Generalized and Customizable Sets in R

We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-definable iterators and matching functions.

The posterity of Zadeh's 50-year-old paper: A retrospective in 101 Easy Pieces – and a Few More

International audienceThis article was commissioned by the 22nd IEEE International Conference of Fuzzy Systems (FUZZ-IEEE) to celebrate the 50th Anniversary of Lotfi Zadeh's seminal 1965 paper on fuzzy sets. In addition to Lotfi's original paper, this note itemizes 100 citations of books and papers deemed “important (significant, seminal, etc.)” by 20 of the 21 living IEEE CIS Fuzzy Systems pioneers. Each of the 20 contributors supplied 5 citations, and Lotfi's paper makes the overall list a tidy 101, as in “Fuzzy Sets 101”. This note is not a survey in any real sense of the word, but the contributors did offer short remarks to indicate the reason for inclusion (e.g., historical, topical, seminal, etc.) of each citation. Citation statistics are easy to find and notoriously erroneous, so we refrain from reporting them - almost. The exception is that according to Google scholar on April 9, 2015, Lotfi's 1965 paper has been cited 55,479 times

A Historical Account of Types of Fuzzy Sets and Their Relationships

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used

Linguistic Interpretation of Mathematical Morphology

Mathematical Morphology is a theory based on geometry, algebra, topology and set theory, with strong application to digital image processing. This theory is characterized by two basic operators: dilation and erosion. In this work we redefine these operators based on compensatory fuzzy logic using a linguistic definition, compatible with previous definitions of Fuzzy Mathematical Morphology. A comparison to previous definitions is presented, assessing robustness against noise.Fil: Bouchet, Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata; ArgentinaFil: Meschino, Gustavo. Universidad Nacional de Mar del Plata; ArgentinaFil: Brun, Marcel. Universidad Nacional de Mar del Plata; ArgentinaFil: Espin Andrade, Rafael. Instituto Superior Politécnico José Antonio Echeverría Cujae; CubaFil: Ballarin, Virginia. Universidad Nacional de Mar del Plata; Argentin