The operational properties of linguistic interval valued q-Rung orthopair fuzzy information and its VIKOR model for multi-attribute group decision making

Novel entropy and distance measures of linguistic interval-valued q-Rung orthopair fuzzy sets

Entropy is an important tool to describe the degree of uncertainty of fuzzy sets. In this study, we first define a new entropy and distance measure in the linguistic q-Rung orthopair fuzzy (LIVqROF) environment, and verify its correctness and rationality. Secondly, in the LIVqROF environment, the new entropy formula is effectively applied to the multi-attribute decision making (MADM) with unknown attribute weights, which provides a new idea for solving the MADM problems. Finally, the feasibility and effectiveness of the proposed method are verified by a numerical example.

Linguistic q-rung orthopair fuzzy multiple-attribute group decision making based on the grey similarity degree and PROMETHEE II method

Linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) are an effective tool for representing fuzzy linguistic information, and they can obtain a wider expression scope than linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers by increasing the value of parameter q. In this paper, we propose a new similarity measure called the grey similarity degree between any two Lq-ROFNs based on the concept of the grey correlation degree. Considering the significance of determining unknown weights, we also propose a grey correlation method to determine each expert’s weight under different alternatives and attributes, and we construct an optimization model to determine incompletely known attribute weights. Furthermore, an approach to linguistic q-rung orthopair fuzzy multiple-attribute group decision making is proposed that combines the grey similarity degree with the PROMETHEE II method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method, and a sensitivity analysis and comparison analysis are also performed.