On measures of fuzziness

Relationships between uncertainty measures, fuzziness measures and divergence measures

Measures of Fuzziness under Different Uses of Fuzzy Sets

In this paper we discuss on the relationship between fuzziness and its measuring on the one side, and the possible uses of fuzzy sets on the other side. We conclude that the usual axioms and measures of fuzziness disregard the commensurability assumption and view the fuzzy set as a collection of fuzzy singletons. We propose new axioms and a relation “less fuzzy than” for a conjunctive view of f...

Entropy and Similarity Measures For Interval-Valued Intuitionistic Fuzzy Sets Based on Intuitionism and Fuzziness

Many authors have developed lots of entropies and similarity measures for interval-valued intuitionistic fuzzy sets(IvIFSs). In this paper, we first review some famous entropies for IvIFSs. Then, a new entropy for IvIFSs based on intuitionism and fuzziness is proposed and proved to satisfy the axiomatic requirements given by Liu and Zhang. Furthermore, a new class of similarity measure for IvIF...

The Fuzziness of Fuzzy Ideals

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...

The interpretation of fuzziness

By analyzing related issues in psychology and linguistics, two basic types of fuzziness can be attributed to similarity and relativity, respectively. In both cases, it is possible to interpret grade of membership as the proportion of positive evidence, so as to treat fuzziness and randomness uniformly.