We consider the general class of strongly Fej er monotone map-pings and some of their basic properties. These properties are useful for a convergence theory of corresponding iterative methods which are widely used to solve convex problems. In part II the geometrical properties of these map-pings are studied. In particular the maximal of such mappings with respect to set inclusion of the images ...

Discrete Interval Encoding Trees (Diets) are data structures for the representation of fat, i.e. densely populated sets over a discrete linear order. In this paper we introduce algorithms for set-theoretic operations like intersection, union, etc. on sets represented as balanced diets. We empirically analyse their performance and show that these algorithms can outperform previously known algori...

Today is a world of uncertainty with its associated problems, which can be well handled by soft set theory. In this paper, we extend sanchez`s approach for medical diagnosis using the representation of an interval valued fuzzy soft matrices. we introduce the definition of union and intersection of Interval valued fuzzy soft matrices with examples.Finally, we extend our approach in application o...

Two of G. Matheron’s seminal contributions have been his development of size distributions (else called ‘granulometries’) and his kernel representation theory. The first deals with semigroups of multiscale openings and closings of binary images (shapes) by compact convex sets, a basic ingredient of which are the multiscale Minkowski dilations and erosions. The second deals with representing inc...

A circle graph is the intersection graph of a set of chords on a circle. A graph is Helly circle if there is a model of chords satisfying the Helly property. In 2003 it was conjectured that Helly circle graphs are exactly diamond-free circle graphs. In this work, we propose a method to compress any Helly circle representation of a graph and give some ideas to advance in an inductive proof of th...

This paper investigates the study of -complex fuzzy sets. The set, where  is a completely distributive lattice, is generalization complex set. fundamental set theoretic operations on sets are discussed properly, including complement, union and intersection. New procedures presented to combine novel concepts -norms -conorms look into conditions that lead comparable representation theorem. W...