2011
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Cover vol. 8, no. 2, June 2011
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POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY
SET THEORIES
POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY
SET THEORIES
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The paper sets forth in detail categoricallyalgebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixedbasis forward powerset operator of L. A. Zadeh. On the next step, we provide a direct lift of the backward powerset operator using the notion of categorical biproduct. The obtained framework is readily extended to the variablebasis case, justifying the powerset theories currently popular in the fuzzy community. At the end of the paper, our general varietybased setting postulates the requirements, under which a convenient varietybased powerset theory can be developed, suitable for employment in all areas of fuzzy mathematics dealing with fuzzy powersets, including fuzzy algebra, logic and topology.
1
The paper sets forth in detail categoricallyalgebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the xedbasis forward powerset operator of L. A. Zadeh. On the next step, we provide a direct lift of the backward powerset operator using the notion of categorical biproduct. The obtained framework is readily extended to the variablebasis case, justifying the powerset theories currently popular in the fuzzy community. At the end of the paper, our general varietybased setting postulates the requirements, under which a convenient varietybased powerset theory can be developed, suitable for employment in all areas of fuzzy mathematics dealing with fuzzy powersets, including fuzzy algebra, logic and topology.
1
46
Sergey A.
Solovyov
Sergey A.
Solovyov
Department of Mathematics, University of Latvia, Zellu iela 8,
LV1002 Riga, Latvia and Institute of Mathematics and Computer Science, University
of Latvia, Raina bulvaris 29, LV1459 Riga, Latvia
Department of Mathematics, University of
Latvia
sergejs.solovjovs@lu.lv
(Backward
forward) powerset (operator
theory), (Bi
co) product, (Composite) (varietybased) topological (space
system), (Convenient) variety, Ground category, (L) fuzzy set, (Localic) algebra, Monadic (category
logic), Ordered category, Pointed category, Quantaloid, (Semi) quantale, (Unital) (quantale
ring) (algebra
module), Zero (morphism
object)
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ACCEPTANCE SINGLE SAMPLING PLAN
WITH FUZZY PARAMETER
ACCEPTANCE SINGLE SAMPLING PLAN
WITH FUZZY PARAMETER
2
2
The acceptance sampling plan problem is an important topic inquality control and both the theory of probability and theory of fuzzy sets maybe used to solve it. In this paper, we discuss the single acceptance samplingplan, when the proportion of nonconforming products is a fuzzy number. We
show that the operating characteristic (𝑂𝐶) curve of the plan is a band havinghigh and low bounds and that for fixed sample size and acceptance number,the width of the band depends on the ambiguity proportion parameter in thelot. When the acceptance number equals zero, this band is convex and the
convexity increases with 𝑛 Finally, we compare the 𝑂𝐶 bands for a given value of 𝑐.
