×

Soft semirings. (English) Zbl 1165.16307

Summary: Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft semirings by using the soft set theory. The notions of soft semirings, soft subsemirings, soft ideals, idealistic soft semirings and soft semiring homomorphisms are introduced, and several related properties are investigated.

MSC:

16Y60 Semirings
03E72 Theory of fuzzy sets, etc.
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338-353, (1965) · Zbl 0139.24606
[2] Zadeh, L.A., Toward a generalized theory of uncertainty (GTU)—an outline, Inform. sci., 172, 1-40, (2005) · Zbl 1074.94021
[3] Pawlak, Z., Rough sets, Int. J. inform. comput. sci., 11, 341-356, (1982) · Zbl 0501.68053
[4] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Inform. sci., 177, 3-27, (2007) · Zbl 1142.68549
[5] Gau, W.L.; Buehrer, D.J., Vague sets, IEEE trans. syst. man cybern., 23, 2, 610-614, (1993) · Zbl 0782.04008
[6] Gorzalzany, M.B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy sets and systems, 21, 1-17, (1987)
[7] Molodtsov, D., Soft set theory—first results, Comput. math. appl., 37, 19-31, (1999) · Zbl 0936.03049
[8] Maji, P.K.; Roy, A.R.; Biswas, R., An application of soft sets in a decision making problem, Comput. math. appl., 44, 1077-1083, (2002) · Zbl 1044.90042
[9] Chen, D.; Tsang, E.C.C.; Yeung, D.S.; Wang, X., The parametrization reduction of soft sets and its applications, Comput. math. appl., 49, 757-763, (2005) · Zbl 1074.03510
[10] Maji, P.K.; Biswas, R.; Roy, A.R., Soft set theory, Comput. math. appl., 45, 555-562, (2003) · Zbl 1032.03525
[11] Aktaş, H.; Çağman, N., Soft sets and soft groups, Inform. sci., 177, 2726-2735, (2007) · Zbl 1119.03050
[12] Jun, Y.B., Soft BCK/BCI-algebras, Comput. math. appl., 56, 1408-1413, (2008) · Zbl 1155.06301
[13] Jun, Y.B.; Park, C.H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. sci., 178, 2466-2475, (2008) · Zbl 1184.06014
[14] Glazek, K., A guide to the literature on semirings and their applications in mathematics and information sciences, (2002), Kluwer Dordrecht · Zbl 1072.16040
[15] Golan, J.S., Semirings and affine equations over them: theory and applications, (2003), Kluwer Dordrecht · Zbl 1042.16038
[16] Henriksen, M., Ideals in semirings with commutative addition, Amer. math. soc. notices, 6, 321, (1958)
[17] Iizuka, K., On the Jacobson radical of a semiring, Tohoku math. J., 11, 2, 409-421, (1959) · Zbl 0122.25504
[18] Ahsan, J.; Saifullah, K.; Farid Khan, M., Fuzzy semirings, Fuzzy sets and systems, 60, 309-320, (1993) · Zbl 0796.16038
[19] Baik, S.I.; Kim, H.S., On fuzzy \(k\)-ideals in semirings, Kangweon-kyungki math. J., 8, 147-154, (2000)
[20] Dutta, T.K.; Biswas, B.K., Fuzzy prime ideals of a semiring, Bull. malays. math. soc., 17, 9-16, (1994) · Zbl 0848.16038
[21] Dutta, T.K.; Biswas, B.K., Fuzzy \(k\)-ideals of semirings, Bull. Calcutta. math. soc., 87, 91-96, (1995) · Zbl 0834.16048
[22] Dutta, T.K.; Biswas, B.K., Fuzzy congruence and quotient semiring of a semiring, J. fuzzy math., 4, 737-748, (1996) · Zbl 0871.16023
[23] Ghosh, S., Fuzzy \(k\)-ideals of semirings, Fuzzy sets and systems, 95, 103-108, (1998) · Zbl 0924.16036
[24] Jun, Y.B.; Öztürk, M.A.; Song, S.Z., On fuzzy \(h\)-ideals in hemirings, Inform. sci., 162, 211-226, (2004) · Zbl 1064.16051
[25] Jun, Y.B.; Neggers, J.; Kim, H.S., Normal \(L\)-fuzzy ideals in semirings, Fuzzy sets and systems, 82, 383-386, (1996) · Zbl 0878.16023
[26] Jun, Y.B.; Neggers, J.; Kim, H.S., On \(L\)-fuzzy ideals in semirings I, Czechoslovak math. J., 48, 123, 669-675, (1998) · Zbl 0954.16032
[27] Kim, C.B., Isomorphism theorems and fuzzy \(k\)-ideals of \(k\)-semirings, Fuzzy sets and systems, 112, 333-342, (2000) · Zbl 0948.16037
[28] Neggers, J.; Jun, Y.B.; Kim, H.S., Extensions of \(L\)-fuzzy ideals in semirings, Kyungpook math. J., 38, 131-135, (1998) · Zbl 0916.16025
[29] Neggers, J.; Jun, Y.B.; Kim, H.S., On \(L\)-fuzzy ideals in semirings II, Czechoslovak math. J., 49, 124, 127-133, (1999) · Zbl 0954.16033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.