Strong tolerance of interval eigenvectors in fuzzy algebra

Gavalec, Martin; Plávka, Ján; Ponce, Daniela

doi:10.1016/j.fss.2018.11.015

Cited by 8 publications

(8 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If there are more interval variables in the formula in consideration, then the quantifiers can be combined. For example, various types of quantified notions in max-min algebra are described in [23,24].…”

Section: Case Study: Interactive Cash-flow Systemmentioning

confidence: 99%

“…Therefore, question Q1 can be solved as one-sided bounded parametric problem studied in Sections 3 and 4. The main result is Theorem 6, which describes a necessary and sufficient condition for solvability of the system ( 9) and (10).…”

Section: Case Study: Interactive Cash-flow Systemmentioning

confidence: 99%

“…The max-T algebras with the above mentioned t-norms have various applications and their steady states and optimization methods have been intensively studied, see, for example, [3][4][5][6][7]. The algebras with interval entries have been studied in [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this paper is to present an algorithm for recognizing solvability of a given one-sided max-Łuk linear system with bounded variables, in dependence of a linear parameter factor on the right side, see ( 9) and (10) for an exact formulation. This problem has not yet been studied in the parametrized version.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra

Gavalec

Němcová

2020

Mathematics

Self Cite

View full text Add to dashboard Cite

The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. The aim of this study is to describe an algorithm recognizing for which values of the parameter the given bounded parametric max-linear system has a solution—represented by an appropriate state of the fuzzy system in consideration. Necessary and sufficient conditions of the solvability have been found and a polynomial recognition algorithm has been described. The correctness of the algorithm has been verified. The presented polynomial algorithm consists of three parts depending on the entries of the transition matrix and the required state vector. The results are illustrated by numerical examples. The presented results can be also applied in the study of the max-Łukasiewicz systems with interval coefficients. Furthermore, Łukasiewicz arithmetical conjunction can be used in various types of models, for example, in cash-flow system.

show abstract

Section: Case Study: Interactive Cash-flow Systemmentioning

confidence: 99%

Section: Case Study: Interactive Cash-flow Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra

Gavalec

Němcová

2020

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Example 1.2 (Security in a computer framework). This example was put forward as a motivation for studying strongly tolerant interval eigenvectors in max-min algebra [13]. A computer network consisting of servers S 1 , .…”

Section: Introductionmentioning

confidence: 99%

(K,L)-eigenvectors in max-min algebra

Gavalec

Němcová

Sergeev

2021

Fuzzy Sets and Systems

View full text Add to dashboard Cite

Link to publication on Research at Birmingham portal General rightsUnless a licence is specified above, all rights (including copyright and moral rights) in this document are retained by the authors and/or the copyright holders. The express permission of the copyright holder must be obtained for any use of this material other than for purposes permitted by law.• Users may freely distribute the URL that is used to identify this publication.• Users may download and/or print one copy of the publication from the University of Birmingham research portal for the purpose of private study or non-commercial research.• User may use extracts from the document in line with the concept of 'fair dealing' under the Copyright, Designs and Patents Act 1988 (?) • Users may not further distribute the material nor use it for the purposes of commercial gain.Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document.When citing, please reference the published version. Take down policyWhile the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.

show abstract

Bases and dimension of interval vector space

Zhu

2021

Comp. Appl. Math.

View full text Add to dashboard Cite

Strong tolerance of interval eigenvectors in fuzzy algebra

Cited by 8 publications

References 8 publications

Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra

Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra

(K,L)-eigenvectors in max-min algebra

Bases and dimension of interval vector space

Contact Info

Product

Resources

About