The Study Of Uncertainty Reasoning Based On Lattice-Valued First Order Logic And Its Application

Uncertainty reasoning is one of key problems in the research of artificial intelligence. Studying uncertainty reasoning based on logic is one of scientific methodlogies. In real life people always use the number in [0,1] or natural language to describe uncertainty information, and reasoning in the Environment of uncertainty, then make judgement and decision making based on it. So investigating uncertainty reasoning based on [0,1] and natural language is not only necessary but also critical.Based on many related internal and external outcomes of researches in these directions, the current dissertation studies the theory and its application in fuzzy reasoning, linguistic reasoning and multi-attribute group decision making of uncertainty reasoning based on lattice-valued first-order logic. The specific contents are as follows:Part One. Study on the structure of linguistic truth-valued lattice implication algebra1. The definition of sum (product)-irreducible element and irreducible finite sum (product)-decomposition are presented;2. The sum (product, join, meet)-irreducible element and irreducible finite sum (product, join, meet)-decomposition of the elements of linguistic truth-valued lattice implication algebra are given;3. The solutions of some special classes of linguistic truth-valued lattice implication algebraic equations are given.Part Two. Study on the theory of uncertainty reasoning based on lattice-valued first-order logic Lvfl1. For some representative single-input-single-output uncertainty reasoning models, some conditions for the consistent of the antecedent, consequent and new information of the rule in uncertainty reasoning model are presented. It is shown that these conditions are reasonable;2. For some representative and practical single-input-single-output uncertainty reasoning models, some concrete methods for selecting appropriate parameters during the uncertainty reasoning process and the conditions for the uncertainty reasoning consequence have not only sound semantic interpretation, but also strict syntactical proof are given.Part There. Study on the theory and application of uncertainty reasoning based on Lukasiewicz first-order logic LufUsing uncertainty reasoning based on Lukasiewicz first-order logic Luf to fuzzy reasoning which makes the uncertainty reasoning consequence have not only sound semantic interpretation, but also strict syntactical proof.Part Four. Study on the theory and application of linguistic uncertainty reasoning based on lattice-valued first-order logic Lvfl1. The linguistic uncertainty reasoning method based on lattice-valued first-order logic Lvfl is proposed, and applies it in the everyday life uncertainty reasoning which expressed in natural language. This lay a strict logic basis for the reasoning process and the consequence;2. For weighted and non-weighted multi-attribute group decision-making, the concrete decision making methods based on lattice-valued first-order logic Lvfl are given which lay a strict logic basis for the decision making.