Browsing by Author "Kocken, Hale Gonce"

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Finding Compromise Solutions for Fully Fuzzy Multi-Objective Linear Programming Problems by Using Game Theory Approach
(IOS Press, 2022) Temelcan, Gizem; Kocken, Hale Gonce; Albayrak, Inci
Solving multi-objective linear programming (MOLP) problems and fully fuzzy multi-objective linear programming (FFMOLP) problems involves the trade-off process among several objectives. A new algorithm extended where FFMOLP problems are solved using a 2-player zero-sum game approach to deal with this case. Firstly, The FFMOLP problem is separated into a certain number of fully fuzzy linear programming (FFLP) problems and each is solved by applying any method. After forming a ratio matrix, a game theory approach is applied for finding the weights of objective functions and a weighted LP problem is constructed by these weights. Solving the weighted LP problem, a fuzzy compromise solution of the FFMOLP problem is found. Constructing different ratio matrices, it is also possible to obtain more than one compromise solution to be offered to the decision-maker(s). Some examples are given to show the applicability of the algorithm.
Fuzzy Modelling of Static System Optimum Traffic Assignment Problem Having Multi Origin-Destination Pair
(Elsevier Science Inc, 2021) Temelcan, Gizem; Kocken, Hale Gonce; Albayrak, Inci
Traffic congestion is an unpreventable problem to avoid in a transportation network and it has negative effects on traffic accident, time wasting, traffic delay and safety problem. Besides, in transportation networks, drivers do not want to deal with traffic jam while traversing between specified origin-destination pair. Therefore, traffic assignment (TA) is imperative to improve traffic management, transportation safety, time, and cost savings. System Optimum Traffic Assignment Problem (SOTAP) is a kind of TA model which aims to minimize the total system travel time on the network, and satisfies the flow conservation constraints. To model the SOTAP more realistically, the imprecise parameters can be taken as fuzzy. Therefore, in this paper, we focus on converting the conventional SOTAP to a fuzzy quadratic programming problem (QPP) which is named System Optimum Fuzzy Traffic Assignment Problem (SOFTAP). Here, link travel time is expressed with BPR function as generally used in the literature by converting to fuzzy except link-dependent parameters. Thus, the nonlinear objective function of SOFTAP is expressed in terms of fuzzy link flows and fuzzy link travel times. A solution approach from the literature is modified to the reconstructed SOFTAP.
Handling Uncertainty in Rheological Properties of Green Eggshell Nanocomposites by a Fuzzy-Hybrid Modeling Approach: A Comparative Study
(IOP Publishing Ltd, 2023) Insel, Mert Akin; Karakus, Selcan; Temelcan, Gizem; Kocken, Hale Gonce; Albayrak, Inci
Fuzzy regression is an attractive application due to its ability to solve problems in the absence of accurate mathematical models. In this study, rheological properties of a bio-nanocomposite were predicted using fuzzy regression. The aim of study is to introduce the methodology and application of fuzziness in detail for handling uncertainty in the experimental data. In this context, rheological properties of green eggshell bio-nanocomposites are investigated using different operating parameters. Since the determination of surface tension is prone to experimental errors, a novel fuzzy-hybrid model is proposed in addition to a crisp model. Statistical error analysis is conducted to assess the validity of the multivariate models proposed. While both models provided satisfactory results, it is observed that the fuzzy-hybrid model outperforms the crisp model in both accuracy and generality. This study highlights that the proposed models have an impressive potential to be used for modeling experimental studies in nanotechnological manufacturing applications.
On Modelling of Surface Tension of Cmc-Α Nanoparticles by Fuzzy-Hybrid Approach: A Comparison Study
(Wiley, 2023) Kocken, Hale Gonce; Insel, Mert Akin; Temelcan, Gizem; Karakus, Selcan; Albayrak, Inci
Surface tension is one of the most important rheological parameters of nanoliquids. It influences the thermophysical and mass transfer properties of nanostructures. Accurate estimation of the surface tension from operating variables is critical for determining optimal production processes. However, the challenges of producing nanoparticles and measuring their properties introduce experimental errors in the data used for mathematical modelling. Crisp regression approaches provide adequate representation of the data, but they do not provide information about the experimental uncertainty. In this study, a fuzzy-hybrid approach is proposed for mathematical modelling of surface tension of carboxymethyl cellulose/chitosan-alpha-Fe2O3 nanoparticles. Then, the proposed model is compared with a crisp model from a previous study. Error analysis is conducted to validate the constructed fuzzy model. It is observed that the fuzzy-hybrid modelling approach has yielded significantly lower error values (a 60%-90% improvement in all error metrics on average), and thus, it is superior to the crisp approach. This study contributes to the subject of modelling rheological properties. It is shown that the fuzzy-hybrid approach has impressive potential to be utilized for modelling the rheological properties of nanostructures.
Solution to the Single Parametric Linear Programming Problems via Simplex-Based Algorithms: Handling the Uncertainties in Costs, Left or Right-Hand Sides
(Croatian Operational Research Society, 2026) Ergenecosar, Gizem Temelcan; Kocken, Hale Gonce; Albayrak, Inci; Sivri, Mustafa
Parametric programming is one of the notable approaches to expressing the uncertainties encountered in real life. Many studies express the parameters of the objective function and right-hand side parametrically, but only a few include the parametric coefficient matrix of the constraints. This paper examines the feasibility and optimality conditions of the simplex table and proposes a simplex-based algorithm (dual-simplex, generalized-simplex, or primal-simplex). In the solution process, each case is considered independently through the mathematical analysis of simplex multipliers. Distinct numerical examples illustrate each case to demonstrate the algorithm's implementation.