Search

This paper deals with knapsack problem in fuzzy nature, where both the objective function and constraints are considered to be fuzzy. Three different models for fuzzy knapsack problem are proposed including, expected value model, chance-constrained model, and dependent-chance model. Credibility ranking method is applied to convert the fuzzy models into a crisp equivalent linear one considering triangular and trapezoidal fuzzy numbers. The solution of the fuzzy problem is obtained with respect to different satisfaction degrees in the objective function and constraints. Several numerical examples are given to demonstrate different models and concepts. The proposed approaches are applied to model and to solve a fuzzy pre-disaster investment decision problem.

The first author would like to appreciate from the research grant of University of Mazandaran. The research of Jose Luis Verdegay is supported in part by the project TIN2017-86647-P (Spanish Ministry of Economy and Competitiveness) which includes FEDER funds from the European Union., Recently fuzzy interval flexible linear programs have attracted many interests. These models are an extension of the classical linear programming which deal with crisp parameters. However, in most of the real-world applications, the nature of the parameters of the decisionmaking problems is generally imprecise. Such uncertainties can lead to increased complexities in the related optimisation efforts. Simply ignoring these uncertainties is considered undesired as it may result in inferior or wrong decisions. Therefore, inexact linear programming methods are desired under uncertainty. In this paper,weconcentrate a fuzzy flexible linear programming model with flexible constraints and the interval objective function and then propose a new solving approach based on solving an associated multi-objective model. Finally, numerical example is included to illustrate the mentioned solving process., University of Mazandaran, Spanish Ministry of Economy and Competitiveness TIN2017-86647-P, European Commission

Neutrosophic set theory is a generalization of the intuitionistic fuzzy set which can be considered as a powerful tool to express the indeterminacy and inconsistent information that exist commonly in engineering applications and real meaningful science activities. In this paper an interval neutrosophic linear programming (INLP) model will be presented, where its parameters are represented by triangular interval neutrosophic numbers (TINNs) and call it INLP problem. Afterward, by using a ranking function we present a technique to convert the INLP problem into a crisp model and then solve it by standard methods.

The aim of this paper is to introduce a formulation of linear programming problems involving intuitionistic fuzzy variables. Here, we will focus on duality and a simplex-based algorithm for these p...

PurposeFor extending the common definitions and concepts of grey system theory to the optimization subject, a dual problem is proposed for the primal grey linear programming problem.Design/methodology/approachThe authors discuss the solution concepts of primal and dual of grey linear programming problems without converting them to classical linear programming problems. A numerical example is provided to illustrate the theory developed.FindingsBy using arithmetic operations between interval grey numbers, the authors prove the complementary slackness theorem for grey linear programming problem and the associated dual problem.Originality/valueComplementary slackness theorem for grey linear programming is first presented and proven. After that, a dual simplex method in grey environment is introduced and then some useful concepts are presented.

The current paper focuses on a multiobjective transportation problem which is a special type of vector minimum problem. In order to deal with such a problem, a new model based on fuzzy goal program...

In this paper, due to increasing competition in the business world, which makes decision makers dealing with multiple options/information for optimal decisions on a single task, we will look at mul...

Today, human decisions are more than ever based on information. But most of this information is not definitive, and in this situation, logical decision making is very difficult based on this uncertainty. Different methods are used to represent this uncertainty, including the fuzzy numbers. The fuzzy linear programming problem is one of the interesting concepts to be addressed in fuzzy optimization. Fully Fuzzy Linear Programming Problems (FFLP) are issues in which all parameters of the coefficients of the variables in the target functions, the coefficients of the variables in the constraints, the right-hand side of the constraints, and the decision variables in them are fuzzy. In this paper, we show that Definition 2.6 which is used by Ezzati et al. [1], failed to compare any arbitrary triangular fuzzy numbers. We demonstrate that their presented method is not well in general, thus the proposed method finds the fuzzy optimal solution of fully fuzzy linear programming problems by Ezzati et al. [1]. Then a new approach is proposed for solving this FFLP problem. An example is also presented to demonstrate the new method.

In developing countries, the demand for old aged people requiring private health care at home is dramatically growing with the improvement of living standards. Since vehicles are used for transferring the medical staff (or doctors) to patient homes, it may be interesting to select a vehicle type based on the cost, capacity, and environmental sustainability (fuel consumption and CO2 gas emission per unit of distance) to maximize profits and social responsibility. In this paper, the first contribution, a new green home health care network for location, allocation, scheduling, and routing problems is developed with uncertain conditions. Another novelty, the time window to serve patients is also considered. In this regard, a novel grey flexible linear programming model is developed to cope with the uncertain nature of costs and capacity parameters that is as one important novelty. Due to this model’s high complexity and difficulty in large-scale instances, this research develops two novel hybrid algorithms. The first hybrid strategy called the HSEOSA algorithm combines the Social Engineering Optimizer algorithm with the Simulated Annealing method. In terms of contribution to the related solution methodology, additionally, the Keshtel Algorithm is incorporated with the Genetic Algorithm called the HGAKA algorithm as the second new hybrid metaheuristic. An extensive comparison among the proposed algorithms is performed to find the most efficient one for the application of home healthcare in real practice. To validate the proposed model, a novel real case study is illustrated in the home healthcare services in Tehran/Iran.

In this paper, a multi-objective model of transportation problem with multi-choice parameters is presented. The alternative choices of the multi-choice parameter are considered as random variables. Due to the conflicting objective functions and the multi-choice of parameters, the problem cannot be solved directly. So, we first consider the interpolating polynomials for the multi -choice parameters. Next, we use the expected value model and the chance constraint approach to convert the original problem into a crisp form which is equivalent to it. Finally, a fuzzy approach is applied to find a compromise solution.