**1. Introduction**

Decision-making is a process which has a wide range of real-life applications which requires a great precision for desirable outcomes. Real-world applications like supply chain management, marketing management, healthcare, telecommunication, finance, energy, banking, forestry, pattern recognition, investment, personnel selection etc., has a set of data which includes information with both certainties and uncertainties. The study of uncertainties can be handled well by fuzzy sets [1] and its extensions [1–7], thus measures of decision-making helps in removing and controlling the existing constraints or uncertainties, it increases productivity, helps in better coordination etc.

To rank fuzzy sets and its generalizations there exists various ranking measures like distance measures, similarity measures, score function, accuracy function, certainty function, divergence measure, CoCfs etc. Although in literature there exist expressions to evaluate the CoCf between fuzzy sets and many of its extensions as proposed by several researchers like, the CoCf between two fuzzy sets [8], the CoCf between two intuitionistic fuzzy sets [9–17], the CoCf between two interval-valued intuitionistic fuzzy sets [18], the CoCf between two Pythagorean fuzzy sets [19, 20], the CoCf between two intuitionistic multiplicative sets [21], the CoCf between two hesitant fuzzy sets [22–27], the CoCf between two dual hesitant fuzzy sets [28–30] etc.. Ye [29] proposed an expressions for evaluating the weighted CoCfs between two DHFSs and solved a real-life problem (finding the best investment company) where the uncertainty is represented as a DHFS. However, after a deep study, it is observed that some mathematical incorrect assumptions are considered in the existing weighted CoCf and hence it is scientifically incorrect to apply existing weighted CoCf in real-life MADM problems for DHFSs in its present form. This limitation is a real motivation to modify the CoCfs for DHFSs which would be applicable for the evaluation of the real-life problems. Considering the existing weighted CoCf [29] for solving DHFSs MADM problems as a base, a modified weighted CoCf for DHFSs is proposed and using the modified expressions, the exact results of the real-life problem, considered in the existing paper [29] have been obtained.

The paper is organized as follows. Section 2. Preliminaries. Section 3. A brief review of the existing CoCf of DHFSs is presented here. Section 3.1. Gaps in the existing weighted CoCf for DHFSs. Section 3.2. Mathematical incorrect assumptions. Section 4. It proposes the modified CoCf for DHFSs. Section 5. Origin of the proposed CoCf for the DHFSs is discussed here. Section 6. It presents the exact solution to the existing real-life problem. Section 7. Advantages of modified CoCf for DHFSs. Section 8. Discussion and Concludes the presented paper.
