採用模糊資訊的推理：方法與應用

Abstract

對於專家系統或是決策支援系統而言，推理是一項重要的工作。現實世界中，有三類常見的推理工作：預測、診斷、與規劃。在形形色色的知識庫與運算機制中，貝氏網路與影響圖是很普遍的圖形化模式，常用來處理不確定情況下的推理與決策。過去有許多學者提出各種演算法，試圖解決貝氏網路或影響圖上的查詢。然而，這些方法通常存在一些限制。首先，相關的參數或機率值，必須是確定而非模糊的。當決策或推理環境中，無法取得確定的知識，而只能取得不完整或是模糊的資訊時，推理工作將難以進行。其次，傳統貝氏網路的推理方法，難以考慮額外的限制。再者，不同的推理工作無法同時完成，例如診斷與決策之規劃。鑑於上述之限制，本論文擴展傳統的貝氏網路，而發展出一般性的貝氏網路，在這一般性的貝氏網路中，有幾個重要的組成集合：離散隨機節點之集合、連續隨機節點之集合、決策節點之集合，確定性參數之集合、與模糊參數之集合。除了傳統上只考慮離散隨機節點與確定參數的推理演算法，本論文研究三類貝氏網路的特殊題型，並提出解答的方法。這三類特殊推理題型為：(1) 考慮離散隨機節點與模糊參數之診斷，(2) 考慮離散隨機節點與模糊參數之診斷及決策，與(3) 考慮連續隨機節點之診斷與決策。 本論文的特色包含下列幾點：(1) 擴展傳統的貝氏網路，而發展出一般性的貝氏網路，其中考慮：離散隨機節點之集合、連續隨機節點之集合、決策節點之集合，確定性參數之集合、與模糊參數之集合。此一般性的貝氏網路，將作為本研究的基礎架構。(2) 解決在一般性貝氏網路上的模糊推理問題，包括牽涉模糊參數與可能性分配的題型。 (3) 在推理的過程中，考慮無法納入正規知識庫的額外的限制或知識。(4) 在靜態與動態的環境下，解答針對貝氏網路的查詢。(5) 將發展的推理模式與方法，應用於醫療資訊或供應鏈管理的個案。所有的應用個案皆有詳細的解說。

Reasoning is a major task to an expert system or a decision support system. Three types of reasoning tasks prevail in real-world applications: prediction, diagnosis and planning. Among the various knowledge bases and computation schema, Bayesian networks and influence diagrams are well-known graphical models for reasoning and decision-making under uncertainty. Many algorithms have been designed to answer the queries on a Bayesian network or an influence diagram. However, several limitations persist in the conventional methods. First, all relevant parameters are assumed to be crisp. Second, extra constraints or knowledge regarding belief propagation in Bayesian networks are difficult to embed. Third, diagnosis and planning cannot be completed in the same place. Motivated by the limitations mentioned above, this dissertation extend the traditional Bayesian networks to general Bayesian networks (GBN) that are composed of several components: the set of discrete random nodes, continuous random nodes, decision nodes, crisp parameters, and fuzzy parameters. In addition to the conventional reasoning problems that consider only crisp nodes and crisp parameters, three categories of reasoning are solved as the special cases (subsets) of general Bayesian networks: (1) diagnosis with discrete random nodes and fuzzy parameters; (2) diagnosis and decision-making with discrete random nodes and fuzzy parameters; and (3) diagnosis and decision-making with continuous random nodes in dynamic environments. The distinguished features of this dissertation include: (1) extend the traditional Bayesian networks to general Bayesian networks, including discrete random nodes, continuous random nodes, decision nodes, crisp parameters, and fuzzy parameters. The general Bayesian networks are induced as the general research framework; (2) solve fuzzy reasoning tasks in three subsets of GBN where fuzzy parameters and possibility distributions are considered; (3) consider extra knowledge or constraints for the belief propagation, which are not implemented in the formal knowledge bases; (4) answer the queries from Bayesian networks in dynamic as well as static environments; (5) the reasoning models and methods are applied to the cases from medical informatics and supply chain management. All the applications are developed and illustrated in details.