Inverse Inference Based on Fuzzy Relational Equations

2012 ◽  
pp. 149-162
Author(s):  
Alexander P. Rotshtein ◽  
Hanna B. Rakytyanska
Keyword(s):  
Fuzzy Relational Equations

A PRIMER ON SOLVING FUZZY RELATIONAL EQUATIONS ON THE UNIT INTERVAL

1994 ◽  
Vol 02 (02) ◽  
pp. 205-225 ◽  
Author(s):  
BERNARD DE BAETS ◽  
ETIENNE E. KERRE
Keyword(s):  
Unit Interval ◽  
Triangular Norm ◽  
Fuzzy Relational Equations ◽  
Number Of Publications

This paper has to be considered as a guide to solving fuzzy relational equations on the unit interval. Although the number of publications on this topic is quite impressive, there doesn't seem to exist a handy structured overview of all types of equations and their solution procedures. Our overview starts with a thorough treatment of [Formula: see text] equations and systems of [Formula: see text] equations, with [Formula: see text] a continuous triangular norm. It is shown that these are the basic problems: all other equations, image and composition equations, can be reduced to these problems. We do not only structure well-known results, we also present some new insights in the solution procedures of fuzzy relational equations.

A NEW KIND OF FUZZY RELATIONAL EQUATIONS

2010 ◽  
Vol 18 (03) ◽  
pp. 333-342 ◽  
Author(s):  
FENG QIN ◽  
PING FANG
Keyword(s):  
Unique Solvability ◽  
Complete Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Solution Set ◽  
Fuzzy Relational Equations ◽  
Necessary And Sufficient

In this paper, a new kind of fuzzy relational equations (FREs for short) A ∘R*x = b is first introduced, and then the problem of solving solution to the FREs is discussed, where A is an m × n matrix, x and b are an n and an m dimensional column vectors, respectively. More specifically, their solvability and unique solvability are investigated, the corresponding necessary and sufficient conditions are presented, the complete solution set is obtained. It is worth noting the method to construct the complete solution set.

Sign in / Sign up

Export Citation Format

Share Document