A method to solve linear programming problem with interval type-2 fuzzy parameters

被引：44

作者：

Kundu, Pradip ^{[1
]}

Majumder, Saibal ^{[2
]}

Kar, Samarjit ^{[3
]}

Maiti, Manoranjan ^{[4
]}

机构：

[1] Indian Inst Sci Educ & Res, Dept Math & Stat, Mohanpur 741246, W Bengal, India

[2] Natl Inst Technol, Dept Comp Sci & Engn, Durgapur 713209, W Bengal, India

[3] Natl Inst Technol, Dept Math Oceanol & Comp Programming, Durgapur 713209, W Bengal, India

[4] Vidyasagar Univ, Dept Appl Math Oceanol & Comp Programming, Midnapore 721102, W Bengal, India

来源：

FUZZY OPTIMIZATION AND DECISION MAKING | 2019年 / 18卷 / 01期

关键词：

Interval type-2 fuzzy variable; Membership function; Generalized credibility measure; Chance-constraint programming; SOLID TRANSPORTATION PROBLEM; VARIABLES;

D O I：

10.1007/s10700-018-9287-2

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper, we propose a method to solve linear programming network problems with constraints using interval type-2 fuzzy variables. The method is developed using generalized credibility measure, and lower and upper membership functions of an interval type-2 fuzzy variable. This method has been applied to solve a solid transportation problem with availabilities and demands of a product, and conveyance capacities, which are represented by trapezoidal interval type-2 fuzzy variables. Moreover, we have also shown that different types of problems with objective function having interval type-2 fuzzy parameters can be solved using the proposed method. Apart from a solid transportation problem, we demonstrate its applicability by solving two different network problems: (i) a shortest path problem and (ii) a minimum spanning tree problem. Suitable numerical examples are provided to illustrate the proposed method

引用

页码：103 / 130

页数：28

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