Multiple attribute group decision making methods based on trapezoidal fuzzy neutrosophic numbers

For the multiple attribute group decision making (MAGDM) problem, in which the attribute weights are unknown and the attribute value of alternatives is in the form of a trapezoidal fuzzy neutrosophic number, this paper proposes two multiple attribute group decision making methods: one based on the trapezoidal fuzzy neutrosophic number hybrid averaging (TrFNNHA) operator, and the other based on the technique for order performance by similarity to ideal solution (TOPSIS) method. First, the attribute weights are obtained using the truth favorite relative expected value, and the distance measure defined using the cosine similarity measure. Next, a proposed trapezoidal fuzzy neutrosophic number ordered weighted arithmetic averaging (TrFNNOWAA) operator and a proposed trapezoidal fuzzy neutrosophic number hybrid weighted arithmetic averaging (TrFNNHWAA) operator are used to aggregate the trapezoidal fuzzy neutrosophic information. Then, the score and accuracy functions of a trapezoidal neutrosophic number are used to rank the alternatives and obtain the best alternative in a trapezoidal fuzzy neutrosophic environment. In addition, an extended TOPSIS method is also proposed to deal with trapezoidal fuzzy neutrosophic information. An illustrative example and sensitivity analysis demonstrate the applicability and effectiveness of the proposed group decision making methods.