Clouds are a concept for uncertainty mediating between the concept of a fuzzy set and that of a probability distribution. A cloud is to a random variable more or less what an interval is to a number. We discuss the basic theoretical and numerical properties of clouds, and relate them to histograms, cumulative distribution functions, and likelihood ratios. We show how to compute nonlinear transf...

In this paper, we study the notion of an ample or complete field, a special case of the well-known fields and σ-fields of sets. These collections of sets serve as candidates for the domains of possibility and necessity measures, and are therefore important for the further development of a general fuzzy set and possibility theory. The existence of a one-one relationship between ample fields and ...

This article deals with a method to describe and manage spatial knowledge. Each georeferenced data is considered as an information source, whose location and value are independently described. The method proposed in this paper uses the information sources to infer the value of any request zone . This method is able to treat imprecise or uncertain, qualitative and quantitative data. It can be ap...

The setting of formal concept analysis presupposes the existence of a relation between objects and properties. Knowing that an unspecified object has a given property induces a formal possibility distribution that models the set of objects known to possess this property. This view expressed in a recent work by the authors of the present paper, has led to introduce the set-valued counterpart to ...

In the last decade a substantial amount of work has been carried out in the context of Description Logics (DLs). DLs are a logical reconstruction of the so-called framebased knowledge representation languages, with the aim of providing a simple wellestablished Tarski-style declarative semantics to capture the meaning of the most popular features of structured representation of knowledge. A main...

Efficient handling of inexact (grey) information is an important issue for the new emerging database technology. Inexact or imprecise information has been represented and manipulated by using different techniques, including fuzzy set theory, possibility theory, IVF (Interval Valued Fuzzy) Sets, Time Petri Nets, Fuzzy Clouds, etc. In this paper, different approaches dealing with uncertainty have...

In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...

We consider the internal rate of return (IRR) decision rule in capital budgeting problems with fuzzy cash flows. The possibility distribution of the IRR at any r ≥ 0, is defined to be the degree of possibility that the (fuzzy) net present value of the project with discount factor r equals to zero. Generalizing our earlier results on fuzzy capital budegeting problems [5] we show that the possibi...