| In this research, we developed uncertainty reasoning frameworks for both two-valued logic systems and multivalued logic systems based on the evidence theory proposed by Dempster and Shafer in the 1960s. The advantage of the Dempster-Shafer theory over probability and fuzzy set theories, which are two well-known approaches to modeling uncertainty reasoning, is its ability to represent ignorance consistently.; First, we proposed a systematic approach to evidence reasoning for two-valued logic systems. After presenting the uncertainty representation system with the truth value space {dollar}{lcub}0{lcub},{rcub}1{rcub}{dollar} as its universe, we developed the procedures to perform all logic operations and a mechanism of approximate reasoning. The procedures performing binary logic operations are studied in terms of various dependency assumptions between the two propositions. The mechanism of approximate reasoning includes forward and backward inference procedures. Different versions of inference procedures can be obtained by choosing different propagation operators.; With the same methodology, we developed an evidence reasoning framework for multivalued logic system. After extending multivalued logic operations into interval logic operations, we presented the corresponding modeling techniques for uncertainty representation as well as procedures for performing logic connectives. Based on three different interpretations of the implication operator and two basic inference procedures, we proposed six approximate reasoning patterns. The relationship between forward and backward inference patterns are examined. All procedures are carried out through two computation levels. At the first level, the possible truth values of the proposition are obtained. At the second level, the corresponding basic probability mass is calculated. We also studied the issue of belief combinations in multivalued logic systems.; Finally, we proposed an interval valued evidence theory, where the basic probability assignment is allowed to take interval values. The corresponding evidence measures as well as the evidence combination rule are defined to cope with the interval valued situations. All calculations are based on the concepts of generalized summation and multiplication, the purpose of which is to ensure that all operations involved in the theory are closed in the unit interval (0,1). It is shown that the original theory is a special case of the proposed one. |
