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We give a complete characterization of tribes with respect to the Łukasiewicz -norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz -norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental -norms, e. g., for the product -norm.
The purpose of this paper is to generalize and develop a mean-square calculus for fuzzy stochastic processes and study their differentiability and integrability properties. Some results for second-order fuzzy stochastic processes are presented.
In this paper, a local approach to the concept of -entropy is presented. Applying the Choquet‘s representation Theorem, the introduced concept is stated in terms of -entropy.
This paper is just a first approach to the idea that the membership function μP of a fuzzy set labelled P is, basically, a measure on the set of linguistic expressions x is P for each x in the corresponding universe of discourse X. Estimating that the meaning of P (relatively to X) is nothing else than the use of P on X, these measures seem to be reached by generalizing to a preordered set the concept of Fuzzy Measure, introduced by M. Sugeno, when the preorder translates the primary use of the...
In a fuzzy measure space we study aggregation operators by means of the hypographs of the measurable functions. We extend the fuzzy measures associated to these operators to more general fuzzy measures and we study their properties.
En este trabajo se propone una estructura de álgebra difusa (borrosa) basada en la distinción entre difusidad extensiva y comprehensiva, desarrollando y conectando los trabajos de Nahmias sobre variables difusas, de Klement sobre medibilidad difusa y de Nowakowska sobre estructuras de conceptos.
The concept of usability of man-machine interfaces is usually judged in terms of a number of aspects or attributes that are known to be subject to some rough correlations, and that are in many cases given different importance, depending on the context of use of the application. In consequence, the automation of judgment processes regarding the overall usability of concrete interfaces requires the design of aggregation operators that are capable of modeling approximate or ill-defined interactions...
Lattice-valued possibilistic measures, conceived and developed in more detail by G. De Cooman in 1997 [2], enabled to apply the main ideas on which the real-valued possibilistic measures are founded also to the situations often occurring in the real world around, when the degrees of possibility, ascribed to various events charged by uncertainty, are comparable only quantitatively by the relations like “greater than” or “not smaller than”, including the particular cases when such degrees are not...
In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...
In this paper, we propose a new method to generate a continuous
belief functions from a multimodal probability distribution function defined
over a continuous domain. We generalize Smets' approach in the sense that
focal elements of the resulting continuous belief function can be disjoint sets
of the extended real space of dimension n. We then derive the continuous
belief function from multimodal probability density functions using the least
commitment principle. We illustrate the approach on two...
In this study we merge the concepts of Choquet-like integrals and the Choquet integral with respect to level dependent capacities. For finite spaces and piece-wise constant level-dependent capacities our approach can be represented as a -ordinal sum of Choquet-like integrals acting on subdomains of the considered scale, and thus it can be regarded as extension method. The approach is illustrated by several examples.
Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given.
In this paper we construct conditional states on semi-simple MV-algebras. We show that these conditional states are not given uniquely. By using them we construct the joint probability distributions and discuss the properties of these distributions. We show that the independence is not symmetric.
A new construction method for aggregation operators based on a composition of aggregation operators is proposed. Several general properties of this construction method are recalled. Further, several special cases are discussed. It is also shown, that this construction generalizes a recently introduced twofold integral, which is exactly a composition of the Choquet and Sugeno integral by means of a min operator.
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