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

被引：47
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
收藏
页码：103 / 130
页数：28
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