Comparison of Different Algorithms of Approximation by Extensional Fuzzy Subsets
نویسندگان
چکیده
How to approximate an arbitrary fuzzy subset by an adequate extensional one is a key question within the theory of Extensional Fuzzy Subsets. In a recent paper by the authors [19] different methods were provided to find good approximations. In this work these methods are compared in order to understand better the performance and improvement they give.
منابع مشابه
Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions
We study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...
متن کاملA Small Course on Indistinguishability Operators
This is a short introduction to indistinguishability operators. Section 1 contains the definition of these operators and gives basic reasons for their study. Section 2 explains the two most popular ways to generate them, depending on the way the data are given. Section 3 introduces the idea of extensionality and shows that extensional fuzzy subsets with respect to a T -indistinguishability oper...
متن کاملPOWERSET OPERATORS OF EXTENSIONAL FUZZY SETS
Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...
متن کاملExact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach
We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...
متن کاملS-APPROXIMATION SPACES: A FUZZY APPROACH
In this paper, we study the concept of S-approximation spaces in fuzzy set theory and investigate its properties. Along introducing three pairs of lower and upper approximation operators for fuzzy S-approximation spaces, their properties under different assumptions, e.g. monotonicity and weak complement compatibility are studied. By employing two thresholds for minimum acceptance accuracy and m...
متن کامل