1
The acceptance sampling plan problem is an important topic in quality control and both the theory of probability and theory of fuzzy sets may be used to solve it . In this paper, we discuss the single acceptance sampling plan, when the proportion of nonconforming products is a fuzzy number. We show that the operating characteristic ( OC ) curve of the plan is a band having high and low bounds and that for fixed sample size and acceptance number, the width of the band depends on the ambiguity proportion parameter in the lot. When the acceptance number equals zero, this band is convex and the convexity increases with n Finally, we compare the OC bands for a given value of .c
47
55
Bahram
Sadeghpour Gildeh
Bahram
Sadeghpour Gildeh
Department of Statistics, Faculty of Basic Science,
University of Mazandaran, P.O. Box 311, Babolsar, Iran
Department of Statistics, Faculty of Basic
Iran
sa deg hpour@umz.ac.ir
Ezzatallah
Baloui Jamkhaneh
Ezzatallah
Baloui Jamkhaneh
PhD student, Science and Research Branch, Islamic
Azad University (IAU), Tehran, Iran
PhD student, Science and Research Branch,
Iran
e_baloui2008@yahoo.com
Gholamhossein
Yari
Gholamhossein
Yari
Iran University of Science and Technology, Tehran, Iran
Iran University of Science and Technology,
Iran
yari@iust.ac.ir
Statistical quality control
Single sampling plan
Fuzzy number
Fuzzy probability of acceptance
[[1] J. J. Buckley, Fuzzy probability: new approach and application, PhysicaVerlag, Heidelberg,##Germany, 2003. ##[2] J. J. Buckley, Fuzzy probability and statistics, SpringerVerlag, Berlin Heidelberg, 2006.##[3] T. K. Chakraborty, A class of single sampling plans based on fuzzy optimization, Opsearch,##29(1) (1992), 1120.##[4] T. K. Chakraborty, Possibilistic parameter single sampling inspection plans, Opsearch, 31(2)##(1994a), 108126.##[5] D. Dubois and H. Prade, Operations of fuzzy numbers, Int. J. of Systems Science, 9 (1978),##[6] M. H. Fazel Zarandi, I. B. Turksen and A. H. Kashan, Fuzzy control chart for variable and##attribute quality characteristics, Iranian Journal of Fuzzy Systems, 3(1) (2006), 3144.##[7] P. Grzegorzewski, A soft design of acceptance sampling by attributes, Proceedings of the VIth##International Workshop on Intelligent Statistical Quality Control. W¨urzburg, September 14##16, (1998), 2938.##[8] P. Grzegorzewski, Acceptance sampling plans by attributes with fuzzy risks and quality levels,##Frontiers in Statistical Quality Control, 6: eds., Wilrich P. Th. Lenz H. J. Springer,##Heidelberg, (2001), 3646.##[9] P. Grzegorzewski, A soft design of acceptance sampling by variables, Technologies for Constructing##Intelligent Systems, eds., Springer, 2 (2002), 275286.##[10] O. Hryniewisz, Statistical acceptance sampling with uncertain information from a sample##and fuzzy quality criteria, Working Paper of SRI PAS, Warsaw, (in Polish), 1992.##[11] O. Hryniewisz, Statistical decisions with imprecise data and requirements, In: R. Kulikowski,##K. Szkatula and J. Kacprzyk, eds., Systems Analysis and Decisions Support in Economics##and Technology. Omnitech Press, Warszawa, (1994), 135143.##[12] O. Hryniewisz, Statistics with fuzzy data in statistical quality control, Soft Computing, 12##(2008), 229234.##[13] A. Kanagawa and H. Ohta, A design for single sampling attribute plan based on fuzzy sets##theory, Fuzzy Sets and Systems, 37 (1990), 173181.##[14] D. C. Montgomery, Introduction to statistical quality control, Wiley, New York, 1991.##[15] H. Ohta and H. Ichihashi, Determination of single sampling attribute plans based on membership##function, Int. J. of Production Research, 26 (1998), 14771485.##[16] E. Pasha, A. Saiedifar and B. Asady, The percentiles of fuzzy numbers and their applications,##Iranian Journal of Fuzzy Systems, 6(1) (2009), 2744.##[17] S. Sampath, Hybrid single sampling plan, World Applied Science Journal, 6(12) (2009),##16851690.##[18] E. G. Schiling, Acceptance sampling quality control, Dekker, New York, 1982.##[19] M. Taheri and M. Mashinchi, Introduction to fuzzy probability and statistics, Shahid Bahonar##University of Kerman Publication, Iran, (in Persian), 2008.##[20] F. Tamaki, A. Kanagawa and H. Ohta, A fuzzy design of sampling inspection plans by attributes,##Japanese Journal of Fuzzy Theory and Systems, 3 (1991), 315327.##]
CREDIBILISTIC PARAMETER ESTIMATION AND ITS
APPLICATION IN FUZZY PORTFOLIO SELECTION
CREDIBILISTIC PARAMETER ESTIMATION AND ITS
APPLICATION IN FUZZY PORTFOLIO SELECTION
2
2
In this paper, a maximum likelihood estimation and a minimum entropy estimation for the expected value and variance of normal fuzzy variable are discussed within the framework of credibility theory. As an application, a credibilistic portfolio selection model is proposed, which is an improvement over the traditional models as it only needs the predicted values on the security returns instead of their membership functions.
