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11-01-2016 | Foundations

Atomicity via regularity for non-additive set multifunctions

Authors: Endre Pap, Alina Gavriluţ, Maricel Agop

Published in: Soft Computing | Issue 12/2016

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Abstract

In this paper, an approach of atomicity problems is presented by means of regularity. Characterizations and physical interpretations of atoms and non-atomicity for set multifunctions taking values in the family of all nonempty subsets of a topological space are given.

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Agahi H, Mesiar R, Ouyang Y (2010) Further development of Chebyshev type inequalities for Sugeno integrals and T-(S-)evaluators. Kybernetika 46(1):83–95MATHMathSciNet

Apreutesei G (2003) Families of subsets and the coincidence of hypertopologies. In: Annals of the Alexandru Ioan Cuza University—Mathematics, vol. XLIX, pp. 1–18

Banakh T, Novosad N (2013) Micro and macro fractals generated by multi-valued dynamical systems. arXiv:1304.7529v1 [math.GN]

Beer G (1993) Topologies on closed and closed convex sets. Kluwer Academic Publishers

Cavaliere P, Ventriglia F (2014) On nonatomicity for non-additive functions. J Math Anal Appl 415(1):358–372CrossRefMATHMathSciNet

Chiţescu I (1975) Finitely purely atomic measures and \({\cal L^{p}}\)-spaces. An Univ Bucureşti Şt Nat 24:23–29

Chiţescu I (2001) Finitely purely atomic measures: coincidence and rigidity properties. Rend Circ Mat Palermo (2) 50(3):455–476

Croitoru A (2014) Convergences and topology via sequences of multifunctions. Inf Sci 282:250–260CrossRefMathSciNet

Dinculeanu N (1964) Measure theory and real functions (in Romanian). Ed. Did. şi Ped., Bucureşti

Gagolewski M, Mesiar R (2014) Monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem. Inf Sci 263:166–174CrossRefMATHMathSciNet

Gavriluţ A (2010) Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Baire multivalued set functions. Fuzzy Sets Syst 160(2009):1308–1317 (Erratum in. Fuzzy Sets and Systems 161:2612–2613)

Gavriluţ A, Croitoru A (2009) Non-atomicity for fuzzy and non-fuzzy multivalued set functions. Fuzzy Sets Syst 160(14):2106–2116CrossRefMATHMathSciNet

Gavriluţ A (2011) Fuzzy Gould integrability on atoms. Iranian J Fuzzy Syst 8(3):113–124MATHMathSciNet

Gavriluţ A, Croitoru A (2008) On the Darboux property in the multivalued case, annals of the University of Craiova. Math Comput Sci Ser 35:130–138MATH

Gavriluţ A, Croitoru A (2010) Pseudo-atoms and Darboux property for set multifunctions. Fuzzy Sets Syst 161(22):2897–2908CrossRefMATHMathSciNet

Gavriluţ A, Agop M (2015) Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity (submitted for publication)

Gavriluţ AC (2010) A Lusin type theorem for regular monotone uniformly autocontinuous set multifunctions. Fuzzy Sets Syst 161(22):2909–2918CrossRefMATHMathSciNet

Gavriluţ AC (2013) On the regularities of fuzzy set multifunctions with applications in variation, extensions and fuzzy set-valued integrability problems. Inf Sci 224:130–142CrossRefMATHMathSciNet

Gavriluţ AC (2014) Remarks on monotone interval-valued set multifunctions. Inf Sci 259:225–230CrossRefMATHMathSciNet

Gong Z, Wang L (2012) The Henstock Stieltjes integral for fuzzy-number-valued functions. Inf Sci 188:276–297CrossRefMATHMathSciNet

Guo C, Zhang D (2004) On set-valued fuzzy measures. Inf Sci 160(14):13–25CrossRefMATHMathSciNet

Hart S, Neyman A (1988) Values of non-atomic vector measure games: are they linear combinations of the measures? J Math Econ 17(1):31–40CrossRefMATHMathSciNet

Hu S, Papageorgiou NS (1997) Handbook of multivalued analysis, vol I. Kluwer Acad. Publ, DordrechtCrossRefMATH

