A method for solving linear programming models with Interval Type-2 fuzzy constraints

Abstract

ABSTRACT. This paper shows a method for solving linear programming problems that includes Interval Type-2 fuzzy constraints. The proposed method finds an optimal solution in these conditions using convex optimization techniques. Some feasibility conditions are presented, and some interpretation issues are discussed. An introductory example is solved using the proposed method, and its results are described and discussed.

A decision-making computational methodology for a class of type-2 fuzzy intervals: An interval-based approach

“…A reflection about the applicability of our approach for extending multicriteria and multiattribute decision-making approaches [26][27] [39][50] to the type-2 fuzzy context should be mentioned. The proposed approach can motivate a certain interest in the frameworks of type-2 automatic control [10][29], type-2 regression and modeling [2][23], type-2 linear programming methods [19], etc. Our type-2 FI representation can be employed to implement several aggregation operators (conjunctive and disjunctive operators, weighted average and ordered weighted average operators, and the Choquet integral).…”

“…According to (19), two extreme situations can be distinguished. The first situation, which corresponds to the optimistic case, is expressed as follows:…”

Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints

“…Among them, Le and Gogne introduced a class of linear programming problems based on the possibility and necessity relation [9]. Figueroa-García and Hernández proposed an extension of the fuzzy linear programming method which 2 Journal of Applied Mathematics was proposed by Zimmermann to an interval type 2 fuzzy linear programming problem with linear membership function [10]. In another work García presented a general model for linear programming where its technological coefficients are assumed as interval type 2 fuzzy sets and it is solved through an -cuts approach [11].…”

Aplicação da Programação Linear para otimizar o mix de produtos em uma empresa de confecção

“…Desta forma, o objetivo deste trabalho é utilizar a PL para identificar um mix de produtos ótimo que maximize o seu lucro e auxilie a empresa na tomada de decisões. Muitos destes problemas envolvem incertezas e estas incertezas podem gerar modelos não lineares, portanto diferentes abordagens podem ser utilizadas [6], entretanto, diferentes modelos podem ser utilizados para aproximar os dados reais dentro da otimização [7]. Além disso, a difusão das tecnologias de informação e de comunicação insere a indústria da confecção da Quarta Revolução Industrial.…”