Cubic Vague Set and its Application in Decision Making
From the hybrid nature of cubic sets, we develop a new generalized hybrid structure of cubic sets known as cubic vague sets (CVSs). We also define the concept of internal cubic vague sets (ICVSs) and external cubic vague sets (ECVSs) with examples and discuss their interesting properties, including...
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2020-08-01
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doaj-435405a6a71548909fd25d7ae4f887052020-11-25T03:02:50ZengMDPI AGEntropy1099-43002020-08-012296396310.3390/e22090963Cubic Vague Set and its Application in Decision MakingKhaleed Alhazaymeh0Yousef Al-Qudah1Nasruddin Hassan2Abdul Muhaimin Nasruddin3Department of Basic Sciences and Mathematics, Faculty of Science, Philadelphia University, Amman 19392, JordanDepartment of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, JordanSchool of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, MalaysiaDepartment of Management and Marketing, School of Business and Economics, Universiti Putra Malaysia, Serdang 43400, MalaysiaFrom the hybrid nature of cubic sets, we develop a new generalized hybrid structure of cubic sets known as cubic vague sets (CVSs). We also define the concept of internal cubic vague sets (ICVSs) and external cubic vague sets (ECVSs) with examples and discuss their interesting properties, including ICVSs and ECVSs under both P and R-Order. Moreover, we prove that the R and R-intersection of ICVSs (or ECVSs) need not be an ICVS (or ECVS). We also derive the different conditions for P-union (P-intersection, R and R-intersection) operations of both ICVSs (ECVSs) to become an ICVS (ECVS). Finally, we introduce a decision-making based on the proposed similarity measure of the CVSs domain and a numerical example is given to elucidate that the proposed similarity measure of CVSs is an important concept for measuring entropy in the information/data. It will be shown that the cubic vague set has the novelty to accurately represent and model two-dimensional information for real-life phenomena that are periodic in nature.https://www.mdpi.com/1099-4300/22/9/963cubic setexternal cubicfuzzy setinternal cubicinterval-valuedperiodic |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Khaleed Alhazaymeh Yousef Al-Qudah Nasruddin Hassan Abdul Muhaimin Nasruddin |
spellingShingle |
Khaleed Alhazaymeh Yousef Al-Qudah Nasruddin Hassan Abdul Muhaimin Nasruddin Cubic Vague Set and its Application in Decision Making Entropy cubic set external cubic fuzzy set internal cubic interval-valued periodic |
author_facet |
Khaleed Alhazaymeh Yousef Al-Qudah Nasruddin Hassan Abdul Muhaimin Nasruddin |
author_sort |
Khaleed Alhazaymeh |
title |
Cubic Vague Set and its Application in Decision Making |
title_short |
Cubic Vague Set and its Application in Decision Making |
title_full |
Cubic Vague Set and its Application in Decision Making |
title_fullStr |
Cubic Vague Set and its Application in Decision Making |
title_full_unstemmed |
Cubic Vague Set and its Application in Decision Making |
title_sort |
cubic vague set and its application in decision making |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2020-08-01 |
description |
From the hybrid nature of cubic sets, we develop a new generalized hybrid structure of cubic sets known as cubic vague sets (CVSs). We also define the concept of internal cubic vague sets (ICVSs) and external cubic vague sets (ECVSs) with examples and discuss their interesting properties, including ICVSs and ECVSs under both P and R-Order. Moreover, we prove that the R and R-intersection of ICVSs (or ECVSs) need not be an ICVS (or ECVS). We also derive the different conditions for P-union (P-intersection, R and R-intersection) operations of both ICVSs (ECVSs) to become an ICVS (ECVS). Finally, we introduce a decision-making based on the proposed similarity measure of the CVSs domain and a numerical example is given to elucidate that the proposed similarity measure of CVSs is an important concept for measuring entropy in the information/data. It will be shown that the cubic vague set has the novelty to accurately represent and model two-dimensional information for real-life phenomena that are periodic in nature. |
topic |
cubic set external cubic fuzzy set internal cubic interval-valued periodic |
url |
https://www.mdpi.com/1099-4300/22/9/963 |
work_keys_str_mv |
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