“Nonfreeness” is the (negative of the) difference between the von Neumann entropies of a given many-fermion state and the free state that has the same 1-particle statistics. It also equals the relative entropy of the two states in question, i.e., it is the entropy of the given state relative to the corresponding free state. The nonfreeness of a pure state is the same as its “particle-hole symme...

Yang and Qiu proposed an expected utility-entropy (EU-E) measure of risk, which reflects an individual’s intuitive attitude toward risk. Luce et al. have derived the numerical representations under behavioral axioms about preference orderings among gambles and their joint receipt, which further demonstrates the reasonability of the EU-E decision model as a normative one. In the paper, combining...

Study of fuzzy entropy on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Built in uncertainty in IFSs, it is named as hesitance. It is contained in fuzzy membership function in itself by definition. Hence, designing fuzzy entropy is not easy because there is no general entropy definition about IFSs. By considering existing fuzzy entropy definitions, fuzzy entropy on IFSs is desig...

Recently, "renormalized entropy" was proposed as a novel measure of relative entropy [P. Saparin et al., Chaos, Solitons and Fractals 4, 1907 (1994)] and applied to several physiological time sequences, including electroencephalograms (EEGs) of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (KL) relative entropy, and it gives similar numerical results...

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...

We give a generator-free formulation of sofic measure entropy using finite partitions and establish a Kolmogorov-Sinai theorem. We also show how to compute the values for general Bernoulli actions in a concise way using the arguments of Bowen in the finite base case.

Traditional approaches to morphology tend to treat inflectional systems not as unstructured sets of forms with shared stems or roots but as structured networks of elements. The interdependency of elements is, as Matthews (1991: 197) notes, ‘the basis of exemplary paradigms’ in the classical grammatical tradition. Although the exemplary patterns and leading forms of traditional descriptions brin...

Non-additive entropy measures are important for many applications. We study Havrda and Charvat entropy for record values and have shown that this characterizes the underlying distribution function uniquely. Also the non-additive entropy of record values has been derived in case of some specific distributions. Further we propose a generalized residual entropy measure for record value.

In the context of multicriteria decision making whose aggregation process is based on the Choquet integral, bi-capacities can be regarded as a natural extension of capacities when the underlying evaluation scale is bipolar. The notion of entropy, recently generalized to capacities to measure their uniformity, is now extended to bi-capacities. We show that the resulting entropy measure has a ver...

Bowen showed that a continuous expansive map with specification has a unique measure of maximal entropy. We show that the conclusion remains true under weaker non-uniform versions of these hypotheses. To this end, we introduce the notions of obstructions to expansivity and specification, and show that if the entropy of such obstructions is smaller than the topological entropy of the map, then t...