Abstract
Based on the equivalence relation on a linear space, in this paper we introduce the definition of rough convex cones and rough convex fuzzy cones and discuss some of the fundamental properties of such rough convex cones.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bhakat SK (1997) (∈ ∨ q)-level subset. Fuzzy Sets Syst 103:529–533
Biswas R (1994) On rough fuzzy sets. Bull Pol Acad Sci Math 42:351–355
Biswas R, Nanda S (1994) Rough groups and rough subgroup. Bull Pol Acad Sci Math 42:251–254
Bonikowaski Z (1995) Algebraic structures of rough sets. In: Ziarko WP (ed) Rough sets, fuzzy sets and knowledge discovery. Springer, Berlin, pp 242–247
Davvaz B (2004) Roughness in ring. Inf Sci 164:147–163
Davvaz B, Mahdavipour M (2006) Roughness in modules. Inf Sci 176:3658–3674
Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J General Syst 17(2–3):191–209
He XG (1999) Fuzzy theories and fuzzy techniques. In: knowledge processing, 2nd edn. (in Chinese). The department of defense press, beijing
Iwinski T (1987) Algebraic approach to rough sets. Bull Pol Acad Sci Math 35:673–683
Jarvinen J (2002) On the structure of rough approximations. Fundam Inform 53:135–153
Kuroki N (1997) Rough ideals in semigroups. Inf Sci 100(1–4):139–163
Kuroki N, Wang PP (1996) The lower and upper approximations in a fuzzy group. Inf Sci 90:203–220
Liu WJ, Hou HJ (2006) Lower and upper Approximatics of Linear Space. J Guangxi Normal Univ (Nat Sci) 24(4):14–17
Mi JS, Zhang WX (2004) An axiomatic characterization of a fuzzy generation of rough sets. Inf Sci 160(1–4):235–249
Mordeson J (2001) Rough set theory applied to (fuzzy) ideal theory. Fuzzy Sets Syst 121:315–324
Morsi NN, Yakout MM (1998) Axiomatics for fuzzy rough sets. Fuzzy Sets Syst 100(1–3):327–342
Nanda S (1992) Fuzzy rough sets. Fuzzy Sets Syst 45:157–160
Pawlak Z (1985) Fuzzy sets and rough sets. Fuzzy Sets Syst 17:99–102
Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341–356
Pawlak Z, Skowron A (2007) Rough sets and boolean reasoning. Inf Sci 117:41–73
Pawlak Z, Skowron A (2007) Rough sets: some extensions. Inf Sci 117:28–40
Pawlak Z, Skowron A (2007) Rudiments of rough sets. Inf Sci 117:3–27
Pomykala J, Pomykala JA (1988) The stone algebra of rough sets. Bull Pol Acad Sci Math 36:495–508
Quafafou M (2000) α-RST: a generalization of rough set theory. Inf Sci 124:301–316
Radzikowska AM, Kerre EE (2002) A comparative study of fuzzy rough sets. Fuzzy Sets Syst 126(2):137–155
Wu WZ, Zhang WX (2002) Neighborhood operator systems and approximations. Inf Sci 144:201–217
Yao YY (1998) A comparative study of fuzzy sets and rough sets. Inf Sci 109:227–242
Yao YY, Lingras PJ (1998) Interpretations of belief functions in the theory of rough sets. Inf Sci 104:81–106
Yao YY (1998) Relational interpretations of neighborhood operations and rough set approximation operator. Inf Sci 111:239–259
Zadeh LA (1965) Fuzzy Sets. Inf Control 8:338–353
Acknowledgments
This work is supported by Program for Innovative Research Team of Jiangnan University (No:200902). Thanks for the reviewers giving me so many important suggestions which improves the quality of the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liao, Z., Zhou, J. Rough convex cones and rough convex fuzzy cones. Soft Comput 16, 2083–2087 (2012). https://doi.org/10.1007/s00500-012-0877-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-012-0877-6