A Linguistic Lattice-Valued Approach for Fuzzy Multi-Objective Decision Making
Xiaobing Li, Da Ruan, Jun Liu and Yang Xu
Most of the present methods for multi-objective decision making can only deal with linearly ordered preference information. In this paper, we focus on investigating methods for multi-objective decision making when the preference information set includes incomparable natural language terms. A logical algebraic structure of lattice implication algebra is then applied to represent both comparable and incomparable information simultaneously. We present a model for multi-objective decision making in which the preference information set is a kind of linguistic-valued lattice implication algebras. And we extend the model to deal with the multi-objective decision making when the preference information set is a generalized linguistic-valued lattice. In these cases, decision makers can supply lattice information on their preference and weights of the individual objectives.
Keywords: decision-making, multi-objective decision making, L-fuzzy set, lattice implication algebra, incomparable information.