A fuzzy morphological approach is here presented to retrieve structural properties of images considered as fuzzy sets. The basic concepts of the possibility theory and of the mathematical morphology are brieey illustrated, together with their suggested integration. Some applications to astronomical images are also shown.

This note provides a brief overview of the main ideas and notions underlying fifty years of research in fuzzy set and possibility theory, two important settings introduced by L. A. Zadeh for representing sets with unsharp boundaries and uncertainty induced by granules of information expressed with words. The discussion is organized on the basis of three potential understanding of the grades of ...

When there is uncertainty about the values of a variable, it is possible to have different pieces of information about it. This can be due to the fact that they represent the points of view of different agents and these agents have followed different criteria when codify the pieces of information by means of numbers. The aim of this paper is to provide tools for the comparison of these represen...

Relational models for diagnosis are based on a direct description of the association between disorders and manifestations. This type of model has been specially used and developed by Reggia and his co-workers in the late eighties as a basic starting point for approaching diagnosis problems. The paper proposes a new relational model which includes Reggia's model as a particular case and which al...

The Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs‎. ‎In Data Envelopment Analysis (DEA)‎, ‎it is highly important to identify the defining hyperplanes and especially the strong defining hyperplanes of the empirical PPS‎. ‎Although DEA models can determine the efficiency of a Decision Making Unit (DMU)‎, ‎but they...

Using super-efficiency, with regard to ranking efficient units, is increasing in DEA. However, this model has some problems such as the infeasibility. Thus, this article studies infeasibility of the input-based super-efficiency model (because of the zero inputs and outputs), and presents a solution by adding two virtual DMUs with mean values (one for inputs and one for outputs). Adding virtual ...

the non-differentiability and implicit definition of boundary of production possibility set (pps) in data envelopment analysis (dea) are two important difficulties for obtaining directional characteristics, including different elasticity measures and marginal rates of substitution. also, imposing weight restrictions in dea models have some shortcomings and misunderstandings. in this paper we ut...

this paper investigates a procedure for identifying all efficient hyperplanes of production possibility set (pps). this procedure is based on a method which recommended by pekka j. korhonen[8]. he offered using of lexicographic parametric programming method for recognizing all efficient units in data envelopment analysis (dea). in this paper we can find efficient hyperplanes, via using the para...