Systems of Fuzzy Relation Equations: New Solvability Criteria Based on the Orthogonality Condition
نویسندگان
چکیده
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 motivated by several fuzzy approximation methods. The study of this new solutions yields new solvability criteria which are introduced.
منابع مشابه
Fuzzy Relation Equations - New Solutions and Solvability Criteria
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.
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 کاملSystem of Fuzzy Relation equations: Criteria of solvability
In this paper, we observe and compare results concerning solvability of systems of fuzzy relation equations with different types of composition. In fact, two types of composition are considered sup−∗ and inf → composition where ∗ is a continuous tnorm and→ is residuation operation with respect to the t-norm ∗.
متن کاملNew concepts on the fuzzy linear systems and an application
As we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. For this reason, many researchers have used various numerical methods to solve fuzzy linear systems. In this paper, we define the concepts of midpoint a...
متن کاملON A LOSSY IMAGE COMPRESSION/RECONSTRUCTION METHOD BASED ON FUZZY RELATIONAL EQUATIONS
The pioneer work of image compression/reconstruction based onfuzzy relational equations (ICF) and the related works are introduced. TheICF regards an original image as a fuzzy relation by embedding the brightnesslevel into [0,1]. The compression/reconstruction of ICF correspond to thecomposition/solving inverse problem formulated on fuzzy relational equations.Optimizations of ICF can be consequ...
متن کامل