Name
Abstract | ||
|---|---|---|
Besides the classical algebraic structures of groups, rings and fields which have long been the almost exclusive reference concepts used in mathematical modelling, other algebraic structures such as dioids and semirings have emerged in the last two or three decades in connection with modelling and solving a rich variety of non-classical problems, e.g. in Decision Analysis, Fuzzy Set Theory, Operations Research, Automatic Control and Mathematical Physics. The present paper aims at providing an overview of applications of dioid and semiring structures, stressing links with Fuzzy Sets and emphasizing linear algebraic problems (solving linear systems, computing eigenvalues and eigenvectors), non-classical path-finding problems (using algebras of endomorphisms) and connections between dioid structure and nonlinear analysis (in view of solving problems in Mathematical Physics). |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.fss.2007.01.016 | Fuzzy Sets and Systems |
Keywords | Field | DocType |
dioid structure,fuzzy sets,fuzzy set,non-classical path-finding problem,mathematical physics,linear system,mathematical modelling,algebraic structure,classical algebraic structure,fuzzy set theory,linear algebraic problem,automatic control,linear algebra,path finding,eigenvalues and eigenvectors,group ring,operations research,decision analysis | Set theory,Discrete mathematics,Algebraic number,Algebra,Linear system,Algebraic structure,Fuzzy set,Decision theory,Fuzzy control system,Calculus,Mathematics,Semiring | Journal |
Volume | Issue | ISSN |
158 | 12 | Fuzzy Sets and Systems |
Citations | PageRank | References |
19 | 1.18 | 18 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. Gondran | 1 | 32 | 4.26 |
| Michel Minoux | 2 | 741 | 100.18 |