Optimal Solution of Neutrosophic Linear Fractional Programming Problems With Mixed Constraints

In this paper, Linear Fractional Programming (LFP) problems have been extended to neutrosophic sets (NSs) and the operations and functionality of these laws are studied. Moreover, the new algorithm is based on aggregation ranking function and arithmetic operations of triangular neutrosophic sets (TNSs). Furthermore, for the first time, in this paper, we take up a problem where the constraints are both equality and inequality neutrosophic triangular fuzzy number. Lead from genuine issue, a few numerical models are considered to survey the legitimacy, profitability and materialness of our technique. At last, some numerical trials alongside one contextual analysis are given to show the novel techniques are better than the current strategies.

Fuzzy solution of fully fuzzy multi-objective linear fractional programming problems

In this study, we present a novel method for solving fully fuzzy multi-objective linear fractional programming problems without transforming to equivalent crisp problems. First, we calculate the fuzzy optimal value for each fractional objective function and then we convert the fully fuzzy multi-objective linear fractional programming problem to a single objective fuzzy linear fractional programming problem and find its fuzzy optimal solution which inturn yields a fuzzy Pareto optimal solution for the given fully fuzzy multi-objective linear fractional programming problem. To demonstrate the proposed strategy, a numerical example is provided.

An Efficient Branch-and-Bound Algorithm for Globally Solving Minimax Linear Fractional Programming Problem

This paper presents an efficient outer space branch-and-bound algorithm for globally solving a minimax linear fractional programming problem (MLFP), which has a wide range of applications in data envelopment analysis, engineering optimization, management optimization, and so on. In this algorithm, by introducing auxiliary variables, we first equivalently transform the problem (MLFP) into the problem (EP). By using a new linear relaxation technique, the problem (EP) is reduced to a sequence of linear relaxation problems over the outer space rectangle, which provides the valid lower bound for the optimal value of the problem (EP). Based on the outer space branch-and-bound search and the linear relaxation problem, an outer space branch-and-bound algorithm is constructed for globally solving the problem (MLFP). In addition, the convergence and complexity of the presented algorithm are given. Finally, numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.

THE LINEAR-FRACTIONAL PROGRAMMING PROBLEM UNDER UNCERTAINTY CONDITIONS

This paper addresses the problem of linear-fractional programming under uncertainty. The uncertainty here is understood as the ambiguity of the coefficients’ values in the optimized functional. We give two mathematical formulations of the problem. In the first one, the uncertainty refers to the numerator: there are several sets of objective function coefficients, each coefficient can determine the numerator of the problem’s criterion at the stage of its solution implementation. The uncertainty in the second formulation refers to the denominator of the functional. We propose several compromise criteria for evaluating solutions to the problem we consider. We study the following two criterions in detail: 1) finding a compromise solution in which the deviation of the values of the partial functionals from their optimal values is within the specified limits; 2) finding a compromise solution according to the criterion of minimizing the total weighted excess of the values of partial functionals in relation to the specified feasible deviations from their optimal values (the values of concessions). We formulate an auxiliary linear programming problem to find a compromise solution to the linear-fractional programming problems by these two criteria. The constraints of the auxiliary problem depend on the optimization direction in the original problem. We carried out a series of experiments of four types to study the properties of the problem. The purposes of the experiments were: 1) to study how changes in the values of the specified feasible deviations of partial objective functions impact the values of actual deviations and the values of concessions; 2) to study how changes in the expert weights of partial objective functions impact the values of actual deviations and the values of concessions for the compromise solutions we obtain. We propose in this work the schemes of experiments and present their results in graphical form. We have found that the obtained relations depend on the optimization direction in the original problem. Keywords: optimization, uncertainty, convolution, linear-fractional programming, linear programming problem, compromise solution