To deal with situations involving uncertainty, Fermatean fuzzy sets are more effective than Pythagorean sets, intuitionistic and sets. Applications for similarity measures can be found in a wide range of fields, including clustering analysis, classification issues, medical diagnosis, etc. The computation the weights criteria multi-criteria decision-making problem heavily relies on entropy measu...

The main aim of this article is to revisit the definitions of subsethood measure which are predomonant in the literature of fuzzy set theory. It is also intended to revisit the relationship between fuzzy entropy and conditioning as proposed by some authors. We wish to analyze these with the extended definition of complementation of fuzzy sets on the basis of reference function. The existing def...

In this paper, we proposed an algorithm to find the optimal threshold value for denoising an image. A new cost function is designed to find the optimal threshold in every image. The cost function is based on the intuitionistic fuzzy divergence measure of the denoised image and original image. In addition, the intuitionistic fuzzy entropy of denoised image is added to the cost function. This is ...

The roughness of a rough set arises from the existence of its boundary region. In such a boundary region, each object has a non-zero rough membership degree. When an object’s rough membership degree is regarded as its fuzzy membership degree, a rough set can induce a fuzzy set. This relationship motivates us to assert that there may exist some inherent relations between the roughness of a rough...

Fuzzy sets (FSs) are an important tool to model uncertainty and vagueness. Entropy is being used measure the fuzziness within a fuzzy set (FS). These entropies find multicriteria decision-making. For measuring with TOPSIS techniques axiomatic definition of entropy for also given in this paper. The proposed provided satisfy all axioms. Several numerical examples presented compare existing entrop...

This paper discusses an extension of the V-measure (Rosenberg and Hirschberg, 2007), an entropy-based cluster evaluation metric. While the original work focused on evaluating hard clusterings, we introduce the Fuzzy V-measure which can be used on data that is inherently ambiguous. We perform multiple analyses varying the sizes and ambiguity rates and show that while entropy-based measures in ge...

They appear often situations in a system’s operation characterized by a degree of vagueness and/or uncertainty. In the present paper we use principles of fuzzy logic to develop a general model representing such kind of situations. We also present 3 alternative methods for measuring a fuzzy system’s effectiveness. These methods include the measurement of the system’s total possibilistic uncertai...

A fuzzy aspect is introduced into L systems and some of its properties are investigated. The relationship between fuzzy L languages and the fuzzy languages generated by fuzzy grammar defined by Lee and Zadeh is elucidated. The concept of fuzzy entropy of a string is proposed as a measure of fuzziness of the latter. Some relationship between fuzzy L systems and the ordinary L systems is discussed.

A fuzzy aspect is introduced into L systems and some of its properties are investigated. The relationship between fuzzy L languages and the fuzzy languages generated by fuzzy grammar defined by Lee and Zadeh is elucidated. The concept of fuzzy entropy of a string is proposed as a measure of fuzziness of the latter. Some relationship between fuzzy L systems and the ordinary L systems is discussed.

Heart rate variability (HRV) is the variation of the time interval between consecutive heartbeats and depends on the extrinsic regulation of the heart rate. It can be quantified using nonlinear methods such as entropy measures, which determine the irregularity of the time intervals. In this work, approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn) and fuzzy measure entr...