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Soft Computing

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07.11.2018 | Foundations

On characterization of \((\mathcal {I},{\mathcal {N}})\)-single valued neutrosophic rough approximation operators

verfasst von: Yan-Ling Bao, Hai-Long Yang, Sheng-Gang Li

Erschienen in: Soft Computing | Ausgabe 15/2019

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Abstract

This paper presents a general framework for the study of \(({\mathcal {I}}, {\mathcal {N}})\)-single valued neutrosophic rough sets from constructive and axiomatic perspectives. In the constructive approach, a pair of single valued neutrosophic rough approximation operators based on single valued neutrosophic implicator \({\mathcal {I}}\) and single valued neutrosophic norm \({\mathcal {N}}\) is first proposed. Moreover, some basic properties of \(({\mathcal {I}},{\mathcal {N}})\)-single valued neutrosophic rough approximation operators are explored. In addition, connections between single valued neutrosophic relations and \((\mathcal {I},{\mathcal {N}})\)-single valued neutrosophic rough approximation operators are systematically discussed. In the axiomatic approach, axiomatic characterization of \(({\mathcal {I}},{\mathcal {N}})\)-single valued neutrosophic approximation operators is studied. Specifically, different axiom sets characterizing the intrinsic properties of \((\mathcal {I},{\mathcal {N}})\)-single valued neutrosophic rough approximation operators associated with diverse single valued neutrosophic relations are investigated in detail.

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Alkhazaleh S (2015) More on neutrosophic norms and conorms. Neutrosophic Sets Syst 9:23–30

Broumi S, Smarandache F (2015) Interval neutrosophic rough set. Neutrosophic Sets Syst 7:23–31

Broumi S, Smarandache F, Dhar M (2010) Rough neutrosophic sets. Ital J Pure Appl Math 32(32):493–502MathSciNetMATH

Bao YL, Yang HL (2017) On single valued neutrosophic refined rough set model and its application. J Intell Fuzzy Syst 33:1235–1248CrossRefMATH

Bao YL, Yang HL, She YH (2018) Using one axiom to characterize L-fuzzy rough approximation operators based on residuated lattices. Fuzzy Sets Syst 336:87–115MathSciNetCrossRefMATH

Cornelis C, Cock MD, Kerre EE (2003) Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert Syst 20(5):260–270CrossRef

Cornelis C, Deschrijver G (2001) The compositional rule of inference in an intuitionistic fuzzy logic setting. In: Striegnitz K (ed) Proceedings ESSLLI 2001 student session, p 83–94

Cornelis C, Deschrijver G, Kerre EE (2004) Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. Int J Approx Reason 35(1):55–95MathSciNetCrossRefMATH

Deschrijver G, Cornelis C, Kerre EE (2004) On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Trans Fuzzy Syst 12(1):45–61CrossRefMATH

Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17(2–3):191–209CrossRefMATH

Guo YH, Cheng HD (2009) New neutrosophic approach to image segmentation. Pattern Recognit 42(5):587–595CrossRefMATH

Guo YH, Sengur A (2015) NCM: neutrosophic c-means clustering algorithm. Pattern Recognit 48(8):2710–2724CrossRef

Li LQ, Jin Q, Hu K, Zhao FF (2017) The axiomatic characterizations on \(L\)-fuzzy covering-based approximation operators. Int J Gen Syst 46(2):1–22MathSciNet

Li TJ, Yang XP (2014) An axiomatic characterization of probabilistic rough sets. Int J Gen Syst Approx Reason 55(1):130–141MathSciNetCrossRefMATH

Liu PD, Wang YM (2016) Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making. J Syst Sci Complex 29(3):681–697CrossRefMATH

Liu GL (2013) Using one axiom to characterize rough set and fuzzy rough set approximations. Inf Sci 223:285–296MathSciNetCrossRefMATH

Ma X, Zhan J, Ali MI, Mehmood N (2018) A survey of decision making methods based on two classes of hybrid soft set models. Artif Intell Rev 49(4):511–529CrossRef

Mi JS, Zhang WX (2004) An axiomatic characterization of a fuzzy generalization of rough sets. Inf Sci 160(1–4):235–249MathSciNetCrossRefMATH

Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341–356CrossRefMATH

Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, BostonCrossRefMATH

Peng JJ, Wang JQ, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput 25:336–346CrossRef

Rivieccio U (2008) Neutrosophic logics: prospects and problems. Fuzzy Sets Syst 159(14):1860–1868MathSciNetCrossRefMATH

Salama AA, Broumi S (2014) Roughness of neutrosophic sets. Elixir Appl Math 74:26833–26837