Kawabe J (2007) Regularity and Lusin’s theorem for Riesz space-valued fuzzy measures. Fuzzy Sets Syst 158(8):895–903CrossRefMATHMathSciNet

Karczmarek P, Pedrycz W, Reformat M, Akhoundi E (2014) A study in facial regions saliency: a fuzzy measure approach. Soft Comput Fusion Found Methodol Appl 18(2):379–391

Khare M, Singh AK (2008) Atoms and Dobrakov submeasures in effect algebras. Fuzzy Sets Syst 159(9):1123–1128CrossRefMATHMathSciNet

Klimkin VM, Svistula MG (2001) Darboux property of a non-additive set function. Mat Sb 192(7):41–50CrossRefMATHMathSciNet

Ko H, Bae K, Choi J, Kim SH, Choi J (2015) Similarity recognition using context-based pattern for cyber-society. Soft Comput. doi:10.1007/s00500-015-1763-9

Kunze H, la Torre D, Mendivil F, Vrscay ER (2012) Fractal-based methods in analysis. Springer, New York

Li J, Mesiar R (2011) Lusin’s theorem on monotone measure spaces. Fuzzy Sets Syst 175:75–86CrossRefMATHMathSciNet

Li J, Mesiar R, Pap E (2014) Atoms of weakly null-additive monotone measures and integrals. Inf Sci 134–139

Li J, Yasuda M, Song J (2005) Regularity properties of null-additive fuzzy measure on metric spaces. Lecture notes in artificial intelligence, vol 3558. Springer, Berlin Heidelberg, pp 59–66

Maghsoudi S (2013) Certain strict topologies on the space of regular Borel measures on locally compact groups. Topol Appl 160(14):1876–1888CrossRefMATHMathSciNet

Marques I, Graña M (2012) Face recognition with lattice independent component analysis and extreme learning machines. Soft Comput Fusion Found Methodol Appl 16(9):1525–1537

Mesiar R, Li J, Pap E (2015) Superdecomposition integral (submitted for publication)

Mesiar R, Li J, Pap E (2010) The Choquet integral as Lebesgue integral and related inequalities. Kybernetika 46(6):1098–1107MATHMathSciNet

Olejček V (1974) Darboux property of regular measures. Mat Cas 24(3): 283–288

Olejček V (2012) Fractal construction of an atomic Archimedean effect algebra with non-atomic subalgebra of sharp elements. Kybernetika 48(2):294–298MATHMathSciNet

Pap E (1990) Regular Borel t-decomposable measures. Univ. u Novom Sadu, Zb Rad Prirod Mat Fak Ser Mat 20(2):113–120

Pap E (1994) The range of null-additive fuzzy and non-fuzzy measures. Fuzzy Sets Syst 65(1):105–115CrossRefMATHMathSciNet

Pap E (1995) Null-additive set functions. Springer, New York, p 337 (Series: Mathematics and Its Applications)

Pap E (2002) Some elements of the classical measure theory, pp 27–82 (Chapter 2 in Handbook of Measure Theory)

Pap E, Strboja M, Rudas I (2014) Pseudo-Lp space and convergence. Fuzzy Sets Syst 238:113–128CrossRefMATHMathSciNet

Rao KPSB, Rao MB (1983) Theory of charges. Academic Press Inc, New YorkMATH

Suzuki H (1991) Atoms of fuzzy measures and fuzzy integrals. Fuzzy Sets Syst 41:329–342CrossRefMATHMathSciNet

Watanabe T, Kawasaki T, Tanaka T (2012) On a sufficient condition of Lusin’s theorem for non-additive measures that take values in an ordered topological vector space. Fuzzy Sets Syst 194:66–75CrossRefMATHMathSciNet

Wicks KR (1991) Fractals and hyperspaces. Springer, Berlin HeidelbergCrossRefMATH

Wu C, Bo S (2007) Pseudo-atoms of fuzzy and non-fuzzy measures. Fuzzy Sets Syst 158:1258–1272CrossRefMATHMathSciNet

Title: Atomicity via regularity for non-additive set multifunctions
Authors: Endre Pap
Alina Gavriluţ
Maricel Agop
Publication date: 11-01-2016
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 12/2016
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-015-2021-x

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