NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

Optimal Operation Model of Park Integrated Energy System Considering Uncertainty of Flexible Electrical, Thermal and Gas Load

Flexible Load (FL) of electricity, heat and gas can improve the operation economy, flexibility and reliability of PIES. Aiming at the uncertainty of FL in the actual operation of the park integrated energy system (PIES), an optimal operation model of PIES with uncertainty of FL is proposed. Firstly, the uncertainty models of shiftable electric load and transferable load response are established, respectively. And then an adjustable heat load response model considering the uncertainty of solar radiation intensity is established. On this basis, an optimal operation model of PIES considering the uncertainty of the FL with the goal of maximizing the total revenue is constructed and is solved by the enhanced-interval linear programming method. Simulation indicate that FL can improve the operating economy of PIES and renewable energy consumption.

Weak optimal inverse problems of interval linear programming based on KKT conditions

In this paper, weak optimal inverse problems of interval linear programming (IvLP) are studied based on KKT conditions. Firstly, the problem is precisely defined. Specifically, by adjusting the minimum change of the current cost coefficient, a given weak solution can become optimal. Then, an equivalent characterization of weak optimal inverse IvLP problems is obtained. Finally, the problem is simplified without adjusting the cost coefficient of null variable.

Reserve of characteristic inclusion for interval linear systems of relations

В работе рассматриваются интервальные линейные включения Cx ⊆ d в полной интервальной арифметике Каухера. Вводится количественная мера выполнения этого включения, названная “резервом включения”, исследуются ее свойства и приложения. Показано, что резерв включения оказывается полезным инструментом при изучении АЕ-решений и кванторных решений интервальных линейных систем уравнений и неравенств. В частности, использование резерва включения помогает при определении положения точки относительно множества решений, при исследовании пустоты множества решений или его внутренности и т.п In this paper, we consider interval linear inclusions Cx ⊆ d in the Kaucher complete interval arithmetic. These inclusions are important both on their own and because they provide equivalent and useful descriptions for the so-called quantifier solutions and AE-solutions to interval systems of linear algebraic relations of the form Ax σ b , where A is an interval m × n -matrix, x ∈ R , b is an interval m -vector, and σ ∈ {= , ≤ , ≥} . In other words, these are interval systems in which equations and non-strict inequalities can be mixed. Considering the inclusion Cx ⊆ d in the Kaucher complete interval arithmetic allows studing simultaneously and in a uniform way all the different special cases of quantifier solutions and AE-solutions of interval systems of linear relations, as well as using interval analysis methods. A quantitative measure, called the “inclusion reserve”, is introduced to characterize how strong the inclusion Cx ⊆ d is fulfilled. In our work, we investigate its properties and applications. It is shown that the inclusion reserve turns out to be a useful tool in the study of AE-solutions and quantifier solutions of interval linear systems of equations and inequalities. In particular, the use of the inclusion reserve helps to determine the position of a point relative to a solution set, in investigating whether the solution set is empty or not, whether a point is in the interior of the solution set, etc