Advances in linguistic data-oriented uncertainty modeling, reasoning, and intelligent decision making

In this dissertation, we focus on data oriented uncertainty modeling, reasoning, and inference, and their applications to intelligent systems that implement the paradigm of Computing with Words (CWW). Computing with Words problems have been classified into at least two categories: Basic Computing with Words, and Advanced Computing with Words. Basic Computing with Words mainly deals with applications of rule-based systems while Advanced Computing with Words deals with implicit assignment of linguistic truth, probability, and possibility through intricate natural language statements. ❧ In this dissertation, we present a Linguistic Goal-Oriented Decision-Making method using rule-based systems. Unlike previous applications of rule-based systems that use them in mere function approximation schemes or apply them to modeling rather uncomplicated expert knowledge, our proposed goal-oriented decision-making method attempts at determining the desired states of a system (described using words) by investigating the linguistic rules that specify the conditions that yield it, and then designs a methodology to move the system states towards more desirable states by changing a decision variable and comparing the rules that describe the conditions that yield each of the states of the system. This approach is another realization of decision making with words or control with words, and can be seen as a bridge between applications of rule-based systems and Computing with Words. We apply our method to the problem of enhanced oil recovery as well. ❧ We also proceed with solving Advanced Computing with Words problems that deal with implicit assignments of truth, probability, and possibility to various attributes through natural languages. We specifically focus on problems that deal with linguistic probabilities. We demonstrate how Interval Type-2 Fuzzy Set (IT2 FS) models of probability words can be synthesized using data collected from subjects, and establish a general framework based on Dempster-Shafer Theory of Evidence to calculate probabilities and perform inference based on natural language information containing linguistic quantifiers and linguistic probabilities via constructs that are called Linguistic Belief Structures. We demonstrate Novel Weighted Averages and Doubly Normalized Weighted Averages as essential tools for inferring from Linguistic Belief Structures. ❧ We also develop an Extension Principle for extending set-valued functions to Interval Type-2 Fuzzy Sets and apply it to inference from Linguistic Belief Structures. We also use Syllogistic Reasoning and the methodology of Linguistic Belief Structures to solve Advanced Computing with Words challenge problems that were proposed by Zadeh. We also implement Zadeh’s methodology of handling linguistic probabilities, which involves the Generalized Extension Principle. When Solving Advanced Computing with Words problems, the Generalized Extension Principle yields functional optimization problems that are very difficult to solve analytically, so we devise a numerical method to deal with those optimization problems. As Zadeh’s methodology is based on Type-1 Fuzzy Sets (T1 FSs), we first implement it for T1 FSs. Then we extend it to Interval Type-2 Fuzzy Sets, since they are viable models of various types of uncertainty that are associated with a word. ❧ A critical review of the status, challenges, and future of Advanced Computing with Words is also presented.