Abstract
The linguistic q-rung orthopair fuzzy sets (Lq-ROFSs) can fully represent linguistic evaluation information by adjusting the parameter q to describe the range of uncertain information. In this paper, we first propose a cosine similarity measure between Lq-ROFSs based on the concept of the cosine similarity measure between intuitionistic fuzzy sets. Considering the cosine similarity measure defined by this method does not satisfy the axiom of similarity measure, we propose the improved similarity measures of Lq-ROFSs according to the corresponding cosine similarity measure and Minkowski distance measure. The improved similarity measures of Lq-ROFSs can deal with the decision information not only from the point of view of algebra but also from the point of view of geometry, which are also proved satisfy the axiom of similarity measure. Furthermore, the similarity measures of Lq-ROFSs based on different linguistic scale functions are defined for considering the semantics of linguistic terms. In addition, we apply the proposed similarity measures of Lq-ROFSs to multi-criteria group decision making problems where the decision makers' weights are determined by the projection of individual decision on the ideal decision results. Finally, a numerical example is applied to illustrate the feasibility of the proposed method and its effectiveness is verified by comparison with some existing methods. The sensitivity analysis and stability analysis of the proposed method are also given.
Highlights
In multi-criteria group decision making (MCGDM) problems, the decision makers evaluate the alternatives based on multi-criteria constrains
The main motivations and contributions of the paper are summarized as follows: (1) Considering the existing similarity measure between linguistic q-rung orthopair fuzzy set (Lq-ROFS) does not satisfy the axiom of similarity measure, we propose a new method to construct some new similarity measures of Lq-ROFSs based on the cosine similarity measure and Minkowski distance measure, which satisfy the axiom of similarity measure and deal with the decision information from the point of view of algebra and geometry
(2) We present the similarity measures of Lq-ROFSs based on the linguistic scale function for semantics of linguistic terms, which have good rationality in comparing with the existing similarity measures and avoid the distortion of decision information during the decision process
Summary
In multi-criteria group decision making (MCGDM) problems, the decision makers evaluate the alternatives based on multi-criteria constrains. Similar to the generalization of IFS, Grag [14] presented a new linguistic Pythagorean fuzzy set(LPFS) by combining the linguistic set and PFS, which can deal with the imprecise information more widely than LIFS. In this paper, we propose some similarity measures between Lq-ROFS and apply the proposed similarity measures to multi-criteria group decision making problem using projection method.
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