Papers by Tofigh Allahviranloo
International Journal of Contemporary Mathematical Sciences, 2007
In this paper, the fuzzy integer linear programming problem (FILP) is considered. This problem is... more In this paper, the fuzzy integer linear programming problem (FILP) is considered. This problem is reduced to crisp integer linear programming problem. This transformation is performed by the related theorems and lemmas. The solution of FILP is obtained by the solutions of ILP's. Finally the method is illustrated by two numerical examples.
International Mathematical Forum, 2007
In many application to wish data envelopment analysis could be applied there is often a fixed or ... more In many application to wish data envelopment analysis could be applied there is often a fixed or common cost , wich is imposed on all decision making units (DM U s ).In proposed approach by Cook and kress (1999)of equitable allocation of shared costs between all DM U s several problems should be solved which gives rise to commputational difficulties. G. r. Jahanshahloo et al.presened an approoch in which without solving linear programmin problems only using simple formulas the equitable allocation is achieved. In this paper this approach is imposed on decision making units (DM U s) with fuzzy inputs and outputs in the case that fixed costs are fuzzy.
Journal of Mathematical Extension, Oct 22, 2014
In this paper, the concept of stability for fuzzy control systems is discussed from a mathematica... more In this paper, the concept of stability for fuzzy control systems is discussed from a mathematical point of view. Our main objective is to investigate the stability of fuzzy linear systems with bounded input and bounded output. Necessary and sufficient conditions for this kind of stability are presented by a theorem and it is illustrated by solving an example.
Fuzzy Sets and Systems, 2016
Applied Mathematics and Computation, Mar 1, 2005
In this paper the Gauss-Sidel iterative method in Allahviranloo [Appl. Math. Comput., in press], ... more In this paper the Gauss-Sidel iterative method in Allahviranloo [Appl. Math. Comput., in press], for solving Fuzzy system of linear equations (FSLE) is transformed to the successive over relaxation (SOR) method. This method is discussed in detail and followed by convergence theorem. Algorithm is compared with the Gauss-Sidel method by solving a numerical example.
Applied Soft Computing, 2011
... techniques and a thorough discussion of the validity issue are key contributions as well. exp... more ... techniques and a thorough discussion of the validity issue are key contributions as well. expand. A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images. Tamalika Chaira. Pages: 1711-1717. doi>.
Adomian decomposition method has been applied to solve many functional equations so far. In this ... more Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy heat equation, which governs on numerous scientific and engineering experimentations. Some special cases of the equation are solved as examples to illustrate ability and reliability of the method.
In this paper, we introduce a computational method to find an ap- proximate analytical solution f... more In this paper, we introduce a computational method to find an ap- proximate analytical solution for fuzzy differential equations. At first, variational iteration method (VIM) is used to solve the crisp problem then with the extension principle we find the fuzzy approximation so- lution. Examples are given , including linear and nonlinear fuzzy first- order differential equations.
In this study, differential transform method (DTM) is applied to fuzzy integro-differential equat... more In this study, differential transform method (DTM) is applied to fuzzy integro-differential equation. The concept of generalized Hdifferentiability is used. If the equation has a solution in terms of the series expansion of known functions; this powerful method catches the exact solution. Some numerical examples are also given to illustrate the superiority of the method. All rights reserved.
Fuzzy Information and Engineering, 2012
ABSTRACT Fuzzy systems have gained more and more attention from researchers and practitioners of ... more ABSTRACT Fuzzy systems have gained more and more attention from researchers and practitioners of various fields. In such systems, the output represented by a fuzzy set sometimes needs to be transformed into a scalar value, and this task is known as the defuzzification process. Several analytic methods have been proposed for this problem, but in this paper, the researchers suggest a modified approach to the problem of defuzzification, using the bi-symmetric weighted distance between two fuzzy numbers. This defuzzification can be used as a crisp approximation with respect to a fuzzy quantity. By considering this and with benchmark between fuzzy numbers, we can present a method for ranking, which can effectively rank variou s fuzzy numbers and their images and overcome the shortcomings of the previous techniques. After illustrating many numerical examples, following our procedure, the ranking results become valid.
ABSTRACT In this paper, we introduce the fuzzy fractional Ostrowski type inequality for preinvex ... more ABSTRACT In this paper, we introduce the fuzzy fractional Ostrowski type inequality for preinvex functions. We use the Holder inequality to find some new bounds for this type of inequality. Then we accommodate this result with the previous works that have been done before. After that we have fuzzy Ostrowski’s inequality for prequasiinvex and logarithmic preinvex via fractional integral. At the end you can see the conclusion of the paper.
