Research On The Theory Of Semi - Ring Algebra And The Theory Of Information Algebra

Valuation algebra is a generic algebraic structure closely related with local com-putation and information processing. Some related studies have shown that valuation algebras cover a wide range of different instances from relational algebra, constraint systems, Dempster-Shafer belief function, Bayesian networks, propositional logic to others. Recent research demonstrates that valuation algebras induced by some special semirings play an important role. In this paper, we first mainly study the issue about the solution configuration of valuation algebra induced by totally ordered semiring and c-semiring, the structures and algorithm of solution configuration; Secondly, we dis-cuss the relations between the information algebra and information systems and give more complete conclusions about their corresponding relations. Lastly, we combine information algebra with soft set and use information algebra to solve the decision making problem of soft set.The main contributions of this thesis is organized as follows:(1) The issue about the solution configuration of valuation algebra induced by totally ordered semiring. First of all, a more particular propositions and the relations of solution configuration and solution extension are further studied, which may simplify some problems of solution configuration. After that, we propose a new idea by means of transfer function solving the solution configuration. But how to ensure the solution configuration to be remained when one valuation is transfered to new system? We conclude that transfer function f preserves solution configuration f is a semiring homomorphism in valuation algebras induced by totally ordered semiring.(2) Solution configuration of valuation algebra induced by c-semiring. Firstly, we propose the notion of solution configuration of valuation algebra induced by c-semiring, and conclude some propositions about solution configuration and solution extension and their relations of solutions,which may make some complicate problems of solution configuration simple. Secondly, Similar to the method used for the solution configuration of valuation algebra induced by totally ordered semiring,we can solve the solution configuration of c-semiring induced valuation algebra by using transfer function. However, we conclude that transfer function f preserves solution configura-tion if f is an order-reflecting semiring homomorphism in valuation algebras induced by c-semiring. Lastly, an algorithm solving the solution configuration of valuation algebra induced by c-semiring is given which shows that Cφ= Models(φF↓(?)(◇)) is true.(3) Information algebra and information systems. This part emphases on the re- lation between information algebra and information systems. First of all we introduce some related concepts of information systems and compact information systems, and present the definition of continuous information system. It is proved that a compact information system is a continuous information system. Secondly, we show that an in-formation system can induce an information algebra without any additional conditions, and a continuous (compact) information system can induce a continuous (compact) information algebra. Conversely, not only an information algebra can induce an in-formation system, but also a continuous (compact) information algebra can induce a continuous (compact) information system. All of these conclusions make the con-tinuity and compactness completely correspondence each other between information algebra and information systems.(4) The model of information algebra and theory of soft set.Firstly, we introduce two new operations and give some propositions about two operations. Furthermore, we present the concept of quotient soft set by regarding "these same content information" soft set as one. The quotient soft set with the new operations of combination and focusing is an information algebra. Moreover, the quotient soft set is also a continuous information algebra if all possible parameters are finite. Therefore, we propose an algorithm of decision making in term of the model of information algebra and give a corresponding example indicating that the model can be successfully applied to many problems. Furthermore, we make a comparison between our algorithm and the others.