Entropy Of Interval-valued Fuzzy Sets Research Articles

A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure

In this contribution, we generalize recent results on the entropy of interval-valued fuzzy sets (IVFSs) based on the intuitionistic distance and its relationship with similarity measure. The intuitionistic distance provides us with a new axiomatic definition of entropy of IVFSs. Based on the set of new axioms, we also prove some theorems that entropy and similarity measure for IVFSs can be transformed by each other in a general way. The contribution ends by deriving a formula that creates a variety of new entropies by the use of given entropies of IVFSs.

Distances and Entropy for Interval-Valued Fuzzy Sets

Distances and Entropy for Interval-Valued Fuzzy Sets

Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure

This article proposes a new axiomatic definition of entropy of interval-valued fuzzy sets (IVFSs) and discusses its relation with similarity measure. First, we propose an axiomatic definition of entropy for IVFS based on distance which is consistent with the axiomatic definition of entropy of a fuzzy set introduced by De Luca, Termini and Liu. Next, some formulae are derived to calculate this kind of entropy. Furthermore we investigate the relationship between entropy and similarity measure of IVFSs and prove that similarity measure can be transformed by entropy. Finally, a numerical example is given to show that the proposed entropy measures are more reasonable and reliable for representing the degree of fuzziness of an IVFS.

Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship

In this paper, we introduce an axiomatic definition of an interval-valued fuzzy sets’ inclusion measure which is different from Bustince’s [H. Bustince, Indicator of inclusion grade for interval-valued fuzzy sets, Applications to approximate reasoning based on interval-valued fuzzy sets, International Journal of Approximate Reasoning, 23 (2000) 137–209]. The relationship among the normalized distance, the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets is investigated in detail. Furthermore, six theorems are proposed showing how the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets can be deduced by the interval-valued fuzzy sets’ normalized distance based on their axiomatic definitions. Some formulas have also been put forward to calculate the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets.