Towards a Unified Logical Framework of Fuzzy Implications to Compare Fuzzy Sets
نویسندگان
چکیده
In fuzzy set theory, comparison of fuzzy sets plays an important role. Among the several ways to compare fuzzy sets, we address the logical theoretic approach using fuzzy implications. We propose a general framework allowing to generate many measures of comparison: inclusion, similarity and distance, and study their properties. Since the literature on the use fuzzy implications for defining such measures is abundant, we also attempt to relate this work to existing research. Keywords— aggregation operators, distance, fuzzy implication, inclusion, similarity
منابع مشابه
PROPERTY ANALYSIS OF TRIPLE IMPLICATION METHOD FOR APPROXIMATE REASONING ON ATANASSOVS INTUITIONISTIC FUZZY SETS
Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitio...
متن کاملUniversal Approximation of Interval-valued Fuzzy Systems Based on Interval-valued Implications
It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy. A formula to compute the lower upper bounds on the number of interval-valued fuzzy sets needed to achieve a pre-specified approximation accuracy for an arbitrary multivariate con...
متن کاملUnifying Quantitative, Semi-quantitative and Qualitative Spatial Relation Knowledge Representations Using Mathematical Morphology
One of the powerful features of mathematical morphology lies in its strong algebraic structure, that finds equivalents in set theoretical terms, fuzzy sets theory and logics. Moreover this theory is able to deal with global and structural information since several spatial relationships can be expressed in terms of morphological operations. The aim of this paper is to show that the framework of ...
متن کاملA Framework for Optimal Attribute Evaluation and Selection in Hesitant Fuzzy Environment Based on Enhanced Ordered Weighted Entropy Approach for Medical Dataset
Background: In this paper, a generic hesitant fuzzy set (HFS) model for clustering various ECG beats according to weights of attributes is proposed. A comprehensive review of the electrocardiogram signal classification and segmentation methodologies indicates that algorithms which are able to effectively handle the nonstationary and uncertainty of the signals should be used for ECG analysis. Ex...
متن کاملA unified approach to fuzzy random variables
The concept of Fuzzy-random-variable was introduced as an analogous notion to randomvariable in order to extend statistical analysis to situations when the outcomes of some random experiment are fuzzy sets. But in contrary to the classical statistical methods no unique definition has been established yet. In this paper a set-theoretical concept of fuzzy-random-variable will be presented. This n...
متن کامل