Abstract
As a combination of q-rung orthopair fuzzy sets (q-ROFSs) and hesitant fuzzy sets (HFSs), q-rung orthopair hesitant fuzzy sets (q-ROHFSs) are more effective, powerful, and meaningful in solving the complexity, ambiguity, and expert hesitancy of membership and non-membership in multi-attribute decision-making (MADM) problems. And so, based on the advantages of q-ROHFSs, we herein propose an improved TOPSIS model in the q-rung orthopair hesitant fuzzy environment. This model can provide more accuracy in expressing fuzzy and ambiguous information. At first, we propose the distance and similarity measures of q-ROHFSs and the properties related to the distance and similarity measures of q-ROHFSs, and secondly, the axiomatized definition and formula for the entropy of q-ROHFSs. Then, for the case where the attribute weights are totally unknown, a combination of subjective and objective attribute weighting model is proposed. This model not only considers the expert's decision preference, but also the objective situation of the attributes. In addition to the above-mentioned outcomes, this paper also improves the relative closeness formula, increases the preference coefficient, and considers the risk-preference of decision makers. Finally, the proposed model is compared with other methods and used to evaluate the effectiveness of military aircraft overhaul. The method is verified to be scientific, reliable and effective for solving MADM problems.
Highlights
Since there are many ambiguities, uncertainties and other phenomena in real life, it is not possible to use a single value to describe multiple decision-making information
THE Q-RUNG ORTHOPAIR FUZZY SET The only requirement that intuitionistic fuzzy sets (IFSs) have, is that the sum of membership degree and non-membership degree must not exceed 1, which limits its development to a certain extent
This paper proposes an improved TOPSIS Method for Multiple Attribute Decision Making with q-rung orthopair hesitant fuzzy set (q-ROHFS)
Summary
Since there are many ambiguities, uncertainties and other phenomena in real life, it is not possible to use a single value to describe multiple decision-making information. As an effective extension of the fuzzy set [5], since the intuitionistic fuzzy set (IFS) [14] can simultaneously consider the membership as well as non-subordination of elements belonging to the set, it can describe the fuzzy nature of the objective world from three crucial aspects: support, opposition and neutrality For that reason, it has been widely concerned by decision-making researchers and has delivered fruitful results [18]- [28], involving various. PFSs has a definite requirement that the sum of squares of membership and non-membership does not exceed 1, which limits the development of PFSs to some extent To this end, Yager [36] proposed q-rung orthopair fuzzy sets (q-ROFSs) represented as:. THE Q-RUNG ORTHOPAIR FUZZY SET The only requirement that IFSs have, is that the sum of membership degree and non-membership degree must not exceed 1, which limits its development to a certain extent. Definition 3 [37]: Let B= a x ,b x , , an accuracy q function can be expressed by the formula:
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