Operation Properties and delta-Equalities of Complex Fuzzy Classes

2015 10th International Conference on Intelligent Systems and Knowledge Engineering (ISKE) Pub Date : 1900-01-01 DOI:10.1109/ISKE.2015.77

Mumtaz Ali, Vahid Behbood

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引用次数: 3

Abstract

A complex fuzzy class is a set of fuzzy sets which is characterized by a pure complex fuzzy grade of membership where both the real and imaginary parts are fuzzy functions. The values that a pure complex fuzzy grade of membership may receive all lie within the unite square or unit circle in the complex plane. In this paper, we investigate different operation properties and propose a distance measure for complex fuzzy classes. The distance of two complex fuzzy classes measures the difference between the memberships of the fuzzy sets in the two complex fuzzy classes as well as the difference between the memberships in the related fuzzy sets in the two complex fuzzy classes. d-equalities of two complex fuzzy classes are then defined which mainly base on this distance measure. If the distance between two complex fuzzy classes is less than or equal to d, then they are said to be d-equal. This paper reveals that different operations between complex fuzzy classes can affect given delta-equalities of complex fuzzy classes. Further, an application of utilizing the concept of d-equalities of complex fuzzy classes in stocks and mutual funds in the stock market is presented.

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复杂模糊类的运算性质和delta等式

复模糊类是一组具有纯复模糊隶属度的模糊集，其中实部和虚部都是模糊函数。一个纯复模糊隶属度等级可能得到的值都在复平面的单位方或单位圆内。本文研究了复杂模糊类的不同运算性质，并提出了一种距离度量方法。两个复杂模糊类的距离度量了两个复杂模糊类中模糊集的隶属度之差，以及两个复杂模糊类中相关模糊集的隶属度之差。在此基础上定义了两个复杂模糊类的d等式。如果两个复杂模糊类之间的距离小于或等于d，则称它们为d相等。本文揭示了复模糊类之间的不同运算会影响复模糊类的给定delta等式。在此基础上，给出了复模糊类d等式概念在股票和共同基金中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2015 10th International Conference on Intelligent Systems and Knowledge Engineering (ISKE)

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