Smarandache F (1998) Neutrosophy: neutrosophic probability, set, and logic. American Research Press, RehobothMATH

Smarandache F (1999) A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press, RehobothMATH

Smarandache F (2013) \(n\)-valued refined neutrosophic logic and its applications in physics. Prog Phys 4:143–146

Smarandache F (2010) N-norm and N-conorm in neutrosophic logic and set, and the neutrosophic topologies. Multispace Multistructrue 4:436–446

Smarandache F (2015) Symbolic neutrosophic logic. Europa Nova, Bruxelles

Smets P, Magrez P (1987) Implication in fuzzy logic. Int J Approx Reason 1(4):327–347MathSciNetCrossRefMATH

Wang HB, Smarandache F, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413MATH

Wang CY (2018) Single axioms for lower fuzzy rough approximation operators determined by fuzzy implications. Fuzzy Sets Syst 336:116–147MathSciNetCrossRefMATH

Wu WZ, Leung Y, Shao MW (2013) Generalized fuzzy rough approximation operators determined by fuzzy implicators. Int J Approx Reason 54(9):1388–1409MathSciNetCrossRefMATH

Wu WZ, Li TJ, Gu SM (2015) Using one axiom to characterize fuzzy rough approximation operators determined by a fuzzy implication operator. Fundam Inf 142:87–104MathSciNetCrossRefMATH

Wu WZ, Xu YH, Shao MW, Wang GY (2016) Axiomatic characterizations of \((S, T)\)-fuzzy rough approximation operators. Inf Sci 334:17–43MATH

Yang HL, Guo ZL, She YH, Liao XW (2014) On single valued neutrosophic relations. J Intell Fuzzy Syst 30(2):1045–1056CrossRefMATH

Yang HL, Zhang CL, Guo ZL, Liu YL, Liao XW (2017) A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model. Soft Comput 21:6253–6267CrossRefMATH

Yang HL, Bao YL (2018) Generalized interval neutrosophic rough sets and its application in multi-attribute decision making. Filomat 32(1):11–33CrossRef

Yao YY (1998) Constructive and algebraic methods of the theory of rough sets. Inf Sci 109(1–4):21–47MathSciNetCrossRefMATH

Yao YY (1998) On generalizing Pawlak approximation operators, In: International conference on rough sets and current trends in computing, Springer, Berlin, pp 298–307

Ye J (2014) A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26(5):2459–2466MathSciNetMATH

Ye J (2014) Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl Math Modell 38(3):1170–1175MathSciNetCrossRefMATH

Zhang ZM (2010) An interval-valued rough intuitionistic fuzzy set model. Int J Gen Syst 39(2):135–164MathSciNetCrossRefMATH

Zhan J, Xu W (2018) Two types of coverings based multigranulation rough fuzzy sets and applications to decision making. Artif Intell Rev. https://doi.org/10.1007/s10462-018-9649-8

Zhan J, Wang Q (2018) Certain types of soft coverings based rough sets with applications. Int J Mach Learn Cybern https://doi.org/10.1007/s13042-018-0785-x

Zhang L, Zhan J, Alcantud JCR (2018) Novel classes of fuzzy soft-coverings-based fuzzy rough sets with applications to multi-criteria fuzzy group decision making, Soft Comput. https://doi.org/10.1007/s00500-018-3470-9

Zhang L, Zhan J (2018) Fuzzy soft -covering based fuzzy rough sets and corresponding decision-making applications. Int J Mach Learn Cybern https://doi.org/10.1007/s13042-018-0828-3

Zhang Q, Wang J, Wang G, Yu H (2015) The approximation set of a vague set in rough approximation space. Inf Sci 300:1–19MathSciNetCrossRefMATH

Zhang Q, Xu K, Wang G (2016) Fuzzy equivalence relation and its multi-granulation spaces. Inf Sci 346–347:44–57CrossRefMATH

Zhou L, Wu WZ, Zhang WX (2009) On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators. Inf Sci 179(7):883–898MathSciNetCrossRefMATH

Zhou NL, Hu BQ (2016) Axiomatic approaches to rough approximation operators on complete completely distributive lattices. Inf Sci 348:227–242MathSciNetCrossRefMATH

Zhu W (2009) Relationship among basic concepts in covering-based rough sets. Inf Sci 179(14):2478–2486MathSciNetCrossRefMATH

Titel: On characterization of -single valued neutrosophic rough approximation operators
verfasst von: Yan-Ling Bao
Hai-Long Yang
Sheng-Gang Li
Publikationsdatum: 07.11.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 15/2019
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-018-3613-z

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