Group decision making using bilateral agreement matrix

Group decision making based on a bilateral agreement matrix is investigated in this paper. To derive a group decision from the opinions of individual decision makers, pairs of decision makers are allowed to negotiate with one another and provide their bilateral negotiation values. Two algorithms are provided to help pairs of decision makers reach bilateral agreements, which enables the construction of the bilateral agreement matrix. The definition of a consistent bilateral agreement matrix is introduced to measure the credibility of the final result and its properties are investigated, based on which a method is provided to construct a consistent bilateral agreement matrix from an inconsistent one. Models are then given to derive the weight vector from the bilateral agreement matrix, based on which a consistency index of the matrix is defined. Two algorithms are then given to improve the level of consistency of the bilateral agreement matrix. The final group decision is obtained by aggregating individual opinions using the weight vector. The proposed methods are further extended to deal with the problem of incomplete bilateral agreement matrices. Several examples are also given to illustrate the proposed approach.