Fuzzy Sets and Systems, 2015
ABSTRACT In this paper a fuzzy heat equation with fuzzy initial values is considered. The concept... more ABSTRACT In this paper a fuzzy heat equation with fuzzy initial values is considered. The concept of generalized Hukuhara differentiation is interpreted thoroughly in the univariate and multivariate cases, and also several properties for generalized Hukuhara differentiability are obtained on the topics, such as switching point, the univariate and multivariate fuzzy chain rules, fuzzy mean value theorem, among others. The objective of this paper is to prove the uniqueness of a solution for a fuzzy heat equation and show that a fuzzy heat equation can be modeled as two systems of fuzzy differential equations by considering the type of differentiability of solutions. Finally, some examples show the behavior of the solutions obtained.
Mathematical Sciences Letters, 2016
Information Processing and Management …, Jan 1, 2010
In this paper, a new approach for solving first order fuzzy differential equations (FDEs) with fu... more In this paper, a new approach for solving first order fuzzy differential equations (FDEs) with fuzzy initial value is considered under strongly generalized H-differentiability. In order to obtain solution of FDE, we extend the 1-cut solution of original problem. This extension is constructed based on the allocating some unknown spreads to 1-cut solution, then created value is replaced in the original FDE. However obtaining solutions of FDE is equivalent to determine the unknown spreads while 1-cut solution is derived via previous step (in ...
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011), 2011
In this paper, we consider two new uniqueness results for fuzzy fractional differential equations... more In this paper, we consider two new uniqueness results for fuzzy fractional differential equations (FFDEs) involving Riemann-Liouville generalized H-differentiability with the Nagumo-type condition and the Krasnoselskii-Krein-type condition. To this purpose, the equivalent integral forms of FFDEs are determined and then these are used to study the convergence of the Picard successive approximations.
Soft Computing, 2012
In this paper, an algebraic solution of interval linear system involving a real square matrix and... more In this paper, an algebraic solution of interval linear system involving a real square matrix and an interval right-hand side vector is obtained. A new approach to solve such systems based on the new concept “inclusion linear system” is proposed. Moreover, new necessary and sufficient conditions are derived for obtaining the unique algebraic solution. Furthermore, based on our method, an
Soft Computing, 2013
ABSTRACT In this paper, We propose a simple and practical method (that works only for triangular ... more ABSTRACT In this paper, We propose a simple and practical method (that works only for triangular fuzzy numbers) to solve an arbitrary fully fuzzy linear system (FFLS) in the form $\widetilde{A}\otimes \widetilde{x}=\widetilde{b},$ where $\widetilde{A}_{n \times n}$ is a fuzzy matrix, $\widetilde{x}$ and $\widetilde{b}$ are n × 1 fuzzy vectors. The idea of the presented method is constructed based on the extending 0-cut and 1-cut solution of original fully fuzzy linear systems (FFLS). We also define a fuzzy solution of FFLS and establish the necessary and sufficient conditions for the uniqueness of a fuzzy solution.
Procedia Computer Science, 2011
Linear systems have important applications in many branches of science and engineering in many ap... more Linear systems have important applications in many branches of science and engineering in many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. So, it is immensely important to develop a numerical procedure that would appropriately treat general fuzzy linear systems and solve them. In this paper, we propose bounded and symmetric solutions of fully fuzzy linear systems in the dual form (DFFLS) based on a 1-cut expansion. To this end, we solve the 1-cut of a DFFLS (we ...
Neural Computing and Applications, 2013
ABSTRACT This paper presented a non-normal p-norm trapezoidal fuzzy number–based fault tree techn... more ABSTRACT This paper presented a non-normal p-norm trapezoidal fuzzy number–based fault tree technique to obtain the reliability analysis for substations system. Due to uncertainty in the collected data, all the failure probabilities are represented by non-normal p-norm trapezoidal fuzzy number. In this paper, the fault tree incorporated with the non-normal p-norm trapezoidal fuzzy number and minimal cut sets approach are used for reliability assessment of substations. An example of 66/11 kV substation is given to demonstrate the method. Further, fuzzy risk analysis problems are described to find out the probability of failure of each components of the system using linguistic variables, which could be used for managerial decision making and future system maintenance strategy.
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Papers by Tofigh Allahviranloo