New types of systems of fuzzy relation inequalities and equations, called weakly linear, have been recently introduced in [J. Ignjatović, M. Ćirić, S. Bogdanović, On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081–3113.]. The mentioned paper dealt with homogeneous weakly linear systems, composed of fuzzy relati...

In this paper, line search based on Sequential Quadratic Programming is implemented in order to find a solution to Fuzzy Relation Equations. Sequential Quadratic Programming is a gradient-based method that uses a quadratic estimation of the objective function in each iteration’s neighborhood. Unlike analytical approaches, the method can handle equations with any combinations of t-norms and t-co...

In some previous works the authors showed the advantages in coding and decoding images in the YUV space by using fuzzy relation equations. Indeed the images in the Y band were less compressed than in the U, V bands and a better Peak Signal to Noise Ratio was obtained with respect to that deduced by coding and decoding the same images in the RGB space. In another foregoing paper we used the fuzz...

An important goal in the fuzzy relation equations framework is to obtain the whole set of solutions. This paper introduces algebraic properties in the multi-adjoint concept lattice setting. Moreover, using the relationship between these concept lattices and multi-adjoint relation equations, the complete set of solutions of these general equations is characterized and computed, avoiding the nece...

We show that the size reduction problem for fuzzy automata is related to the problem of solving a particular system of fuzzy relation equations. This system consists of infinitely many equations, and finding its general solution is a very difficult task, so we first consider one of its special cases, a finite system whose solutions, called right invariant fuzzy equivalences, are common generali...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

Current computer security systems are based on the premise that once a user presents valid credentials to the authentication system (e.g. valid ID and password), they are granted access permission to all resources assigned to the user that they claim to be. However, numerous studies have shown that most security breaches are done by unauthorized users impersonating as authorized users (e.g. by ...

Fuzzy relation-based models for handling uncertainty (in a non-probabilistic way) in diagnosis problems have been introduced by Sanchez about twenty years ago, and since then applied and developed by several researchers. The paper first reviews the existing proposals, also including the association-based abductive model proposed by Reggia and his co-workers, which uses non-fuzzy relations. A ne...