Trigonometric function-driven interval type-2 trapezoidal fuzzy information measures and their applications to multi-attribute decision-making.

Small and medium-sized enterprises (SMEs) play a vital role in economic and social development. Among them, scientific and technological innovation ability and investment choice ability are the key factors to evaluate the competitiveness of SMEs. Aiming at the capability evaluation of SMEs, this paper designs a multi-attribute decision-making (MADM) method with interval type-2 trapezoidal fuzzy information measure, which is driven by trigonometric function. Interval type-2 trapezoidal fuzzy numbers (IT2TrFNs) help us to model fuzzy information. Firstly, this paper discusses the three main concepts of entropy, similarity and cross-entropy, and introduces their properties in IT2TrFNs. Secondly, the information measurement formulas related to IT2TrFNs are constructed by using trigonometric functions: IT2TrF trigonometric information entropy, IT2TrF trigonometric similarity measure and IT2TrF trigonometric cross-entropy. They are used to measure the ambiguity and similarity of decision information. Then, taking into account the interdependence between the different attributes, we use entropy and cross-entropy to determine the unknown attribute weights. IT2TrF trigonometric similarity measure is utilized to determine the optimal alternative. Finally, the numerical example is given to evaluate the scientific and technological innovation ability and investment choice ability of SMEs. The feasibility and effectiveness of the proposed MADM method are verified by comparative analysis. • Axiomatic definitions of information measures of IT2TrFS are introduced. • Trigonometric information measure formulas for IT2TrFS are constructed. • The relationship among the information measures is discussed. • A MADM method is developed. • Two examples are given to illustrate the behavior of the proposed method. [ABSTRACT FROM AUTHOR]