Most search applications in use today employ a keyword based search mechanism, which do not have any deductive abilities and are therefore unable to understand human perceptions underlying any given search. This paper proposes a framework for a Fuzzy Expert System for question-answer support while searching within a specific domain. Development of such a framework requires computing theories which can understand and manipulate the knowledge inherent in natural language based documents. To this end, we can now employ the newly introduced theory of Computing with Words (CW). The recent introduction of CW, by Lofti Zadeh, signifies a break from the traditional computing model and promises to enable analysis of natural language based information. In order to provide a bridge between raw natural language text and CW, the use of Probabilistic Context Free Grammar (PCFG) is proposed. Together the two theories form the core of the proposed framework that allows search applications to be constructed with the capabilities of deduction and perception analysis using a natural language interface.

The Generalized Constraint Language (GCL), introduced by Zadeh, is the essence of Computing with Words (CW). It provides an genda to represent the meaning of imprecise words and phrases in natural language and introduces advanced techniques to perform reasoning on imprecise knowledge. Despite its fundamental role, the definition of GCL has remained informal since its introduction by Zadeh and, to our knowledge, no attempt has been made to formalize GCL or to build a working GCL deduction system. In this dissertation, two main interrelated objectives are pursued: First, the syntax and semantics of GCL are formalized in a logical setting. The notion of soundness of a GCL argument is defined and Zadeh's inference rules are proven sound in the defined language. Second, a CW Expert System Shell (CWSHELL) is implemented for the realization of a GCL deduction system. The CWSHELL software allows users to express their knowledge in terms of GCL formulas and pose queries to a GCL knowledge base. The richness of GCL language allows CWSHELL to greatly surpass current fuzzy logic expert systems both in its knowledge representation and reasoning capabilities. While many available fuzzy logic toolboxes can only represent knowledge in terms of fuzzy-if-then rules, CWShell goes beyond simple fuzzy conditional statements and performs a chain of reasoning on complex fuzzy propositions containing generalized constraints, fuzzy arithmetic expressions, fuzzy quantifiers, and fuzzy relations. To explore the application of CWSHELL, a realistic case study is developed to compute the auto insurance premium based on an imprecise knowledge base. The alpha version of CWSHELL along with the case study and documentation is available for download at http://cwjess.cs.siu.edu/.

Computing with words (CW) provides symbolic and semantic methodology to deal with imprecise information associated with natural language. The CW paradigm rooted in fuzzy logic, when coupled with an expert system, offers a general methodology for computation with fuzzy variables and a fusion of natural language propositions for this purpose. Fuzzy variables encode the semantic knowledge, and hence, the system can understand the meaning of the symbols. The use of words not only simplifies the knowledge acquisition process, but can also eliminate the need of a human knowledge engineer. CW encapsulates various fuzzy logic techniques developed in past decades and formalizes them. Z-number is an emerging paradigm that has been utilized in computing with words among other constructs. The concept of Z-number is intended to provide a basis for computation with numbers that deals with reliability and likelihood. Z-numbers are confluence of the two most prominent approaches to uncertainty, probability and possibility, that allow computations on complex statements. Certain computations related to Z-numbers are ambiguous and complicated leading to their slow adaptation into areas such as computing with words. Moreover, as acknowledged by Zadeh, there does not exist a unique solution to these problems. The biggest contributing factor to the complexity is the use of probability distributions in the computations. This dissertation seeks to provide an applied model of Z-number based on certain realistic assumptions regarding the probability distributions. Algorithms are presented to implement this model and integrate it into an expert system shell for computing with words called CWShell. CWShell is a software tool that abstracts the underlying computation required for computing with words and provides a convenient way to represent and reason on a unstructured natural language.

Decision support systems have emerged over five decades ago to serve decision makers in uncertain conditions and usually rapidly changing and unstructured problems. Most decision support approaches, such as Bayesian decision theory and computing with words, compare and analyze the consequences of different decision alternatives. Bayesian decision methods use probabilities to handle uncertainty and have been widely used in different areas for estimating, predicting, and offering decision supports. On the other hand, computing with words (CW) and approximate reasoning apply fuzzy set theory to deal with imprecise measurements and inexact information and are most concerned with propositions stated in natural language. The concept of a Z-number [69] has been recently introduced to represent propositions and their reliability in natural language. This work proposes a methodology that integrates Z-numbers and Bayesian decision theory to provide decision support when precise measurements and exact values of parameters and probabilities are not available. The relationships and computing methods required for such integration are derived and mathematically proved. The proposed hybrid methodology benefits from both approaches and combines them to model the expert knowledge and its certainty (reliability) in natural language and apply such model to provide decision support. To the best of our knowledge, so far there has been no other decision support methodology capable of using the reliability of propositions in natural language. In order to demonstrate the proof of concept, the proposed methodology has been applied to a realistic case study on breast cancer diagnosis and a daily life example of choosing means of transportation.

Computing with Words based Question Answering (CWQA) system provides a foundation to develop futuristic search engines where more of reasoning and less of pattern matching and statistical methods are used for information retrieval. In order to perform successful reasoning, these systems should analyze the semantic of the query and the related information in the Knowledge Base. The concept of Computing with Words (CW) which is a kind of perception based reasoning where manipulation of perceptions using fuzzy set theory and fuzzy logic play a key role in recognition, decision and execution processes can be utilized for this purpose. Two concepts that were introduced by Computing with Words are the Generalized Constraint Language (GCL) and the Generalized Theory of Uncertainty (GTU) . In GCL propositions, i.e. perceptions in natural language, are denoted using generalized constraints. The Generalized Theory of Uncertainty (GTU) uses GCL to express proposition drawn from natural language as a generalized constraint. The GCL plays a fundamental role in GTU by serving as a precisiation language for propositions, commands and questions in natural language. In GTU, deduction rules are used to propagate generalized constraints to accomplish reasoning under uncertainty. In the previous work a CW-based QA-system methodology was introduced which uses a knowledge tree data structure, called as a Constraint Propagation Tree (CPT) that utilizes the concepts briefed above. The realization of Constraint Propagation Tree, the first phase, and partial implementation of constraint propagation and node combination, the second phase, is the main goal of this work.