International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

We first survey the basic results in recent paper on fuzzy queueing theory based on possibility theory. Then we apply this to two application problems: (1) machine servicing problem (optimal size of service crews); and (2) then a queueing decision problem where we find the optimal number of servers.

An overview of the use of the discrete Sugeno integral as either an aggregation tool or a preference functional is presented in the qualitative framework of two decision paradigms: multi-criteria decision-making and decision-making under uncertainty. The parallelism between the representation theorems in both settings is stressed, even if a basic requirement like the idempotency of the aggregation scheme should be explicitely stated in multi-criteria decision-making, while its counterpart is implicit in decision under uncertainty by equating the utility of a constant act with the utility of its consequence. Important particular cases of Sugeno integrals such as prioritized minimum and maximum operators, their ordered versions, and Boolean max-min functions are studied.

The main goal of the present paper is to extend such classical constructions as limits and derivatives making them appropriate for management of imprecise, vague, uncertain, and incomplete information. In the second part of the paper, going after introduction, elements of the theory of fuzzy limits are presented. The third part is devoted to the construction of fuzzy derivatives of real functions. Two kinds of fuzzy derivatives are introduced: weak and strong ones. It is necessary to remark that the strong fuzzy derivatives are similar to ordinary derivatives of real functions being their fuzzy extensions. The weak fuzzy derivatives generate a new concept of a weak derivative even in a classical case of exact limits. In the fourth part fuzzy differentiable functions are studied. Different properties of such functions are obtained. Some of them are the same or at least similar to the properties of the differentiable functions while other properties differ in many aspects from those of the standard differentiable functions. Many classical results are obtained as direct corollaries of propositions for fuzzy derivatives, which are proved in this paper. Some of the classical results are extended and completed. The fifth part of the paper contains several interpretations of fuzzy derivatives aiming at application of fuzzy differential calculus to solving practical problems. At the end, some open problems are formulated.

Data mining is the process of extracting desirable knowledge or interesting patterns from existing databases for specific purposes. Most conventional data-mining algorithms identify the relationships among transactions using binary values. Transactions with quantitative values are however commonly seen in real-world applications. We proposed a fuzzy mining algorithm by which each attribute used only the linguistic term with the maximum cardinality int he mining process. The number of items was thus the same as that of the original attributes, making the processing time reduced. The fuzzy association rules derived in this way are not complete. This paper thus modifies it and proposes a new fuzzy data-mining algorithm for extrating interesting knowledge from transactions stored as quantitative values. The proposed algorithm can derive a more complete set of rules but with more computation time than the method proposed. Trade-off thus exists between the computation time and the completeness of rules. Choosing an appropriate learning method thus depends on the requirement of the application domains.

In this paper we wish to solve multi-objective fully fuzzified linear programming problems which are multi-objective linear programming problems where all the parameters and variables are fuzzy numbers. We change this problem into a single objective fuzzy linear programming problem and then show that our solution procedure can be used to explore the whole undominated set. An evolutionary algorithm is then designed to generate undominated solutions. An example is presented showing our evolutionary algorithm solution.

This paper focuses on the decomposition problem of fuzzy relations using the concepts of multiuniverse fuzzy propositional logic. Given two fuzzy propositions in different universes, it is always possible to construct a fuzzy relation in the common universe through a prescribed combination. However, the converse is not so obvious, if possible at all. In other words, given a fuzzy relation, how would we know if it really represents a certain relationship between some fuzzy propositions? It is important to recognize whether the given fuzzy relation is a meaningful representation of information according to certain criteria applicable to some fuzzy propositions that constitute the fuzzy relation itself. Two basic structures of decomposition are investigated. Necessary and sufficient conditions for decomposition of multiuniverse fuzzy truth functions in terms of one-universe truth functions are presented. An algorithm for decomposition is proposed.

This section is maintained by Vladik Kreinovich. Please send your abstract (or copies of papers that you want to see reviewed here), to vladik@cs.utep.edu, or by regular mail to: Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.