Comparison and data analysis to the similarity measures and entropy for fuzzy sets are studied. The distance proportional value between the fuzzy set and the corresponding crisp set is represented as fuzzy entropy. We also verified that the sum of the similarity measure and the entropy between fuzzy set and the corresponding crisp set constitutes the total information. Finally, we derive a simi...

We apply fuzzy techniques to incorporate external data into p-median problems. So we can detect certain solutions that would be discarded by usual crisp and fuzzy algorithms but that contrasted with this additional information can be advantageous. This usually reveals a pathology of the model and hence our methods provide some fuzzy validation criteria for p-median models. Ó 2001 Elsevier Scien...

Given a piecewise invertible map T : X → X and a weight g : X →]0,∞[, a conformal measure ν is a probability measure on X such that, for all measurable A ⊂ X with T : A→ TA invertible, ν(TA) = λ ∫

In this paper, we propose a fuzzy generalized ‘useful’ parametric mean length and bounds are obtained in terms of useful fuzzy measure. The bounds obtained are new and some known results are the particular cases of the proposed measure and bounds.

We present some interesting properties related to the area compensation procedure to compare fuzzy numbers. It has been proved that this method produces more than a fuzzy interval order: it induces a ranking of fuzzy numbers. Some further results are given about the transitivity property and about computational aspects. Extensions to non-normal fuzzy numbers and fuzzy quantities are also proposed.

Graphical log-linear models are effective for representing complex structures that emerge from high-dimensional data. It is challenging to fit an appropriate model in the setting and many existing methods rely on a convenient class of models, called decomposable which lend well stepwise approach. However, these restrict pool candidate they can search, difficult scale. be shown non-decomposable ...

The pseudometric generating property of non-additive set functions also plays an important role as the autocontinuity in fuzzy measure theory 2, 9]. A further research on this property has been presented in 4]. The aim of this paper is to prove the Egoroo's theorem and Lusin's theorem for measurable functions on metric spaces hold for those fuzzy measures with the exhaustivity and pseudometric ...

In this paper, we propose a fuzzy generalized ‘useful’ parametric mean length and bounds are obtained in terms of useful fuzzy measure. The bounds obtained are new and some known results are the particular cases of the proposed measure and bounds.

Distorted probabilities are an important family of fuzzy measures. In a recent paper we introduced m-dimensional distorted probabilities, which generalize the former and permit us to have a smooth transition from distorted probabilities to unconstrained ones. In this paper we introduce the union condition and the strict union condition, and we show that when these conditions hold for a fuzzy me...

In this paper, the well-known Egoroff’s theorem in classical measure theory is established on Sugeno fuzzy measure spaces. Taylor’s theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff’s theorem is obtaine...