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A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case

Fateme Kouchakinejad, Alexandra Šipošová (2017)


For an aggregation function A we know that it is bounded by A * and A * which are its super-additive and sub-additive transformations, respectively. Also, it is known that if A * is directionally convex, then A = A * and A * is linear; similarly, if A * is directionally concave, then A = A * and A * is linear. We generalize these results replacing the directional convexity and concavity conditions by the weaker assumptions of overrunning a super-additive function and underrunning a sub-additive function, respectively.

A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

Kravvaritis, D., Pantelidis, G. (1996)

Serdica Mathematical Journal

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

An inquiry-based method for Choquet integral-based aggregation of interface usability parameters

Miguel-Ángel Sicilia, Elena García Barriocanal, Tomasa Calvo (2003)


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...

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.

Completely generalized nonlinear variational inclusions for fuzzy mappings

Nan-jing Huang (1999)

Czechoslovak Mathematical Journal

In this paper, we introduce and study a new class of completely generalized nonlinear variational inclusions for fuzzy mappings and construct some new iterative algorithms. We prove the existence of solutions for this kind of completely generalized nonlinear variational inclusions and the convergence of iterative sequences generated by the algorithms.

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