1
In this paper, a maximum likelihood estimation and a minimum entropy estimation for the expected value and variance of normal fuzzy variable are discussed within the framework of credibility theory. As an application, a credibilistic portfolio selection model is proposed, which is an improvement over the traditional models as it only needs the predicted values on the security returns instead of their membership functions.
57
65
Xiang
Li
Xiang
Li
The State Key Laboratory of Rail Traffic Control and Safety, Beijing
Jiaotong University, Beijing 100044, China
The State Key Laboratory of Rail Traffic
China
xiangli04@mail.tsinghua.edu.cn
Zhongfeng
Qin
Zhongfeng
Qin
School of Economics and Management, Beihang University, Beijing
100191, China
School of Economics and Management, Beihang
China
qin@buaa.edu.cn
Dan
Ralescu
Dan
Ralescu
Department of Mathematical Sciences, University of Cincinnati, Cincin
nati, Ohio 45221, USA
Department of Mathematical Sciences, University
United States
ralescd@uc.edu
Normal fuzzy variable
Credibility theory
Condence interval
Point estimation
Portfolio selection
[[1] A. R. Arabpour and M. Tata, Estimating the parameters of a fuzzy linear regression model,##Iranian Journal of Fuzzy Systems, 5(2) (2008), 120.##[2] K. Cai, Parameter estimations of normal fuzzy variables, Fuzzy Sets and Systems, 55 (1993),##[3] H. Dishkant, About membership functions estimation, Fuzzy Sets and Systems, 5 (1981),##[4] D. Dubois and H. Prade, Possibility theory: an approach to computerized processing of un##certainty, Plenum, New York, 1998.##[5] H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, A note on evaluation of fuzzy linear##regression models by comparing membership functions, Iranian Journal of Fuzzy Systems,##6(2) (2009), 16.##[6] X. Huang, Portfolio selection with fuzzy returns, Journal of Intelligent & Fuzzy Systems,##18(4) (2007), 383390.##[7] M. Javadian, Y. Maali and N. MahdaviAmiri, Fuzzy linear programming with grades of##satisfaction in constraints, 6(3) (2009), 1735.##[8] X. Li and B. Liu, A sucient and necessary condition for credibility measures, International##Journal of Uncertainty, Fuzziness & KnowledgeBased Systems, 14(5) (2006), 527535.##[9] X. Li and B. Liu, Maximum entropy principle for fuzzy variables, International Journal of##Uncertainty, Fuzziness & KnowledgeBased Systems, 15(Supp.2) (2007), 4352.##[10] X. Li, Z. Qin and S. Kar, Meanvarianceskewness model for portfolio selection with fuzzy##parameter, European Journal of Operational Research, 202(1) (2010), 239247.##[11] P. Li and B. Liu, Entropy of credibility distributions for fuzzy variables, IEEE Transactions##on Fuzzy Systems, 16(1) (2008), 123129.##[12] B. Liu, Uncertainty theory, 2nd ed., SpringerVerlag, Berlin, 2007.##[13] B. Liu and Y. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE##Transactions on Fuzzy Systems, 10(4) (2002), 445450.##[14] H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 7791.##[15] S. Nahmias, Fuzzy variables, Fuzzy Sets and Systems, 1 (1978), 97110.##[16] Z. Qin, X. Li and X. Ji, Portfolio selection based on fuzzy crossentropy, Journal of Compu##tational and Applied Mathematics, 228(1) (2009), 139149.##[17] D. Ralescu, Toward a general theory of fuzzy variables, Journal of Mathematical Analysis##and Applications, 86 (1982), 176193.##[18] M. Sugeno, Theory of fuzzy integrals and its applications, PhD. Thesis, Tokyo Institute of##Technology, 1974. ##[19] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1##(1978), 328.##]
LATTICEVALUED CATEGORIES OF LATTICEVALUED
CONVERGENCE SPACES
LATTICEVALUED CATEGORIES OF LATTICEVALUED
CONVERGENCE SPACES
2
2
We study Lcategories of latticevalued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a latticevalued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some Lsubcategories. Finally we usethis approach to quantify how close certain latticevalued convergence spacesare to being latticevalued topological spaces.
