An Fuzzy Approache Of Decision Making Based On The Linguistic-valued Intuitionistic Lattice

In the real world, there exists a lot of inaccurate and imperfect information. In most ofcases, people use linguistic terms in natural language to express their evaluations inmulti-criteria decision making problems instead of numerical values. The evaluations arealways relevant to people’s experience and not only the evaluations but the decision makingproblem itself have vague. Therefore it is more natural way to deal with and express theevaluations in the form of linguistic value instead of numerical values. The traditionalapproaches require translation from linguistic values into numeric values because of thelanguage is different from the numerical values of some of the features. There will be someloss in process. In this paper, the linguistic decision making approach is modeled based onlinguistic-value intuitionistic fuzzy lattice. It processes linguistic value directly, and considersboth the incomparability and comparability of the linguistic value, making the result morerational. Hence, the study on the linguistic-value intuitionistic fuzzy lattice implicationalgebra is important in the multi-criteria decision-making area. Based on the linguistic-valueintuitionistic fuzzy lattice implication algebra, we study the evaluation depict, clusteringmethod and decision making approach. The main results as follows:1. A clustering method based on18-element linguistic-valued fuzzy similar matrix.Clustering is one of the essential problems in the multi-criteria decision making problem.The concepts of linguistic-valued fuzzy sets and linguistic-valued fuzzy matrix are definedbased on18-element linguistic-valued fuzzy lattice. We propose the linguistic-valued fuzzysimilarity of linguistic-valued fuzzy set. In addition, the calculating formula for averagelinguistic-valued fuzzy similarity formula is given and proved. Furthermore, linguistic-valuedfuzzy similar matrix, linguistic-valued fuzzy equivalent matrix and-cut matrix oflinguistic-valued fuzzy matrix are constructed. We give a method to calculatelinguistic-valued fuzzy equivalent matrix from linguistic-valued fuzzy similar matrix. At last,we propose a new fuzzy clustering method based on linguistic-valued fuzzy similar matrix, aswell as, an example is given to illustrate its efficient in fuzzy clustering problem.2. Linguistic-valued intuitionistic fuzzy2-tuple representation model.To overcome the limitation of the information lost in the linguistic-value intuitionisticfuzzy lattice algebra aggravation process, we propose a kind of2-tuple linguistic-valuedintuitionistic fuzzy representation model based on the linguistic intuitionistic fuzzy lattice ininformation modeling and computational processes. Operations of the linguistic intuitionisticfuzzy pair are introduced and the properties are obtained. Based on the2-tuplelinguistic-valued intuitionistic fuzzy representation model, a kind of approach for linguistic-valued intuitionistic fuzzy aggregation is defined. Arithmetic mean aggregation andweighted average aggregation are given respectively. Using the operations of thelinguistic-valued intuitionistic fuzzy pairs and the linguistic intuitionistic fuzzy aggregations,a case study is given to illustrate the proposed approach seems more effective for under alinguistic fuzzy environment with both positive evidence and negative evidence. A decisionmaking example of the disease diagnosis is given, using the pattern recognition approach. Theexperiment on the decision making on the initial diagnosis of disease is taken on.