Fully Fuzzy Quadratic programming with unrestricted Fully Fuzzy variables and Parameters

In this paper, we propose a method of solving the fully fuzzy linear fractional programming problems, Express all the parameters and variables are triangular fuzzy numbers. Convert all the triangular fuzzy numbers in their parametric form, we convert the fractional programming problem in to a single objective linear programming problem in parametric form. We put new fuzzy arithmetic and fuzzy ranking, we obtain the optimal solution the given fully fuzzy linear fractional programming problem without converting to its equivalent crisp linear programming problem. A numerical example is provided to illustrate the efficiency of the proposed method.

Using different dominance criteria in stochastic fuzzy linear multiobjective programming: A case of fuzzy weighted objective function

We present an approach for ordering fuzzy numbers, then we utilize it to suggest two models for solving the fuzzy linear programming (FLP) problem. In this research we present a new approach for ordering two fuzzy numbers and show some practical advantages of it over other methods. We also utilize the suggested approach to introduce two techniques to solve the FLP problem. In the first technique, we convert the fuzzy linear program into a crisp bicriteria linear program. In this new model the fuzzy objective function is replaced by two crisp objectives to be optimized, and each fuzzy constraint is replaced by two or three crisp constraints depending on the level of certainty /spl alpha/-whether /spl alpha/ has or has not been assigned. In the second technique we find the possibility distribution of the objective function over all possible feasible decisions directly.

In this paper, an efficient approach is presented to solve fully fuzzy linear fractional programming problems. In this approach, first by Alpha-cuts on the objective function and the constraints, the problem is transforming into a bi-objective linear programming problem, and then the resulting problem is converted into two crisp linear programming problems. A numerical example is presented to illustrate the proposed approach. The obtained results demonstrate the acceptable performance of the proposed solution approach.

The fuzzy set theory is being applied massively in many fields these days. One of these is linear programming problems. Kheirfam and Hasani (Sensitivity analysis for fuzzy linear programming problems with fuzzy variables, Advanced Modeling and Optimization, 12 (2010) 257-272), proposed a method for the sensitivity analysis for fuzzy linear programming (FLP) problems with fuzzy variables. There are some important cases that are not considered by Kheirfam and Hasani. In this paper, those cases are considered and numerical examples are solved.

ABSTRACTIn this paper, we consider a Fuzzy Stochastic Linear Fractional Programming problem (FSLFP). In this problem, the coefficients and scalars in the objective function are the triangular fuzzy number and technological coefficients and the quantities on the right side of the constraints are fuzzy random variables with the specific distribution. Here we change an FSLFP problem to an equivalent deterministic Multi-objective Linear Fractional Programming (MOLFP) problem. Then by using Fuzzy Mathematical programming approach transformed MOLFP problem is reduced single objective Linear programming (LP) problem. A numerical example is presented to demonstrate the effectiveness of the proposed method.

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations.

In this paper we deal with multiobjective linear and quadratic programming problem with uncertain information. So far in the field of statistical analysis and data mining, e.g., mean-variance portfolio problem, support vector machine and their varieties, we have encountered various kinds of quadratic and linear programming problems with multiple criteria. Moreover coefficients in such problems have uncertainty that is expressed by interval, probabilistic distribution or possibilistic (fuzzy) distribution. In this paper, we define a robust basis for all possible perturbation of coefficients within intervals in objective functions and constraints that is regarded as secure and conservative solution under uncertainty. According to the conventional multi-objective programming literature, it is required to solve test subproblem for each basis. Therefore, in case of our interval problem excessive computational demand is estimated. In this paper investigating the properties of robust basis by means of combination of interval extreme points we obtained the result that the robust basis can be examined by working with only a finite subset of possible perturbations of the coefficients

In this paper, shortcomings and limitations of the existing methods for solving fuzzy linear programming (FLP) problems are pointed out. To overcome the limitations as well as to resolve the shortcomings, a new method is proposed for solving FLP problems. To show the advantage of the proposed method over existing methods, a FLP problem is solved by the existing methods as well as the proposed method, and the obtained results are compared.

