Introduction to Fuzzy Set Operations

Blending Implicit Shapes Using Fuzzy Set Operations

Implicit modelling is a powerful technique to design geometric shapes, where a geometric object is described by a real function. In general, the real functions used in implicit modelling are unbounded and can take any values in space R. In general, the shapes described by different level sets of an unbounded implicit function can be varied significantly and are very unpredictable. In addition, ...

Leximin optimality and fuzzy set-theoretic operations

Interactive visualization of fuzzy set operations

Fuzzy sets refer to the datasets which do not have separate, distinct clusters, and they contain data elements whose membership values are between 0 and 1. Often each element belongs to several groups. We design a disk diagram with an augmented frequency graph to visualize elements in a fuzzy set. It shows the distribution of the elements within the set with respect to the membership function v...

Fuzzy Answer Set Programming: An Introduction

In this chapter, we present a tutorial about fuzzy answer set programming (FASP); we give a gentle introduction to its basic ideas and definitions. FASP is a combination of answer set programming and fuzzy logics which has recently been proposed. From the answer set semantics, FASP inherits the declarative nonmonotonic reasoning capabilities, while fuzzy logic adds the power to model continuous...

Some Classes of Associative Binary Operations in Fuzzy Set Theory

The main aim of this paper is to summarize recent advances on some new classes of associative operations (uninorms, nullnorms, t-operators) used in fuzzy set theory.