Fuzzy Sets in Clustering: On Fuzzy Partitions

During last years, lots of the fuzzy rule based classifier (FRBC) design methods have been proposed to improve the classification accuracy and the interpretability of the proposed classification models. Most of them are based on the fuzzy set theory approach in such a way that the fuzzy classification rules are generated from the grid partitions combined with the pre-designed fuzzy partitions using fuzzy sets. Some mechanisms are studied to automatically generate fuzzy partitions from data such as discretization, granular computing, etc. Even those, linguistic terms are intuitively assigned to fuzzy sets because there is no formalisms to link inherent semantics of linguistic terms to fuzzy sets. In view of that trend, genetic design methods of linguistic terms along with their (triangular and trapezoidal) fuzzy sets based semantics for FRBCs, using hedge algebras as the mathematical formalism, have been proposed. Those hedge algebras-based design methods utilize semantically quantifying mapping values of linguistic terms to generate their fuzzy sets based semantics so as to make use of fuzzy sets based-classification reasoning methods proposed in design methods based on fuzzy set theoretic approach for data classification. If there exists a classification reasoning method which bases merely on semantic parameters of hedge algebras, fuzzy sets-based semantics of the linguistic terms in fuzzy classification rule bases can be replaced by semantics - based hedge algebras. This paper presents a FRBC design method based on hedge algebras approach by introducing a hedge algebra- based classification reasoning method with multi-granularity fuzzy partitioning for data classification so that the semantic of linguistic terms in rule bases can be hedge algebras-based semantics. Experimental results over 17 real world datasets are compared to existing methods based on hedge algebras and the state-of-the-art fuzzy sets theoretic-based approaches, showing that the proposed FRBC in this paper is an effective classifier and produces good results.

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Spaces with fuzzy partitions and fuzzy sets

The Oxford Journal of Intelligent Decision and Data Science ◽

10.5899/2017/ojids-00011 ◽

2017 ◽

Vol 2017 (2) ◽

pp. 25-33 ◽

Cited By ~ 1

Author(s):

Jiří Močkoř ◽

Michal Holčapek

Keyword(s):

Fuzzy Sets ◽

Fuzzy Partitions

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On Many-Valued Partitions and Many-Valued Equivalence Relations

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s021848850300203x ◽

2003 ◽

Vol 11 (02) ◽

pp. 235-253 ◽

Cited By ~ 16

Author(s):

Mustafa Demirci

Keyword(s):

Fuzzy Sets ◽

Finite Family ◽

Equivalence Relations ◽

Fuzzy Partitions

For a fixed integral commutative cl-monoid M=(L, ≤, *), introducing the notions of M-partitions and M-equivalence relations as the extensions of T-partitions and T-equivalence relations to the integral commutative cl-monoid M=(L, ≤, *), respectively, it is shown that the previous approaches on T-partitions and T-equivalence relations can be unified, and most of the results in these works can be easily stated based on the integral commutative cl-monoid M=(L, ≤, *). Modifying the notion of T-redundancy of finite family of fuzzy sets of a nonempty ordinary set X, it is extended to arbitrary family of L-fuzzy sets on the basis of the integral commutative cl-monoid M, and is shown that the proposed definition has more desirable properties than the previous one. Furthermore, handling the works of Höhle, Klawonn, Gebhardt and Kruse on fuzzy partitions and fuzzy equivalence relations, some of their results are improved, and several new results in this direction are pointed out.

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