1
We study Lcategories of latticevalued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a latticevalued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some Lsubcategories. Finally we usethis approach to quantify how close certain latticevalued convergence spacesare to being latticevalued topological spaces.
67
89
Gunther
Jager
Gunther
Jager
Department of Statistics, Rhodes University, 6140 Grahamstown,
South Africa
Department of Statistics, Rhodes University,
South Africa
g.jager@ru.ac.za
Lfuzzy convergence
Ltopology
Llter
Llimit space
Lcategory
Fuzzy category
[[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New##York, 1989.##[2] T. M. G. Ahsanullah and J. AlMufarrij, Frame valued stratied generalized convergence##groups, Quaest. Math., 31 (2008), 279302.##[3] A. Craig and G. Jager, A common framework for latticevalued uniform spaces and proba##bilistic uniform convergence spaces, Fuzzy Sets and Systems, 160 (2009), 11771203.##[4] U. Hohle, Commutative, residuated Lmonoids, In: Nonclassical Logics and Their Applications##to Fuzzy Subsets (U. Hohle, E.P. Klement, eds.), Kluwer, Dordrecht, (1995), 53106.##[5] U. Hohle, Locales and Ltopologies, In: Categorical Methods in Algebra and Topology (H. E.##Porst, eds.), MathematikArbeitspapiere 48, Univ. Bremen, (1997), 223250.##[6] U. Hohle and A. P. Sostak, Axiomatic foundations of xedbasis fuzzy topology, In: Mathematics##of Fuzzy Sets: Logic, Topology and Measure Theory (U. Hohle, S. E. Rodabaugh,##eds.), Kluwer, Dordrecht, (1999), 123272.##[7] G. Jager, Fuzzy properties in fuzzy convergence spaces, Int. J. Math. Math. Sci., 29 (2002),##[8] G. Jager, A category of Lfuzzy convergence spaces, Quaest. Math., 24 (2001), 501517.##[9] G. Jager, Subcategories of lattice valued convergence spaces, Fuzzy Sets and Systems, 156##(2005), 124.##[10] G. Jager, Pretopological and topological latticevalued convergence spaces, Fuzzy Sets and##Systems, 158 (2007), 424435.##[11] G. Jager, Fischer's diagonal condition for latticevalued convergence spaces, Quaest. Math.,##31 (2008), 1125. ##[12] G. Jager, Latticevalued convergence spaces and regularity, Fuzzy Sets and Systems, 159##(2008), 24882502.##[13] G. Jager, Compactication of latticevalued convergence spaces, Fuzzy Sets and Systems, 161##(2010), 10021010.##[14] T. Kubiak and A. P. Sostak , A fuzzication of the category of Mvalued Ltopological spaces,##App. Gen. Top., 5 (2004), 137154.##[15] E. Lowen and R. Lowen, On measures of compactness in fuzzy topological spaces, J. Math.##Anal. Appl., 131 (1988), 329340.##[16] H. Poppe, Compactness in general function spaces, VEB Deutscher Verlag Der Wissenschaften,##Berlin, 1974.##[17] A. Sostak, On compactness and connectedness degrees of fuzzy sets in fuzzy topological spaces,##In: General Topology and Its Relations to Modern Analysis and Algebra, VI (Prague, 1986),##Res. Exp. Math., Heldermann, Berlin, 16 (1988), 519532.##[18] A. Sostak, Fuzzy categories versus categories of fuzzily structured sets: elements of the theory##of fuzzy categories, In: Categorical Methods in Algebra and Topology (H. E. Porst, eds.),##MathematikArbeitspapiere 48, Univ. Bremen, (1997), 407437.