Complete solution sets of inf-→ interval-valued fuzzy relation equations

2013 ◽  
Vol 219 ◽  
pp. 111-123 ◽  
Author(s):  
De-chao Li ◽  
Yong-jian Xie ◽  
Sheng-ling Geng
Keyword(s):  
Complete Solution ◽  
Fuzzy Relation ◽  
Solution Sets ◽  
Fuzzy Relation Equations ◽  
Interval Valued

scholarly journals Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Xiaobin Yang ◽  
Haitao Lin ◽  
Gang Xiao ◽  
Huanbin Xue ◽  
Xiaopeng Yang
Keyword(s):  
Complete Solution ◽  
Order Relation ◽  
Fuzzy Relation ◽  
Solution Set ◽  
Network System ◽  
Resolution Method ◽  
Index Set ◽  
Fuzzy Relation Equation ◽  
Fuzzy Relation Equations ◽  
Interval Valued

Considering the application background on P2P network system, we investigate the max-product fuzzy relation equation with interval-valued parameter in this paper. Order relation on the set of all interval-valued numbers plays key role in the construction and resolution of the interval-valued-parameter fuzzy relation equation (IPFRE). The basic operations supremum (a∨b) and infimum (a∧b) in the IPFRE should be defined depending on the order relation. A novel total order is introduced for establishing the IPFRE. We also discuss some properties of the IPFRE system, including the consistency and structure of the complete solution set. Concepts of close index set and open index set are defined, helping us to construct the resolution method of the IPFRE system. We further provide a detailed algorithm for obtaining the complete solution set. Besides, the solution set is compared to that of the classical max-T fuzzy relation equations system.

Solving interval-valued fuzzy relation equations

1998 ◽  
Vol 6 (2) ◽  
pp. 321-324 ◽  
Author(s):  
Guangzhi Li ◽  
Shu-Cherng Fang
Keyword(s):  
Fuzzy Relation ◽  
Fuzzy Relation Equations ◽  
Interval Valued

Covering Problem for Solutions of Max-Archimedean Bipolar Fuzzy Relation Equations

2020 ◽  
Vol 28 (04) ◽  
pp. 613-634
Author(s):  
Vijay Lakshmi Tiwari ◽  
Antika Thapar
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Complete Solution ◽  
Fuzzy Relation ◽  
Solution Set ◽  
Covering Problem ◽  
Integer Programming Problem ◽  
Fuzzy Relation Equations ◽  
Reduction Methods

This paper discusses the resolution of max-Archimedean bipolar fuzzy relation equations. In the literature, many methods have been proposed based on 0-1 integer programming problem or reduction methods for the optimization with bipolar fuzzy relation equations. A new concept based on the idea of covering and the notions of leading, non-leading variables are introduced in the present paper for finding the solutions of max-Archimedean bipolar fuzzy relation equations. It is shown that the problem of finding the complete solution set of the system of max-Archimedean bipolar fuzzy relation equations is equivalent to solving a covering problem and the solutions of such equations correspond to irredundant coverings of the covering problem. The proposed method is illustrated with some examples.

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