In order to deal with the decision making problem including some linguistic values uncertainty information, we propose an approach for decision making with linguistic weighted and unavoidable incomparable ranking based on Linguistic-valued lattice implication algebra (LV-LIA). The properties of binary operations  and  are discussed in LV-LIA, and used to handle importance degree of the attributes expressed by linguistic values. We define a linguistic-real valuation function which is a positive valuation function and a linguistic-real metric distance implied by the linguistic-real valuation function is introduced, to process incomparable linguistic values in the results which need further procedure to make a certain decision. Illustrating examples show the effectiveness of the proposed approach which can rank the incomparable elements elastic.


Y. Zhang, D. Huang, W. Gao, V.G. Kaburlasos, “A decision making approach with linguistic weight and unavoidable incomparable ranking”, International Journal of Computational Intelligence Systems, vol. 12, no. 2, pp. 1102-1112, 2019.