Semirings in operations research and computer science: More algebra

Fundamenta Informaticae

Volumn 61, Issue 1, 2004, Pages 61-85

  Rudeanu, Sergiu ^a   Vaida, Dragoş ^a  

^a UNIVERSITY OF BUCHAREST   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTER SCIENCE; COMPUTER SIMULATION; GRAPH THEORY; MEMBERSHIP FUNCTIONS; SEMANTICS; SET THEORY;

COMPLETE EXISTENTIAL THEORY; FUZZY MODELING; OPTIMAL PATH PROBLEM; PARTIAL ADDITIVE SEMANTICS; PROCESS ALGEBRA; SEMIRING;

OPERATIONS RESEARCH;

EID: 3142661965     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. J.C.M. Baeten, W.P.Weijland: [1990] Process Algebra, Cambridge Tracts in Theoretical Computer Science, Cambridge Univ. Press, Cambridge.
2. M. Benado: [1955] Les ensembles partiellement ordonnés et le théorème de raffinement de Schreier, Czechoslovak Math. J. 5(80,3), 308-344.
3. C. Benzaken: [1968] Contribution des structures algébriques ordonnées à la théorie des réseaux, Thèse, Univ. Grenoble.
4. J.H. Bevis: [1974] Free gerbiers and nets, Math. Systems Theory 8,127-131.
5. G. Birkhoff: [1967] Lattice Theory, Third ed. Third printing, 1979. Amer. Math. Soc., Providence, RI.
6. D. Butnariu, E.P. Klement: [1993] Triangular Norm-Based Measures and Games with Fuzzy Coalitions, Series C: Game Theory, Math. Programming and Operations Res. vol. 10, Kluwer Acad. Publ., Dordrecht.
7. Z.-Cao, K.H. Kim, F.W. Roush: [1984] Incline Algebra and Applications, Ellis Horwood Ltd, Chichester, &J. Wiley, New York.
8. B.A. Carré: [1971] An algebra for network routing problems, J. Inst. Math. Appl., 7, 273-294.
9. R. Cruon, Ph. Hervé: [1965] Quelques résultats relatifs à une structure algébrique et à son application au problème central de l'ordonnancement, Rev. Française Rech. Opér. 34, 3-19.
10. R. Cuninghame-Green: [1979] Minimax Algebra, Lecture Notes Econ. Math. Systems no. 166, Springer-Verlag, Berlin.
11. R. Dedekind: [1894] Über die Theorie der ganzen algebraischen Zahlen, Supplement XI to P.G. Lejeune Dirichlet, Vorlesungen über Zahlentheorie, 4te Aufl., Druck und Verlag, Braunschweig.
12. J.S. Golan: [1992] The Theory of Semirings with Aplications in Mathematics and Theoretical Computer Science, Pitman Monographs and Surveys Pure Appl. Math. vol. 54. Longman Sci. &Techn.
13. M. Gondran: [1975] Algèbre linéaire et cheminement dans un graphe, Rev. Française Autom. Informat. Rech. Opér. Sér. Verte 9, 77-99.
14. H. Hashimoto: [1983] Transitivity of matrices over a path algebra, Preprint, Yamaguchi Univ., Yamaguchi.
15. U. Hebisch, H.J. Weinert: [1999] Semirings - Algebraic Theory and Applications in Computer Science, Ser. Alg., vol. 5. World Sci., Singapore.
16. G.J. Klir, B. Yuan: [1995] Fuzzy Sets and Fuzzy Logic, Prentice Hall, New Jersey.
17. E.G. Manes, M.A. Arbib: [1986] Algebraic Approach to Program Semantics, Springer-Verlag, Berlin.
18. M. Minoux: [1976] Structures algébriques généralisées des problèmes de che-minement dans les graphes: théorèmes, algorithmes et applications, Rev. Fran- çaise Informat. Rech. Opér. (RAIRO) Rech. Opér. 10, 33-62.