##[19] A. Sostak, Fuzzy categories related to algebra and topology, Tatra Mt. Math. Publ., 16 (1999),##[20] A. P. Sostak, Fuzzy functions and an extension of the category LTOP of ChangGoguen L##topological spaces, In: Proceedings of the 9th Prague Topological Symposium (Prague 2001),##Topology ATLAS, Totoronto, (2002), 271294.##[21] A. P. Sostak, On some fuzzy categories related to category LTOP of Ltopological spaces,##In: Topological and Algebraic Structures in Fuzzy Sets (eds., S. E. Rodabaugh and E. P.##Klement), Kluwer, (2003), 337372.##[22] A. P. Sostak, Lvalued categories: generalities and examples related to algebra and topology,##In: Categorical Structures and Their Applications (eds., W. Gahler and G. Preuss), World##Scientic, (2004), 291312.##[23] W. Yao, On manyvalued stratied Lfuzzy convergence spaces, Fuzzy Sets and Systems, 159##(2008), 25032519.##[24] W. Yao, On Lfuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6 (2009),##[25] M. S. Ying, A new approach to fuzzy topology, part I, Fuzzy Sets and Systems, 39 (1991),##[26] Y. Yue and J. Fang, Fuzzy ideals and fuzzy limit structures, Iranian Journal of Fuzzy Systems,##5 (2008), 5564.##]
$(A)_ {Delta}$  double Sequence Spaces of fuzzy numbers via Orlicz Function
$(A)_ {Delta}$  double Sequence Spaces of fuzzy numbers via Orlicz Function
2
2
The aim of this paper is to introduce and study a new concept ofstrong double $(A)_ {Delta}$convergent sequence offuzzy numbers with respect to an Orlicz function and also someproperties of the resulting sequence spaces of fuzzy numbers areexamined. In addition, we define the double$(A,Delta)$statistical convergence of fuzzy numbers andestablish some connections between the spaces of strong double$(A)_ {Delta}$convergent sequence and double $(A,Delta)$statistical convergent sequence.
1
The aim of this paper is to introduce and study a new concept ofstrong double $(A)_ {Delta}$convergent sequence offuzzy numbers with respect to an Orlicz function and also someproperties of the resulting sequence spaces of fuzzy numbers areexamined. In addition, we define the double$(A,Delta)$statistical convergence of fuzzy numbers andestablish some connections between the spaces of strong double$(A)_ {Delta}$convergent sequence and double $(A,Delta)$statistical convergent sequence.
91
103
E.
Savas
E.
Savas
Istanbul Ticaret University, Department of Mathematics, UskudarIstanbul,
Turkey
Istanbul Ticaret University, Department of
Turkey
ekremsavas@yahoo.com
Orlicz function
Double statistical convergence
Fuzzy number
[bibitem{DK}##P. Diomand and P. Kloeden, emph{Metric spaces of fuzzy sets},##Fuzzy Sets and Systems, textbf{33} (1989), 123126. ##bibitem{Fa} H. Fast, emph{Sur la convergence statistique}, Collog. Math., textbf{2} (1951), 241244.##bibitem{FS} A. R. Freedman and J. J. Sember, emph{Densities and summability}, Pacific J. Math., textbf{95} (1981), 293305.##bibitem{Ham1} H. J. Hamilton, emph{Transformations of multiple sequences}, Duke Math. J., textbf{2} (1936), 2960.##bibitem{KR} M. A. Krasnoselskii and Y. B. Rutisky, emph{Convex##function and Orlicz spaces}, Groningen, Netherlands, 1961.##bibitem{mu1} M. Mursaleen and M. Basarir, emph{$A$statistical convergence of a sequence of fuzzy numbers}, Indian J. Pure appl. Math.,##textbf{34} (2003), 13511357.