Arbitrary-term-absent max-product fuzzy relation inequalities and its lexicographic minimal solution

2021 ◽  
Vol 567 ◽  
pp. 167-184
Author(s):  
Jianjun Qiu ◽  
Guanrong Li ◽  
Xiaopeng Yang
Keyword(s):  
Minimal Solution ◽  
Fuzzy Relation ◽  
Arbitrary Term

scholarly journals A New Characterisation of the Minimal Solution Set to Max-min Fuzzy Relation Inequalities

2017 ◽  
Vol 9 (4) ◽  
pp. 423-435 ◽  
Author(s):  
Xiao-bin Yang ◽  
Xiao-peng Yang ◽  
Khizar Hayat
Keyword(s):  
Minimal Solution ◽  
Fuzzy Relation ◽  
Solution Set

scholarly journals An Algorithm for Finding a Minimal Solution to Fuzzy Relation Inequalities with Addition-Min Composition

2021 ◽  
Author(s):  
Xue-Ping Wang ◽  
Xiao Mi
Keyword(s):  
Minimal Solution ◽  
Fuzzy Relation ◽  
Necessary Condition ◽  
Numerical Examples ◽  
Sufficient And Necessary Condition

Abstract We first show a sufficient and necessary condition that a solution of fuzzy relation inequalities with addition-min composition is a minimal one. We then prove that for every solution of the fuzzy relation inequalities there exists a minimal solution that is less than or equal to the solution in a very different way. We finally give an algorithm to find a minimal solution for a given solution, which is illustrated by numerical examples.

Minimal solutions of fuzzy relation inequalities with addition-min composition1

2021 ◽  
pp. 1-7
Author(s):  
Xiao Mi ◽  
Xue-Ping Wang
Keyword(s):  
Computational Complexity ◽  
Minimal Solution ◽  
Fuzzy Relation

This paper investigates minimal solutions of fuzzy relation inequalities with addition-min composition. It first shows the conditions that an element is a minimal solution of the inequalities, and presents the conditions that the inequalities have a unique minimal solution. It then proves that every solution of the inequalities has a minimal one and proposes an algorithm to searching for a minimal solution with computational complexity O (n 2) where n is the number of unknown variables of the inequalities. This paper finally describes all minimal solutions of the inequalities.

Fuzzy relation equations theory as a basis of fuzzy modelling: An overview

1991 ◽  
Vol 40 (3) ◽  
pp. 415-429 ◽  
Author(s):  
A. Di Nola ◽  
W. Pedrycz ◽  
S. Sessa ◽  
E. Sanchez
Keyword(s):  
Fuzzy Relation ◽  
Fuzzy Modelling ◽  
Fuzzy Relation Equations
Sign in / Sign up

Export Citation Format

Share Document