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This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized by uncertainty and imprecision. Traditional linear programming methods often fall short in handling the inherent vagueness in real-world problems. To address this gap, an innovative method has been proposed which incorporates fuzzy logic to model the uncertain parameters as TFNs, allowing for a more realistic and flexible representation of the problem space. The proposed method stands out due to its integration of fuzzy arithmetic into the optimization process, enabling the handling of fuzzy constraints and objectives directly. Unlike conventional techniques that rely on crisp approximations or the defuzzification process, the proposed approach maintains the fuzziness throughout the computation, ensuring that the solutions retain their fuzzy characteristics and better reflect the uncertainties present in the input data. In summary, the proposed method has the ability to directly incorporate fuzzy parameters into the optimization framework, providing a more comprehensive solution to FFLP problems. The main findings of this study underscore the method's effectiveness and its potential for broader application in various fields where decision-making under uncertainty is crucial. [ABSTRACT FROM AUTHOR]

The study of the time‐fractional vibration equation (VE) of large membranes is vital due to its widespread applications. Various researchers have investigated the titled problem in which the variables and parameters have been considered as crisp/exact. However, in actual practice, this may contain uncertainty because of errors in observations, maintenance induced error, and other errors. In this investigation, we have considered these uncertainties as interval/fuzzy, and a method, namely double parametric form of fuzzy numbers are used to solve the uncertain fractional vibration model of order α(1<α≤2). The titled problem has been solved under various cases using the Residual power series method (RPSM). The performance of the present method is well in terms of computational efficiency. The consistency of the method is displayed by providing numerical solutions for various cases. Obtained results are depicted in terms of figures and are also compared with individual cases. [ABSTRACT FROM AUTHOR]

Purpose – The solution of dynamic problems of structures using finite element method leads to generalised eigenvalue problem. In general, if the material properties are crisp (exact) then the authors get crisp eigenvalue problem. But in actual practice, instead of crisp material properties the authors may have only bounds of values as a result of errors in measurements, observations and calculations or it may be due to maintenance induced error, etc. Such bounds of values may be considered in terms of interval or fuzzy numbers. The purpose of this paper is to develop a fuzzy filtering procedure for finding real eigenvalue bounds of different structural problems. Design/methodology/approach – The proposed fuzzy filtering algorithm has been developed in terms of fuzzy number to solve the fuzzy eigenvalue problem. The initial bounds of fuzzy eigenvalues are filtered to obtain precise eigenvalue bounds which are depicted by fuzzy (triangular fuzzy number) plots using α-cut. Findings – Previously, bounds of eigenvalues of interval matrices have been investigated by few authors. But when the structural problem consists of fuzzy material properties, then the interval eigenvalue bounds may be obtained for each interval of the fuzzy number. The proposed algorithm has been applied for standard fuzzy eigenvalue problems which may be extended to generalised fuzzy eigenvalue problems for obtaining filtered fuzzy bounds. Originality/value – The developed fuzzy filtering method is found to be efficient for different structural dynamics problems with fuzzy material properties. [ABSTRACT FROM AUTHOR]

This paper investigates the identification procedure of the column stiffness of multistorey frame structures by using the prior (known) uncertain parameters and dynamic data. Uncertainties are modelled through triangular convex normalized fuzzy sets. Bounds of the identified uncertain stiffness are obtained by using a proposed fuzzy based iteration algorithm with Taylor series expansion. Example problems are solved to demonstrate the reliability and efficiency of the identification process. [ABSTRACT FROM AUTHOR]

The present paper investigates the numerical solution of an imprecisely defined nonlinear coupled time-fractional dynamical model of marriage (FDMM). Uncertainties are assumed to exist in the dynamical system parameters, as well as in the initial conditions that are formulated by triangular normalized fuzzy sets. The corresponding fractional dynamical system has first been converted to an interval-based fuzzy nonlinear coupled system with the help of a single-parametric gamma-cut form. Further, the double-parametric form (DPF) of fuzzy numbers has been used to handle the uncertainty. The fractional reduced differential transform method (FRDTM) has been applied to this transformed DPF system for obtaining the approximate solution of the FDMM. Validation of this method was ensured by comparing it with other methods taking the gamma-cut as being equal to one. [ABSTRACT FROM AUTHOR]