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VAGUE RINGS AND VAGUE IDEALS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 12، دوره 8، شماره 1، اردیبهشت 2011، صفحه 145-157 اصل مقاله (189.18 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2011.258 | ||
| نویسنده | ||
Sevda Sezer 
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| Faculty of Education, Akdeniz University, 07058, Antalya, Turkey | ||
| چکیده | ||
| In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated. | ||
| کلیدواژه‌ها | ||
| Vague group؛ Generalized vague subgroup؛ Vague ring؛ Vague subring؛ Vague ideal؛ Vague prime ideal؛ Vague maximal ideal | ||
| مراجع | ||
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[1] M. Demirci, Fuzzy functions and their fundamental properties, Fuzzy Sets and Systems, 106 (1999), 239-246. [2] M. Demirci, Vague groups, J. Math. Anal. Appl., 230 (1999), 142-156. [3] M. Demirci, Fundamentals of M-vague algebra and M-vague arithmetic operations, Int. J. Uncertain. Fuzziness Knowl.-Based Syst., 10 (2002), 25-75. [4] M. Demirci, Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part I: fuzzy functions and their applications, Int. J.Gen. Syst., 32(2) (2003), 123-155. [5] M. Demirci, Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part II: vague algebraic notions, Int. J. Gen. Syst., 32(2) (2003), 157-175. [6] M. Demirci, Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part III: constructions of vague algebraic notions and vague arithmetic operations, Int. J. Gen. Syst., 32(2) (2003), 177-201. [7] M. Demirci and D. Coker, Remarks on vague groups, J. Fuzzy Math., 10 (2002), 657-668. [8] M. Demirci and J. Recasens, Fuzzy groups, fuzzy functions and fuzzy equvalence relation, Fuzzy Sets ans Systems, 144 (2004), 441-458. [9] P. Dheena and S. Coumaressane, Characterization of regular Γ-semigroups through fuzzy ideals, Iranian Journal of Fuzzy Systems, 4(2) (2007), 57-68. [10] Y. B. Jun and C. H. Park, Ideals of pseudo MV-algebras based on vague set theory, Iranian Journal of Fuzzy Systems, 6(2) (2009), 31-45. [11] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517. [12] S. Sezer, Vague subgroups, 15th Turkish National Mathematical Symposium Procedings- Mersin University/Turkey (in Turkish), (2004), 119-133 . [13] S. Sezer, Vague groups and generalized vague subgroups on the basis of ([0, 1],≤,∧), Information Sciences, 174 (2005), 123-142. [14] S. Sezer, Vague normal subgroups, J. Fuzzy Math., 16(3) (2008). | ||
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