A linguistic truth-valued reasoning approach in decision making with incomparable information

In the framework of the linguistic truth-valued logic, a linguistic truth-valued reasoning approach for decision making with both comparable and incomparable truth values is proposed in this paper. By using the lattice implication algebra, an 18-element linguistic truth lattice-valued logic system with linguistic hedges is established for the linguistic truth-valued logic to better express both comparable and incomparable truth values. Mathematical properties of disjunction, conjunction, negation and implication for the linguistic truth-valued propositional logic are further investigated respectively. As reasoning and operation are directly acted by linguistic truth values in the decision process, the issue on how to obtain the weight for rational decision making results is discussed. An illustration example shows the proposed approach seems more effective for decision making under a fuzzy environment with both comparable and incomparable linguistic truth values.

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