Linguistic-valued Multiple Attribute Decision Making Method Based On Lattice Implication Algebra

With the development of science and technology,people's life is becoming more and more intelligent in real life.In the evaluation of many problems,due to the uncertainty and complexity of objective things and the vagueness of human thinking,numerical preferences often fail to reflect the preferences of decision-makers effectively and accurately.Therefore,when evaluating many decision-making problems with qualitative indicators,Policy makers like to use language to express.However,in the calculation of linguistic value evaluation information,the conversion of numerical information into linguistic value information will result in the lack of information.In this paper,linguistic-valued lattice implication algebra(L_V?n×2?)is used to express linguistic value information with comparability and incomparability,which directly calculates linguistic values and avoids the lack of information.Based on the linguistic-valued lattice implication algebra,a PROMETHEE decision-making method based on linguistic value lattice implication algebra and TOPSIS method based on the entropy method for linguistic-valued lattice implication algebra are proposed and applied to the evaluation of online goods and decision-making of car purchase respectively.The main research results are as follows:First,a PROMETHEE decision-making method based on linguistic value lattice implication algebra is proposed.Aiming at the problem of decision making with comparable and incomparable linguistic-valued information,a multi-attribute decision making method based on L_V?n×2?is proposed.This paper discusses the linguistic-valued evaluation matrix and its properties on L_V?n×2?,and puts forward the priority function and the lattice-valued difference of lattice-valued on L_V?n×2?.Taking full account of the attribute value disparity information,the lattice-valued difference is applied to the preference ranking.By using the linguistic-valued vector,linguistic-valued vector synthesis matrix can be established to deal with the decision problem of multi-expert and multi-attribute at the same time.The linguistic-valued evaluation matrix weighted aggregation operator?LMWAA?is introduced to aggregate the linguistic-valued evaluation matrix.By using the noncompensatory nature of PROMETHEE decision method,a PROMETHEE decision model based on linguistic-valued lattice implication algebra is constructed.The effectiveness and practicability of the method are illustrated by an example of network commodity evaluation.Then we propose a TOPSIS method based on the entropy method for linguistic-valued lattice implication algebra.Aiming at the decision problem that the attribute weights are unknown and the attribute value is the linguistic-valued lattice implication algebra,a TOPSIS method of linguistic-valued lattice implication algebra based on entropy weight method is proposed.The distance between the linguistic values on L_V?n×2?and its properties are studied.The Euclidean distance formula and weighted Euclidean distance based on the form of L_V?n×2?are defined,and the similarity between the linguistic values on L_V?n×2?is obtained.According to the entropy weight method of L_V?n×2?,the attributes weights are determined.The TOPSIS method is used to compare and sort the alternatives,and the feasibility and effectiveness of the method are verified by case analysis.