Study On Latice-Valued Concept Lattice Based On Lattice Implication Algebra And Its Uncertainty Reasoning And Decision Making

This paper belongs to the theoretical and applied researches about artificial intelligence with uncertainty, which aims to establish a kind of mathematical model directly used for uncertainty information analysis and processing. The basic starting points of this research mainly include two aspects:one is that not only does there exist various kinds and large portions of uncertainty in the real world but also the uncertainty is naturally generalized in the course of outer information being reflected to human brain; the other is that human intelligence actions are always involved with the qualitative concepts with uncertainty, e.g., fuzziness and incomparability, etc. Correspondingly, the theoretical bases are the lattice implication algebra for depicting uncertainty information and the mathematical model of the concept lattice for describing the concepts and the relation among them.This paper established the lattice-valued concept lattice and researched its constructing method, reduction method, decomposition and combination operations; uncertainty reasoning, as the one of important research directions in artificial intelligence, this paper further researched uncertainty reasoning based on lattice-valued concept lattice, and applied this uncertainty reasoning method into the decision making and established the lattice-valued single-target decision concept lattice and the multi-target decision concept lattice, which provides the mathematical tools for the research of decision making with uncertainty information. The concrete research contents include the following two parts:Part one:The theoretical study of lattice-valued concept lattice1. The mathematical model of lattice-valued concept lattice is established on the lattice implication algebra and some properties are talked about.2. The matrix constructing method of lattice-valued concept lattice is proposed, where the non-numerical matrix operations are defined and the flow chart of matrix implication operation is given.3. Reduction methods of lattice-valued concept lattice are proposed, where attribute reduction methods and object reduction methods of lattice-valued concept lattice based on attributes set and objects set are studied and their reduction algorithms are presented. 4. Decomposition and combination theories of lattice-valued concept lattice are proposed, where representation algorithm of extended lattice-valued formal context is given, and the decomposition operation and combination operation of lattice-valued concept lattice are presented.Part two:The application study of lattice-valued concept lattice1. Uncertainty reasoning methods based on lattice-valued concept lattice are proposed, where according to the relation between the extent and intent of the lattice-valued formal concept and approximation theory of sets, internal approximate uncertainty reasoning methods and external approximate uncertainty reasoning methods based on lattice-valued concept lattice are given and their rationality and the relationship between them are talked about.2. Two kinds of decision models based on lattice-valued concept lattice are proposed, the single-target decision model and multi-target decision model based on lattice-valued concept lattice are given, the decision rules extracting algorithms are presented and some properties of decision rules are talked about.