Decision making under uncertainty is a crucial issue and most demanding area of research now a days. Intuitionistic hesitant fuzzy set plays important role in dealing with the circumstances in which decision makers judge an alternative with a collection membership grades and a collection of non-membership grades. This paper contributes a novel and advanced distance measure between Intuitionistic Hesitant fuzzy sets (IHFSs). A comparative analysis of the present distance measure with existing measures is performed first. Afterwards, a case study is carried in multi-criteria decision making problem to exhibit the applicability and rationality of the proposed distance measure. The advantage of the proposed distance measure over the existing distance measures is that in case of deficit number of elements in IHFs, a decision maker can evaluate distance measure without adding extra elements to make them equivalent and furthermore, it works in successfully in all the situations.
Executive Summary In the contemporary time, the reliability of any product has become a big issue from the customer’s perspective due to exponentially mushrooming markets of electronics and digital gadgets. Since the use of digital equipment is tremendously increasing, as a consequence, the production and availability of products are also increasing rampantly. Due to the flooding of digital products, customers often end up in a dilemma regarding the abundant choice and subsequently, become very much dependent upon the reviews of experts and fellow customers as well. In many cases, unfortunately, it is encountered that the products are not reliable enough as suggested by the reviewers. Besides, it is often seen that the manufacturing companies provide almost similar types of features and facilities for products and customers usually end up in a dilemma The confusion gets triggered when varieties of commodities are manufactured and supplied by different manufacturers bearing almost the same features nearly at the same price. In such situations, the reviews of experts and customers already using the product become essential. The reliability of a product relies upon the reviews of the previous customers of the same product. In this article, fuzzy multi-criteria decision-making methodology has been employed to find the reliability of a product considering different features of the product based on the reviews of customers and experts. This paper presents a neo distance measure on hesitant fuzzy set which is found on the notion of score function and mean deviation. Explanatory instances are provided to reveal the distinctiveness and merit of our proposed idea on distance measure over existing distance measures. After that, the proposed distance measure is applied in the decision-making approach for taking up the best electronic products. It is evidenced that the proposed distance measure is beneficial to measure distance degree between two unequal Hesitant Fuzzy Elements (HFEs) without putting extra elements in the shorter HFE. The proposed distance measures can be utilized in the decision-making field in the near future under diverse conditions to display undetermined particulars in a much-clarified manner.
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