Quotients with respect to similarity relations
Fuzzy Sets and Systems - Mathematics and Fuzziness, Part 1
Fuzzy congruences and compatible fuzzy partitions
Fuzzy Sets and Systems
Similarity relations: the calculation of minimal generating families
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Similarity relations, fuzzy partitions, and fuzzy orderings
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Fuzzy partitions with the connectives T∞,S∞
Fuzzy Sets and Systems
The entropy of fuzzy dynamical systems and generators
Fuzzy Sets and Systems
q-similitudes and q-fuzzy partitions
Fuzzy Sets and Systems
Equality relations as a basis for fuzzy control
Fuzzy Sets and Systems
Fuzzy partitions and fuzzy-quotient rings
Fuzzy Sets and Systems
Complement of fuzzy k-partitions
Fuzzy Sets and Systems
A new approach to the similarity relations in the fuzzy set theory
Information Sciences: an International Journal
Degenerate and non-degenerate convex decomposition of finite fuzzy partitions—I
Fuzzy Sets and Systems
Fuzzy Sets and Systems - Special issue: fuzzy relations, part 2
On aggregation of T-transitive fuzzy binary relations
Fuzzy Sets and Systems - Special issue on fuzzy relations, part 1
Fuzzy equivalence relation redefined
Fuzzy Sets and Systems
On the redundancy of fuzzy partitions
Fuzzy Sets and Systems - Special issue on methods for data analysis in classificatin and control
T -partitions of the real line generated by idempotent shapes
Fuzzy Sets and Systems - Special issue: fuzzy arithmetic
Fuzzy Sets and Systems
Entropy of fuzzy partitions: a general model
Fuzzy Sets and Systems
Connectives for fuzzy partitions
Fuzzy Sets and Systems
Comparison of fuzzy partitions based on their &agr;-cuts
Fuzzy Sets and Systems
One-to-one correspondences between ɛ-partitions, (1 - ɛ)-equivalences and ɛ-pseudometrics
Fuzzy Sets and Systems
Information Sciences: an International Journal
Equivalent finite fuzzy sets and Stirling numbers
Information Sciences: an International Journal
Fuzzy equivalence relations and their equivalence classes
Fuzzy Sets and Systems
Compatibility of t-norms with the concept of ε-partition
Information Sciences: an International Journal
(S, N)- and R-implications: A state-of-the-art survey
Fuzzy Sets and Systems
Representations of T-similarity relations
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Building a class of fuzzy equivalence relations
Fuzzy Sets and Systems
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
Confluence and termination of fuzzy relations
Information Sciences: an International Journal
A characterization of residual implications derived from left-continuous uninorms
Information Sciences: an International Journal
Systemic approach to fuzzy logic formalization for approximate reasoning
Information Sciences: an International Journal
On a new class of fuzzy implications: h-Implications and generalizations
Information Sciences: an International Journal
Threshold generation method of construction of a new implication from two given ones
Fuzzy Sets and Systems
Transitivity of fuzzy relations under discretization
Information Sciences: an International Journal
R-implications and the exchange principle: The case of border continuous t-norms
Fuzzy Sets and Systems
On the vertical threshold generation method of fuzzy implication and its properties
Fuzzy Sets and Systems
A method for deriving order compatible fuzzy relations from convex fuzzy partitions
Fuzzy Sets and Systems
Hi-index | 0.07 |
A T-fuzzy equivalence relation is a fuzzy binary relation on a set X which is reflexive, symmetric and T-transitive for a t-norm T. Recently, Mesiar et al. [R. Mesiar, B. Reusch, H. Thiele, Fuzzy equivalence relations and fuzzy partitions, J. Multi-Valued Logic Soft Comput. 12 (2006) 167-181] have generalised the t-norm T to any general conjunctor C and investigated the minimal assumptions required on such operations, called duality fitting conjunctors, such that the fuzzification of the equivalence relation admits any value from the unit interval and also the one-one correspondence between the fuzzy equivalence relations and fuzzy partitions is preserved. In this work, we conduct a similar study by employing a related form of C-transitivity, viz., I-transitivity, where I is an implicator. We show that although every I-fuzzy equivalence relation can be shown to be a C-fuzzy equivalence relation, there exist C-fuzzy equivalence relations that are not I-fuzzy equivalence relations and hence these concepts are not equivalent. Most importantly, we show that the class of duality fitting implicators I is much richer than the residuals of the duality fitting conjunctors in the study of Mesiar et al. We also show that the I-fuzzy partitions have a ''constant-wise'' structure.