Three-Dimensional Generalized Discrete Fuzzy Number and Applications in Color Mathematical Morphology

Zengtai Gong,Guicang Zhang,Na Qin

doi:10.1109/access.2021.3057623

Zengtai Gong, Guicang Zhang + Show 1 more

Open Access

https://doi.org/10.1109/access.2021.3057623

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Journal: IEEE Access	Publication Date: Jan 1, 2021
Citations: 40	License type: CC BY 4.0

Affiliation: Northwest Normal University

Abstract

In this paper, the definition of three-dimensional generalized discrete fuzzy number (3-GDFN) is introduced based on the representation theorem of one-dimensional discrete fuzzy number and the similarity measure definition of two 3-GDFNs is given. Then the concept above mentioned is applied to color image representation and color mathematical morphology (CMM) in RGB space. The basic morphology operators, erosion and dilation, are extended to the CMM by defining the total preorder relation based on similarity measure between two 3-GDFNs instead of general vector sorting methods. The corresponding structuring elements in CMM are variable. Finally, the effectiveness and potential of the theoretical results are verified by comparative experiments. The proposed CMM operators are efficiently used in color image processing.

Highlights

The concept of fuzzy numbers can be traced back to 1972, Chang and Zadeh [1] called a fuzzy set with special properties on the real number field R a fuzzy number
Based on the inspiration of the above literature, we explored the application of three-dimensional generalized discrete fuzzy number theory in the color mathematical morphology
It is worth noting that when we investigate the properties of these operators, the shape of the structuring elements is fixed, which means that the value of λ defined in Section IV-C is 0

Summary

Introduction

The concept of fuzzy numbers can be traced back to 1972, Chang and Zadeh [1] called a fuzzy set with special properties on the real number field R a fuzzy number. Riera et al [8] proposed a fuzzy decision-making model and introduced some interesting properties of the fuzzy linguistic model based on discrete fuzzy numbers. In this linguistic computational model, the experts can use different language levels to evaluate the alternatives more flexibly. Some weak orders on the one-dimensional generalized discrete fuzzy number space were introduced based on the definition of new addition and multiplication operation. Wang et al [11] presented the definition of two-dimensional discrete fuzzy numbers They set up the weak orders in the two-dimensional discrete fuzzy number space based on the concepts of mass center and ambiguity degree of fuzzy numbers.

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