Fuzzy programming has been developed mainly under the assumption of non-interaction among fuzzy coefficients. However, this assumption is not always suitable in the treatment of real world problems. Several approaches have been proposed to treat the interaction among fuzzy coefficients. In this paper, we review treatments of interaction among fuzzy coefficients in fuzzy linear programming problems. Using a necessity fractile model of a simple linear program with fuzzy coefficients, we will see the differences between non-interactive and interactive problems. We review the five approaches to interactive fuzzy numbers, i.e., weak independent fuzzy numbers, a fuzzy vector with a quadratic membership function, scenario decomposed fuzzy numbers, an oblique fuzzy vector, and a fuzzy polytope.KeywordsMembership FunctionFuzzy NumberLinear Programming ProblemUncertain ParameterMultivariate Normal DistributionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper develops an approach for solving non-linear programming problem in intuitionistic fuzzy environment. Since, fuzziness may occur in some or all parameters of a system, we discuss both situations in this study. We transform the intuitionisti

The problem of fully fuzzy programming was one of the problems that many treatments have appeared for due to ambiguity and inaccuracy of its ambiguous coefficients. In this study, finding the optimal numerical solution for fully fuzzy linear fractional programming problems (FFLFPP) using the ranking functions was obtained. The proposed pentagonal ranking function (PPRF) multiplied by γ5 has been derived, as well as the proposed heptagonal ranking function (PHRF) multiplied by γ5 has been derived too. Two laws were obtained the first one was the novel ranking membership pentagonal and the second one was the heptagonal function then utilized to solve FFLFPP after converting the problems into FFLPP by utilizing the complementary method, then converting them to crisp linear programming problems and finding the optimal numerical solution for problems by using the proposed ranking functions. The paper included numerical example to illustrate the applied technique and the accuracy of the solution, and a comparison with available techniques were add the novelty of this study.

Ranking in quadratic integer programming problems

The difficulty in solving either multi-objective linear programming (MOLP) problems or fuzzy multi-objective linear programming (FMOLP) problems is the trade-off among objectives. To deal with this difficulty, we proposed a new algorithm for solving FMOLP problems by using zero-sum game. First, FMOLP problem given is converted to a crisp MOLP problem by using ranking function, and then a payoff matrix is constructed to find the weights of each objective function of the MOLP problem. After that, each weight is multiplied with the corresponding objective function, a single-objective LP problem is obtained and thus, FMOLP problem is solved. The proposed algorithm is illustrated by numerical examples for the FMLOP problems having fuzzy constraints or not.

<abstract><p>The primary goal of optimization theory is to formulate solutions for real-life challenges that play a fundamental role in our daily lives. One of the most significant issues within this framework is the Linear Fractional Programming Problem (LFrPP). In practical situations, such as production planning and financial decision-making, it is often feasible to express objectives as a ratio of two distinct objectives. To enhance the efficacy of these problems in representing real-world scenarios, it is reasonable to utilize fuzzy sets for expressing variables and parameters. In this research, we have worked on the Fully Fuzzy Linear Fractional Linear Programming Problem (FFLFrLPP). In our approach to problem-solving, we simplified the intricate structure of the FFLFrLPP into a crisp Linear Programming Problem (LPP) while accommodating the inherent fuzziness. Notably, unlike literature, our proposed technique avoided variable transformation, which is highly competitive in addressing fuzzy-based problems. Our methodology also distinguishes itself from the literature in preserving fuzziness throughout the process, from problem formulation to solution. In this study, we conducted a rigorous evaluation of our proposed methodology by applying it to a selection of numerical examples and production problems sourced from the existing literature. Our findings revealed significant improvements in performance when compared to established solution approaches. Additionally, we presented comprehensive statistical analyses showcasing the robustness and effectiveness of our algorithms when addressing large-scale problem instances. This research underscores the innovative contributions of our methods to the field, further advancing the state-of-the-art in problem-solving techniques.</p></abstract>