Aggregation operators of quadripartitioned single-valued neutrosophic Z-numbers with applications to diverse COVID-19 scenarios. (March 2023) - Borah, Gourangajit; Dutta, Palash
Abstract: Z-number, proposed by Zadeh is an ordered pair of fuzzy numbers which have the capability to depict both the reliability and certainty of any available information. Likewise, based upon Belnap's four-valued logic, Quadripartitioned Single-Valued Neutrosophic Sets (QSVNSs) are characterized by four independent components of truth, contradiction, ignorance, and falsity degrees to represent uncertain information or data at hand. In fact, QSVNSs are extensions of Single-Valued Neutrosophic Sets (SVNSs) where the indeterminacy component is further partitioned into two parts — contradiction and ignorance. However, QSVNSs alone cannot reflect the reliability measure of decision maker's preferences or allocations. Thus, for better modeling of uncertainty and to combine the information of truth, contradiction, ignorance, and falsity degrees with their respective reliability attributes, we put forward a hybrid framework for the first time in this study. Hence, we propose a notion of Quadripartitioned Single-Valued Neutrosophic Z-number (QSVNZN), which is constructed as a generalization of the Z-number and the QSVNSs. Some basic operations and a score function are also defined for ranking QSVNZNs. Moreover, we also aggregate QSVN information with the help of three weighted aggregation operators viz ., QSVNZN weighted arithmetic averaging (QSVNZNWAA) operator, QSVNZN weighted geometric averaging (QSVNZNWGA) operator, and QSVNZN weighted hybrid averaging (QSVNZNWHA) operator. Several suitable properties and relations between these operators are also presented. The applicability of our newly proposed operators and the score function is demonstrated in three multi-criteria decision making (MCDM) occasions specifically in the COVID-19 context. Meticulous comparative analysis, the validity of our proposed approaches, sensitivity analysis, and runtime analysis is also carried out to depict the legitimacy, veracity, and feasibility of our theoretical construct. The obtained results shall greatly benefit the decision-makers to deal with indeterminate and inconsistent information efficiently. Or in other words, the new framework shall exhibit sufficient descriptive ability from the human-cognition-based perspective. Graphical abstract: Highlights: A novel and hybrid framework of Quadripartitioned Single-Valued Neutrosophic Z-number (QSVNZN) is introduced. A valid score function is defined for ranking QSVNZNs. Legitimate aggregation operators are proposed in QSVNZN setting to aggregate uncertain information. An efficient multiple criteria governed decision making algorithm is developed. Some complex COVID-19 scenarios are discussed highlighting the applicability and feasibility of our constructed framework.