Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for multisemigroups. Special attention is paid to simple and nilpotent multisemigroups. We also show that “almost all” randomly chosen multivalued binary operations defi...

In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.

In a previous article, an algorithm for identifying therapeutic targets in Boolean networks modelling pathological mechanisms was introduced. In the present article, the improvements made on this algorithm, named kali, are described. These improvements are (i) the possibility to work on asynchronous Boolean networks, (ii) a finer assessment of therapeutic targets and (iii) the possibility to us...

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. Keywords—Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

We investigate the convergence of measurable selectors for the limit of measurable multivalued maps. The relationship between the convergence of measurable selectors and lower and upper limits of measurable multivalued mappings with closed images is also derived. c © 2007 Elsevier Ltd. All rights reserved.

Abstract Multivalued $$*$$ ∗ -nonexpansive mappings are studied in Banach spaces. The demiclosedness principle is established. Here we focus on the problem of solving a variational inequality which defined set fixed points multivalued mapping. For this purpose, introduce tw...

The idea of approximate entailment has been proposed by Schaerf and Cadoli [Tractable reasoning via approximation, Artif. Intell. 74(2) (1995) 249–310] as a way of modelling the reasoning of an agent with limited resources. In that framework, a family of logics, parameterised by a set of propositional letters, approximates classical logic as the size of the set increases. The original proposal ...

Data mining is defined as the process of extracting or mining knowledge from vast and large database. Data mining is an interdisciplinary field that brings together techniques from machine learning, pattern recognition, statistics, databases, and visualization to address the issue of information extraction from large databases. Bioinformatics is defined as the science of organizing and analyzin...

Multi-valued Model Checking extends classical, twovalued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued one...

Problems in logic are well-known to be hard to solve in the worst case. Twodi erent strategies for dealing with this aspect are known from the literature:language restriction and theory approximation.In this paper we are concerned with the second strategy. Our main goalis to de ne a semantically well-founded logic for approximate reasoning, whichis justi able from the in...