For theoretical fuzzy control it is a well known strategy to transform a system of control rules into a system of relation equations. Because these systems of relation equations are not always solvable, solvability criteria and approximate solutions have been discussed. We reconsider some of the results in this field and extend them using more recent results on t-norm based fuzzy logics and on ...

this paper studies a new multi-objective fuzzy optimization prob- lem. the objective function of this study has dierent levels. therefore, a suitable optimized solution for this problem would be an optimized solution with preemptive priority. since, the feasible domain is non-convex; the tra- ditional methods cannot be applied. we study this problem and determine some special structures related...

The aim of this paper is to show that the normalizing rank aggregation method can not only be used to derive the priority vector for a multiplicative preference relation, but also for the additive transitive fuzzy preference relation. To do so, a simple functional equation between fuzzy preference’s element and priority weight is derived firstly, then, based on the equation, three methods are p...

The focus of this paper is to clarify the concepts of solutions of linear equations in interval, probabilistic, and fuzzy sets setting for real world tasks. There is a fundamental difference between formal definitions of the solutions and physically meaningful concepts of solution in applied tasks, when equations have uncertain components. For instance, a formal definition of the solution in te...

In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–Găvruţa. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces ...

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 a recent paper, de baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. in this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. the reasoninglargely ...

This paper aims to solve the problem of multiple-objective linear optimization model subject to a system of inf-! composition fuzzy relation equations, where ! is R-, Sor QL-implications generated by continuous Archimedean t-norm (s-norm). Since the feasible domain of inf-! relation equations constraint is nonconvex, these traditional mathematical programming techniques may have difficulty in c...

in this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $h(cdot,cdot)$-$phi$-$eta$-accretive operator in real  uniformly smooth banach spaces. it is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. this equivalence is used to define an iterative algorithm for solving fu...