Ranking of Z‐numbers based on value and ambiguity at levels of decision making

Abstract

The concept of Z-number, is very new in the literature, proposed by Zadeh in 2011. The Z-number Z A B = (,) is a pair of fuzzy numbers where the first component represents the restriction and the second component represents the certainty of the first component. Further, its application is evident in decision-making problems, risk assessment, linear programming problems, and so forth. Hence, under such circumstances ranking of Z-numbers need an utmost attention, as such, a few methods of ranking Z-numbers are proposed by various researcher. However, in many situations the existing methods depict drawbacks and limitations as discussed in this paper. Hence, a new method of ranking Z-numbers is essential for an appropriate decision-making. In this paper, a new method of ranking Z-numbers based on the concept of value and ambiguity at levels of decision-making have been proposed. The method seems to deliver a reasonable decision and proper ranking of Z-numbers of various types. A few numerical examples are discussed which show the out-performance of the proposed method.

Exploring the mutual influence among the social innovation factors amid the COVID-19 pandemic

“…Zadeh [57] proposed Z-numbers as a special type of fuzzy method that measures the confidence of experts in the evaluation. Z-numbers have been widely used in various decision-making problems [13] , [14] to address these issues. The computational process of Z-numbers is detailed below.…”

“…As the second contribution, the Rough-Z-DEMATEL technique is proposed to effectively investigate the interdependencies among the social innovation factors during the COVID-19 pandemic situation. Z-numbers reflect the uncertainty and confidence of experts in the evaluation [13] , [14] and the opinions of multiple experts can be aggregated using rough numbers [15] .…”

Ordering single‐valued neutrosophic numbers based on flexibility parameters and its reasonable properties

“…Two important notions, namely value and ambiguity are numerously used, by Chutia, 35,36 Chutia and Saikia, 37,38 Chutia and Chutia, 39 Chutia and Gogoi, 40 Deli and Subas, 27 Biswas et al 28 which are being discussed here, in various methodology of ranking fuzzy numbers as well as IFNs. Although several notions are being used in ranking methodologies, yet these two notions are reliable and robust.…”

A Review on Ranking of Z-numbers

“…They obtained values and ambiguities for both constraint and reliability part. After that, they combined the scores as in the method of Jiang W. et al [27] .…”