##bibitem{Na}##S. Nanda, emph{On sequence of fuzzy numbers}, Fuzzy Sets and Systems,## textbf{33} (1989), 123126.##bibitem{NE}##F. Nuray and E. Savas, emph{Statistical convergence of fuzzy numbers},##Math. Slovaca, textbf{45} (1995), 269273.##bibitem{Nu}##F. Nuray, emph{Lacunary statistical convergence of sequences of##fuzzy numbers}, Fuzzy Sets and Systems, textbf{99} (1998), 353355.##bibitem{PC}##S. D. Parashar and B. Choudhary, emph{Sequence spaces defined##by Orlicz functions}, Indian J. Pure appl. Math., textbf{25} (1994), 419428.##bibitem{pringsheim} A. Pringsheim, emph{Zur theorie der zweifach##unendlichen Zahlenfolgen}, Math. Ann., textbf{53} (1900), 289321.##bibitem{robison} G. M. Robison, emph{Divergent double sequences and series}, Amer. Math. Soc. Trans., textbf{28} (1926), 5073.##bibitem{Es96}## E. Savac{s}, emph{A note on double sequence of fuzzy numbers}, Turk J. Math., textbf{20} (1996), 175178.##bibitem{Es00}## E. Savac{s}, emph{A note on sequence of fuzzy numbers}, Information Sciences, textbf{124} (2000), 297300.##bibitem{E00}## E. Savac{s}, emph{On strongly $lambda$summable sequences of fuzzy numbers},##Information Sciences, textbf{125} (2000), 181186.## bibitem{Es01}## E. Savac{s}, emph{On statistically convergent sequence of fuzzy numbers}, Information Sciences, textbf{137} (2001),## 272282.##bibitem{Es06}## E. Savac{s}, emph{Difference sequence spaces of fuzzy numbers}, J. Fuzzy##Math., textbf{14} (2006), 967975. ## bibitem{Es08}## E. Savac{s}, emph{On lacunary statistical convergent double sequences of fuzzy numbers},## Appl. Math. Lett., textbf{21} (2008), 134141. ## bibitem{EM}## E. Savac{s} and M. Mursaleen, emph{On statistically convergent double sequence of fuzzy numbers}, Information Sciences, textbf{162} (2004),## 183192.## bibitem{EP}## E. Savac{s} and R. F. Patterson, emph{$(A_{sigma})_{Delta}$double sequence spaces via Orlicz functions## and double statistical convergence}, Iran. J. Sci. Technol. Trans. A, textbf{31} (2007), 357367. ## bibitem{T007}## B. C. Tripathy and A. J. Dutta, emph{On fuzzy realvalued double sequence space}, Math. Comput. Modelling,## textbf{46} (2007), 12941299.##bibitem{007}## B. C. Tripathy and A. J. Dutta, emph{Statistically convergent and Ces`{a}ro summable double sequences of fuzzy real numbers}, Soochow J. Math.,## textbf{33} (2007), 835848. ## bibitem{009}## W. Yao, emph{On Lfuzzifying convergence spaces}, Iranian Journal of Fuzzy Systems, textbf{6(1)} (2009), 6380. ## bibitem{65}## A. Zadeh, emph{Fuzzy Sets}, Information and Control, textbf{8} (1965), 338353.##]
BIPOLAR FUZZY HYPER BCKIDEALS IN HYPER
BCKALGEBRAS
BIPOLAR FUZZY HYPER BCKIDEALS IN HYPER
BCKALGEBRAS
2
2
Using the notion of bipolarvalued fuzzy sets, the concepts of bipolarfuzzy (weak, 𝑠weak, strong) hyper BCKideals are introduced, and theirrelations are discussed. Moreover, several related properties are investigated.
1
Using the notion of bipolarvalued fuzzy sets, the concepts of bipolarfuzzy (weak, 𝑠weak, strong) hyper BCKideals are introduced, and theirrelations are discussed. Moreover, several related properties are investigated.
