Novel arithmetic operations on type-2 intuitionistic fuzzy and its applications to transportation problem

Pacific Science Review A: Natural Science and Engineering Pub Date : 2016-11-01 DOI:10.1016/j.psra.2016.09.008

Dipak Kumar Jana

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引用次数: 30

Abstract

Type-2 intuitionistic fuzzy sets possess many advantages over type-1 fuzzy sets because their membership functions are themselves fuzzy, making it possible to model and minimize the effects of uncertainty in type-1 intuitionistic fuzzy logic systems. This paper presents generalized type-2 intuitionistic fuzzy numbers and its different arithmetic operations with several graphical representations. Basic generalized trapezoidal intuitionistic fuzzy numbers considered for these arithmetic operations are formulated on the basis of $(α, β)$ -cut methods. The ranking function of the generalized trapezoidal intuitionistic fuzzy number has been successively calculated. To validate the proposed arithmetic operations, we solved a type-2 intuitionistic fuzzy transportation problem by the ranking function for mean interval method. Transportation costs, supplies and demands of the homogeneous product are type-2 intuitionistic fuzzy in nature. A numerical example is presented to illustrate the proposed model.

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二类直觉模糊的新算法及其在运输问题中的应用

2型直觉模糊集比1型直觉模糊集具有许多优点，因为它们的隶属函数本身是模糊的，因此可以对1型直觉模糊逻辑系统中的不确定性进行建模并最小化其影响。本文给出了广义2型直觉模糊数及其不同的算术运算，并给出了几种图形表示。这些算术运算所考虑的基本广义梯形直觉模糊数是在(α，β)-切方法的基础上形成的。先后计算了广义梯形直觉模糊数的排序函数。为了验证所提算法的有效性，利用平均区间排序函数法求解了一类2型直觉模糊运输问题。同质产品的运输成本、供给和需求在本质上是2型直觉模糊的。给出了一个数值算例来说明所提出的模型。

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Pacific Science Review A: Natural Science and Engineering

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