Linear Searching Method for Solving Approximate Solution to System of Max-Min Fuzzy Relation Equations With Application in the Instructional Information Resources Allocation

Xiao, Gang; Tianxiang, Zhu; Chen, Yanhua; Yang, Xiaopeng

doi:10.1109/access.2019.2912217

Cited by 17 publications

(18 citation statements)

References 46 publications

(55 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different from the inconsistent system studied in [18], the above system (1) considered in this paper is assumed to be consistent. We investigate the interval solution of system (1) in this work.…”

Section: A Nmentioning

confidence: 99%

“…(i) In the existing works [18], [46], [47], the system of max-min fuzzy relation inequalities or equations was assumed to be inconsistent. Under this assumption, there was no solution for such a system.…”

Section: Comparison With the Existing Workmentioning

confidence: 99%

“…Recently, the max-min fuzzy relation system was applied to instructional information resource allocation [18], [46] (see Fig. 1.).…”

Section: Introductionmentioning

confidence: 99%

“…In [18], the authors investigated the approximate solution(s) of the max-min fuzzy relation equations system in cases where the system is inconsistent. In some existing works, the total deviations, i.e., the sum of all deviations with respect to each equation, were applied to characterize the approximate solution.…”

Section: Introductionmentioning

confidence: 99%

“…In some existing works, the total deviations, i.e., the sum of all deviations with respect to each equation, were applied to characterize the approximate solution. Instead of the total deviations, the authors defined the approximate solution based on the largest deviation [18]. They also proposed a linear searching algorithm for obtaining the approximate solution of the inconsistent system.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Interval Solution to Fuzzy Relation Inequality With Application in P2P Educational Information Resource Sharing Systems

2021

Self Cite

View full text Add to dashboard Cite

Max-min fuzzy relation inequalities have recently been introduced to describe the peerto-peer (P2P) network systems. It is well known that the complete solution set of the max-min fuzzy relation system is fully determined by its minimal solutions. However, solving all the minimal solutions has been proven to be equivalent to the set-covering problem, which is NP-hard. Without solving the complete solution set, some specific solutions can be obtained through the corresponding fuzzy relation optimization problems. However, these solutions are usually unstable and fragile. Any minor fluctuations to the components of these specific solutions will cause them to be no longer feasible. In this work, we define and study the widest interval solution of a max-min fuzzy relation inequality system for the first time. The interval solution allows the solution to fluctuate within some range. The fluctuation range is determined by the width of the interval solution. We propose a novel resolution method for searching for the widest interval solution. The resolution method is carried out by detailed procedures and illustrated by a numerical example.

show abstract

Section: A Nmentioning

confidence: 99%