-life applications, Fuzzy CSLE (FCSLE) arises. The fuzziness enables the modeling of the CSLE in a more natural and direct way, and thus, the FCSLE has attracted the attention of many researchers and become a significant area both in theory and application. With this motivation, a short review of the FCSLE has been conducted to guide the future studies of new researchers in this area. This review will give a general framework about the progression of the area, its solution approaches, and provide a bibliography on the topic. © 2023 by IGI Global. All rights reserved.
A Numerical Method for Integration of a Fuzzy Function Over a Fuzzy Interval
(Springer Science and Business Media Deutschland GmbH, 2022) Temelcan, G.T.; Gonce Kocken, H.; Albayrak, I.
A numerical method is presented for evaluating the integration of a fuzzy function (FF) over a fuzzy interval (FI) by combining the integration methods proposed by Zimmerman, which is known as the fuzzy Riemann integral (FRI) of type-II. In this study, monotonic increasing (or nondecreasing) nonnegative continuous FFs are considered for integration. In the proposed method, first, a fuzzy-valued function (FvF) is induced by a real-valued function (RvF) via extension principle and then each component of the triangular fuzzy valued-function, which is a RvF, is determined as a triangular fuzzy number (TFN) by integrating over the FI. The left and right components of fuzzy integral value are determined from the TFNs obtained by taking the minimum of the left components and the maximum of right components, and the middle component is provided using a ranking function. Some numerical examples are given to explain the methodology. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.