Cubic Vague Set and its Application in Decision Making

• Published in: Entropy (Basel, Switzerland) Vol. 22; no. 9; p. 963
• Main Authors: Alhazaymeh, Khaleed, Al-Qudah, Yousef, Hassan, Nasruddin, Nasruddin, Abdul Muhaimin
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 31.08.2020; MDPI
• Subjects: cubic set; Decision making; external cubic; fuzzy set; Fuzzy sets; Hybrid structures; internal cubic; interval-valued; periodic; Set theory; Similarity; Similarity measures; Two dimensional models; similarity measure; fuzzy set; internal cubic; interval-valued; periodic; vague set; external cubic; cubic set
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e22090963

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.