Vague Entropy Measure for Complex Vague Soft Sets.

Ganeshsree Selvachandran,Harish Garg,Shio Quek

doi:10.3390/e20060403

Ganeshsree Selvachandran, Harish Garg + Show 1 more

Open Access

https://doi.org/10.3390/e20060403

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Abstract

The complex vague soft set (CVSS) model is a hybrid of complex fuzzy sets and soft sets that have the ability to accurately represent and model two-dimensional information for real-life phenomena that are periodic in nature. In the existing studies of fuzzy and its extensions, the uncertainties which are present in the data are handled with the help of membership degree which is the subset of real numbers. However, in the present work, this condition has been relaxed with the degrees whose ranges are a subset of the complex subset with unit disc and hence handle the information in a better way. Under this environment, we developed some entropy measures of the CVSS model induced by the axiomatic definition of distance measure. Some desirable relations between them are also investigated. A numerical example related to detection of an image by the robot is given to illustrate the proposed entropy measure.

Highlights

Classical information measures deal with information which is precise in nature, while information theory is one of the trusted ways to measure the degree of uncertainty in data
The proposed measures have the following characteristics: (1) they serve as a complement to the complex vague soft set (CVSS) model and its relations in representing and modeling time-periodic phenomena; (2) they have elegant properties that increase their reach and applicability; (3) they have important applications in many real-world problems in the areas of image detection, pattern recognition, image processing; (4) they add to the existing collection of methodologies and techniques in artificial intelligence and soft computing, where it is often necessary to determine the degree of vagueness of the data, in order to make optimal decisions
The rest of the manuscript is organized as follows: in Section 2, we briefly review the basic concepts of soft set (SS) and CVSSs

Summary

Introduction

Classical information measures deal with information which is precise in nature, while information theory is one of the trusted ways to measure the degree of uncertainty in data. Due to an increase of the system day-by-day, decision makers may have to give their judgments in an imprecise, vague and uncertain environment To deal with such information, Zadeh [1] introduced the theory of fuzzy sets (FSs) for handling the uncertainties in the data by defining a membership function with values between 0 and 1. (4) they add to the existing collection of methodologies and techniques in artificial intelligence and soft computing, where it is often necessary to determine the degree of vagueness of the data, in order to make optimal decisions This provides support of the increasingly widespread trend in the use of mathematical tools to complement scientific theories and existing procedures, in the handling and solving of real-life problems that involve vague, unreliable and uncertain two-dimensional information.

Preliminaries

Axiomatic Definition of Distance Measure and Vague Entropy

Relations between the Proposed Distance Measure and Vague Entropy

Illustrative Example

The Scenario

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The sets of colors image

Formation ofLet

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, Tables

∈,Tables

Tables are as