19. Gr.C. Moisil: [1960] Asupra unor reprezentari aie grafurilor ce intervin in probleme de economia transporturilor, Com. Acad. R.P.Române 10, 647-652.
20. E.H. Moore: [1910] Introduction to a Form of General Analysis, New Haven Colloq., 1906. New Haven.
21. L. Nolin: [1964] Traitement des données groupées, Inst. Blaise Pascal, Paris.
22. V. Peteanu: [1967]: An algebra of optimal paths in networks, Mathematica (Cluj) 9(32), 335-342.
23. _: [1969] Optimal paths in networks and generalizations, I. Mathematica (Cluj) 11(34), 311-327. ibid. 12(35) (1970), 159-187.
24. _: [1969] Optimal paths in networks and generalizations, I. Mathematica (Cluj) 11(34), 311-327. ibid. 12(35) (1970), 159-187.
25. G.N. Povarov: [1960] Qualitative analysis of electrical circuits with finite conductibilities by means of the theory of cumulative nets (Russian), Doklady Akad. Nauk SSSR 136, no.2.
26. _: [1962] The theory of numeroids in the algebra of automata (Russian), Problemy peredachi informacii no. 11, Izd-vo Akad. Nauk SSSR, Moskva.
27. P. Robert, J. Ferland: [1968]. Généralisation de l'algorithme de Warshall, Rev. Française Informat. Rech. Opér. (RIRO) 2, 71-85.
28. B. Roy: [1959] Transitiviteé et connexité, C.R. Acad. Sci. Paris 249, 216-218.
29. S. Rudeanu: [1963] Axiomele laticilor şi ale algebrelor booleene, Ed. Acade-miei R.P.Române, Bucharest.
30. M. Sholander : [1951] Postulates for distributive lattices, Canad. J. Math. 3, 28-30.
31. F.A. Smith: [1966] A structure theory for a class of lattice-ordered semi-rings, Fund. Math. 59, 49-64.
32. M.E. Steenstrup: [1985] Sum-ordered partial semirings, PhD Thesis, Univ. Massachusetts, Boston, February 1985.
33. I. Tomescu: [1966] Sur les méthodes matricielles dans la théorie des réseaux, C.R. Acad. Sci. Paris 263, 826-829.
34. _: [1967] Asupra unor metode matriciale care intervin in teoria reţelelor, Stud. Cerc. Mat. 19, 105-118.
35. _: [1968] Sur l'algorithme matriciel de B. Roy, Rev. Française Informat. Rech. Opér. (RIRO) 2, 87-91.
36. _: [1972] Structuri algebrice ordonate in teoria grafurilor, Stud. Cerc. Mat. 24, 469-476.
37. _: [2001] A cascade version of Dantzig's inductive algorithm for matrices over semilatticeordered semigroups, Multiple Val. Logic 6, 217-228.
38. D. Vaida: [2001] On partially additive semirings and applications, Mult.-Val. Logic 6, 251-266.
39. H.S. Vandiver: [1939] On some simple types of semi-rings, Amer. Math. Monthly 46, 22-26.
40. H.S. Vandiver, M.H. Weaver: [1956] A development of associative algebra and an algebraic theory of numbers, IV. Math. Mag. 30, 1-8.
41. S. Warshall: [1962] A theorem on Boolean matrices, J. Assoc. Comput. Mach. 9, 11-12.
42. M. Yoeli: [1961] Note on a generalization of Boolean matrix theory, Amer. Math. Monthly 68, 552-557.
43. L.A. Zadeh: [1965] Fuzzy sets, Information and Control 8, 338-353.
44. H.J. Zassenahus: [1958] The Theory of Groups (2nd ed), Chelsea, New York.
45. U. Zimmerman: [1981] Linear and Combinatorial Optimization in Ordered Algebraic Structures, North-Holland, Amsterdam.