Fuzzy Relation Equations - New Solutions and Solvability Criteria
نویسندگان
چکیده
Systems of fuzzy relation equations are considered as models of fuzzy inference systems. A proper use of an inference mechanism connected to a fuzzy relation modelling a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations and introduces new solvability criteria.
منابع مشابه
Systems of Fuzzy Relation Equations: New Solvability Criteria Based on the Orthogonality Condition
Inference mechanisms and interpretations of fuzzy rule bases are studied together from the point of view of systems of fuzzy relation equations. A proper use of an inference mechanism connected to a fuzzy relation interpreting a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations which are motiva...
متن کاملSystem of fuzzy relation equations with inf → composition: solvability and solutions
In this paper I investigate the System of fuzzy relation equations with inf → composition. I compare this system with the system of fuzzy relation equations with sup − ∗-composition. The purpose of this contribution is to show that there are many things which are common for both systems with sup−∗ and inf →-composition operations. K e y w o r d s: System of fuzzy relation equations; sup − ∗-com...
متن کاملSystems of Fuzzy Relation Equations in a Space with Fuzzy Preorder
In this paper, we consider the problem of solving systems of fuzzy relation equations in a space with fuzzy preorder. Two types of these systems with different compositions are considered. New solvability criteria are proposed for systems of both types. The new criteria are weaker than all the known ones that are based on the assumption that fuzzy sets on the left-hand side of a system establis...
متن کاملFuzzy relation equations and approximate solutions. Some recent results
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 ...
متن کاملApproximate solutions of systems of fuzzy relation equations
In this paper, we eneralize our previous results regarding approximate solutions of fuzzy relation e uations [lo] to systems offuzzy relation equations. By employing the e uality index proposed by Gottwald 731, we introduce a goodness measure of the performance of approximate sAutions and derive a lower bound and an upper bound of solvability of s stems of fuzzy relation equations. We also show...
متن کامل