International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

This paper examines the problem of selecting an alternative in situations in which there exists uncertainty in our knowledge of the state of the world. We show how the ordered weighted averaging aggregation operators provide a unifying approach to selecting alternatives under uncertainty. In particular, we see how these operators provide a type of probability associated with our degree of optimism. We also show how the Dempster-Shafer belief structure provides a general framework for representing the information a decision maker has regarding relevant events. We then propose a methodology for decision making under uncertainty, integrating the ordered weighted averaging aggregation operators and the Dempster-Shafer belief structure. The proposed methodology is applied to a real world case involving risk management at one of the nation’s largest banks.

Homomorphisms and admissible relations of fuzzy Mealy machines are studied. Admissible relations play a role similar to normal subgroups in group theory. The kernel of a homomorphism is shown to be an admissible relation. Conversely, corresponding to an admissible relation, there exists a homomorphism. The fundamental theorem on homomorphisms; and the existence and uniqueness of minimal machines are also presented.

We add a binary operator ≥ to the logical language, with intended meaning of φ<ψ: ‘φ is at least as likely, probable, or trustworthy, as ψ’. The operator ≥ is interpreted on Kripke structures, making it possible to define the standard necessity operator □ in terms of ≥. The operator ≥ provides us with an intermediate for the K-axiom, in the sense that we have both □(p→q)→(q≥p) and (q≥p)→(□p→□q). We discuss two semantics for this binary modal operator. It turns out that, as shown by Gärdenfors and Segerberg, ≥ is not only too weak to distinguish finite models from infinite ones or to distinguish countable additivity from finite additivity, ≥ also cannot distinguish sophisticated ways of assigning exact probabilities to events (‘measuring’) from the conceptually simpler task of just counting them.

A formal tool, the High Level Fuzzy Petri Net, is proposed for representing and processing fuzzy production rules in a knowledge base. The basic net structures to model inference patterns in approximate reasoning are introduced. The chaining mechanism used and the modeling of rules with fuzzy quantifiers and certainty factors are discussed. We have also investigated the representation of parallel and conflicting rules. Two types of fuzzy reasoning algorithms, to answer data driven and goal driven queries are described. The issue of time complexity of the algorithms is also addressed.

In this paper the concepts of Urysohn-convergence of filters and Urysohn-closedness on fuzzy lattices are introduced. Some important results with respect to fuzzy lattices are obtained.