International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper the theory of coherent imprecise previsions is applied to risk measurement. We introduce the notion of coherent risk measure defined on an arbitrary set of risks, showing that it can be considered a special case of coherent upper prevision. We also prove that our definition generalizes the notion of coherence for risk measures defined on a linear space of random numbers, given in literature. Consistency properties of Value-at-Risk (VaR), currently one of the most used risk measures, are investigated too, showing that it does not necessarily satisfy a weaker notion of consistency called 'avoiding sure loss'. We introduce sufficient conditions for VaR to avoid sure loss and to be coherent. Finally we discuss ways of modifying incoherent risk measures into coherent ones.

A characterization of all idempotent uninorms satisfying the distributive property is given. The special cases of left-continuous and right-continuous idempotent uninorms are presented separately and it is also proved that all idempotent uninorms are autodistributive. Moreover, all distributive pairs of idempotent uninorms (pairs U₁, U₂ such that U_l is distributive over U₂ and U₂ is distributive over U₁) are also characterized.

This paper presents the comparative study for fuzzy regression model using linear programming and fuzzy regression model using genetic algorithms. Two cases were considered: crisp X – crisp Y and crisp X – fuzzy Y. Simulation was carried out with a tool developed in MATLAB.

Using optimization tools such as genetic algorithms to construct a fuzzy expert system (FES) focusing only on its accuracy without considering the comprehensibility may not result in a system that produces understandable expressions. To exploit the transparency characteristics of FES for reasoning in a higher-level knowledge representation, a FES should provide high comprehensibility while preserving its accuracy. The completeness of fuzzy sets and rule structures should also be considered to guarantee that every data point has a response output. This paper proposes some quantitative measures for a FES to determine the degree of the accuracy, the comprehensibility of the fuzzy sets, and the completeness of fuzzy rule structure. These quantitative measures are then used as a fitness function for a genetic algorithm in optimally refining a FES.

In this paper, deriving the type-m fuzzy sets, intuitionistic fuzzy sets, Φ-fuzzy sets, rough sets, fuzzy rough sets and rough fuzzy sets as particular genuine sets, and establishing their connections with genuine sets, it is demonstrated that the theory of genuine sets provides a powerful tool to model various different kinds of uncertainty in a mathematical way. Furthermore, it is also shown that the genuine set theoretic descriptions of type-m fuzzy sets, intuitionistic fuzzy sets and fuzzy rough sets point out new features of these set notations, originated from the peculiar characteristics of genuine sets.

This paper presents an agent-based approach to identification of prediction models in two-dimensional data spaces. A number of agents are sent to the two-dimensional data space that people want to investigate. At the micro-level, every agent tries to build a local linear model by competing with others, and then at the macro-level all surviving agents build the global model by cooperating with each other. And a genetic algorithm is introduced for improving the global model built by the agents. Two examples that apply this approach are given. The advantages of this approach are it does not need people to give a certain formula in advance; and most of time, it can give more precise prediction models than those given by traditional methods.

This section is maintained by Vladik Kreinovich. Please send you 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.