Interval-Valued Intuitionistic Fuzzy Ordered Weighted Cosine Similarity Measure and Its Application in Investment Decision-Making

Xiaohong Chen,Donghai Liu,Dan Peng

doi:10.1155/2017/1891923

Xiaohong Chen, Donghai Liu + Show 1 more

Open Access

https://doi.org/10.1155/2017/1891923

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Abstract

We present the interval-valued intuitionistic fuzzy ordered weighted cosine similarity (IVIFOWCS) measure in this paper, which combines the interval-valued intuitionistic fuzzy cosine similarity measure with the generalized ordered weighted averaging operator. The main advantage of the IVIFOWCS measure provides a parameterized family of similarity measures, and the decision maker can use the IVIFOWCS measure to consider a lot of possibilities and select the aggregation operator in accordance with his interests. We have studied some of its main properties and particular cases such as the interval-valued intuitionistic fuzzy ordered weighted arithmetic cosine similarity (IVIFOWACS) measure and the interval-valued intuitionistic fuzzy maximum cosine similarity (IVIFMAXCS) measure. The IVIFOWCS measure not only is a generalization of some similarity measure, but also it can deal with the correlation of different decision matrices for interval-valued intuitionistic fuzzy values. Furthermore, we present an application of IVIFOWCS measure to the group decision-making problem. Finally the existing similarity measures are compared with the IVIFOWCS measure by an illustrative example.

Highlights

The similarity measure is an important tool for measuring the degree of similarity between two objects, which is very useful in some areas, such as decision-making, machine learning, pattern recognition, and medical diagnosis [1,2,3,4,5,6]
(0.4, 0.3, 0.3) and λ = 3; we develop different methods based on the IVIFOWCS measure for selection of an investment
We presented the IVIFOWCS measure by combining the interval-valued intuitionistic fuzzy cosine similarity measure with the generalized OWA operator, which is very useful to deal with the decision information under uncertain situations

Summary

Introduction

The similarity measure is an important tool for measuring the degree of similarity between two objects, which is very useful in some areas, such as decision-making, machine learning, pattern recognition, and medical diagnosis [1,2,3,4,5,6]. The aim of this paper is to introduce the intervalvalued intuitionistic fuzzy ordered weighted cosine similarity (IVIFOWCS) measure. It combines the intervalvalued intuitionistic fuzzy cosine similarity measure with the generalized OWA operator. A more complete formulation of the cosine similarity measure is obtained because it can consider parameterized families of operators that include the maximum, the minimum, and the average as special cases.

Basic Concepts of IFSs and IVIFSs

Cosine Similarity Measures for IVIFSs

Multiple Attribute Group Decision-Making with the IVIFOWCS Measure

Illustrative Example

Conclusions