Please use this identifier to cite or link to this item: https://knowledgecommons.lakeheadu.ca/handle/2453/2488
Title: Interval-based uncertain reasoning
Authors: Wang, Jian
Keywords: Interval analysis (Mathematics);Fuzzy sets
Issue Date: 1996
Abstract: This thesis examines three interval based uncertain reasoning approaches: reasoning under interval constraints, reasoning using necessity and possibility functions, and reasoning with rough set theory. In all these approaches, intervals are used to characterize the uncertainty involved in a reasoning process when the available information is insufficient for single-valued truth evaluation functions. Approaches using interval constraints can be applied to both interval fuzzy sets and interval probabilities. The notion of interval triangular norms, or interval t-norms for short, is introduced and studied in both numeric and non-numeric settings. Algorithms for computing interval t-norms are proposed. Basic issues on the use of t-norms for approximate reasoning with interval fuzzy sets are studied. Inference rules for reasoning under interval constraints are investigated. In the second approach, a pair of necessity and possibility functions is used to bound the fuzzy truth values of propositions. Inference in this case is to narrow the gap between the pair of the functions. Inference rules are derived from the properties of necessity and possibility functions. The theory of rough sets is used to approximate truth values of propositions and to explore modal structures in many-valued logic. It offers an uncertain reasoning method complementary to the other two.
URI: http://knowledgecommons.lakeheadu.ca/handle/2453/2488
metadata.etd.degree.discipline: Mathematical Sciences
metadata.etd.degree.name: Master of Science
metadata.etd.degree.level: Master
metadata.dc.contributor.advisor: Yao, Yiyu
Appears in Collections:Retrospective theses

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