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A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic

Enrique de Amo, Manuel Díaz Carrillo, Juan Fernández-Sánchez (2016)

Open Mathematics

We study a parameterized family of singular functions which appears in a paper by H. Okamoto and M. Wunsch (2007). Various properties are revisited from the viewpoint of fractal geometry and probabilistic techniques. Hausdorff dimensions are calculated for several sets related to these functions, and new properties close to fractal analysis and strong negations are explored.

A New Approach to Fuzzy Arithmetic

Popov, Antony (2010)

Serdica Journal of Computing

This work shows an application of a generalized approach for constructing dilation-erosion adjunctions on fuzzy sets. More precisely, operations on fuzzy quantities and fuzzy numbers are considered. By the generalized approach an analogy with the well known interval computations could be drawn and thus we can define outer and inner operations on fuzzy objects. These operations are found to be useful in the control of bioprocesses, ecology and other domains where data uncertainties exist.* This work...

Applications of contractive-like mapping principles to fuzzy equations

Juan J. Nieto, Rosana Rodríguez López (2006)

Revista Matemática Complutense

We recall a recent extension of the classical Banach fixed point theorem to partially ordered sets and justify its applicability to the study of the existence and uniqueness of solution for fuzzy and fuzzy differential equations. To this purpose, we analyze the validity of some properties relative to sequences of fuzzy sets and fuzzy functions.

Entropy of T -sums and T -products of L - R fuzzy numbers

Anna Kolesárová, Doretta Vivona (2001)


In the paper the entropy of L R fuzzy numbers is studied. It is shown that for a given norm function, the computation of the entropy of L R fuzzy numbers reduces to using a simple formula which depends only on the spreads and shape functions of incoming numbers. In detail the entropy of T M –sums and T M –products of L R fuzzy numbers is investigated. It is shown that the resulting entropy can be computed only by means of the entropy of incoming fuzzy numbers or by means of their parameters without the...

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