105
120
Young Bae
Jun
Young Bae
Jun
Department of Mathematics Education (and RINS), Gyeongsang National
University, Chinju 660701, Korea
Department of Mathematics Education (and
Korea
skywine@gmail.com
Min Su
Kang
Min Su
Kang
Department of Mathematics, Hanyang University, Seoul 133791, Korea
Department of Mathematics, Hanyang University,
Korea
sinchangmyun@hanmail.net
Hee Sik
Kim
Hee Sik
Kim
Department of Mathematics, Hanyang University, Seoul 133791, Korea
Department of Mathematics, Hanyang University,
Korea
heekim@hanyang.ac.kr
(Strong
weak
sweak) hyper BCKideal
Bipolar fuzzy hyper BCKideal
Bipolar fuzzy strong hyper BCKideal
Bipolar fuzzy weak hyper BCKideal
Bipolar fuzzy sweak hyper BCKideal
infsup property
[[1] B. Davvaz, Fuzzy hyperideals in ternary semihyperrings, Iranian Journal of Fuzzy Systems,##6(4) (2009), 2136.##[2] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Academic Press,##[3] H. Harizavi, Prime weak hyper BCKideals of lower hyper BCKsemilattice, Sci. Math. Jpn.,##68 (2008), 353360.##[4] Y. B. Jun and W. H. Shim, Fuzzy implicative hyper 𝐵𝐶𝐾ideals of hyper 𝐵𝐶𝐾algebras,##Internat. J. Math. Math. Sci., 29(2) (2002), 6370.##[5] Y. B. Jun and X. L. Xin, Scalar elements and hyperatoms of hyper 𝐵𝐶𝐾algebras, Scientiae##Mathematicae, 2(3) (1999), 303309.##[6] Y. B. Jun and X. L. Xin, Fuzzy hyper 𝐵𝐶𝐾ideals of hyper 𝐵𝐶𝐾algebras, Sci. Math. Jpn.,##53(2) (2001), 353360.##[7] Y. B. Jun, X. L. Xin, E. H. Roh and M. M. Zahedi, Strong hyper 𝐵𝐶𝐾ideals of hyper##𝐵𝐶𝐾algebras, Math. Japonica, 51(3) (2000), 493498.##[8] Y. B. Jun, M. M. Zahedi, X. L. Xin and R. A. Borzooei, On hyper 𝐵𝐶𝐾algebras, Italian J.##of Pure and Appl. Math., 8 (2000), 127136.##[9] K. M. Lee, Bipolarvalued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent##Technologies, Bangkok, Thailand, (2000), 307312.##[10] K. M. Lee, Comparison of intervalvalued fuzzy sets, intuitionistic fuzzy sets, and bipolarvalued##fuzzy sets, J. Fuzzy Logic Intelligent Systems, 14(2) (2004), 125129.##[11] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves,##Stockholm, (1934), 4549.##[12] L. Torkzadeh, M. Abbasi and M. M. Zahedi, Some results of intuitionistic fuzzy weak dual##hyper Kideals, Iranian Journal of Fuzzy Systems, 5(1) (2008), 6578.##[13] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##[14] H. J. Zimmermann, Fuzzy set theory and its applications, KluwerNijhoff Publishing, 1985.##]
NETTHEORETICAL LGENERALIZED
CONVERGENCE SPACES
NETTHEORETICAL LGENERALIZED
CONVERGENCE SPACES
2
2
In this paper, the denition of nettheoretical Lgeneralized convergencespaces is proposed. It is shown that, for L a frame, the category ofenriched Lfuzzy topological spaces can be embedded in that of Lgeneralizedconvergence spaces as a reective subcategory and the latter is a cartesianclosedtopological category.
1
In this paper, the denition of nettheoretical Lgeneralized convergencespaces is proposed. It is shown that, for L a frame, the category ofenriched Lfuzzy topological spaces can be embedded in that of Lgeneralizedconvergence spaces as a reective subcategory and the latter is a cartesianclosedtopological category.
121
131
Wei
Yao
Wei
Yao
Department of Mathematics, Hebei University of Science and Technology,
Shijiazhuang 050018, P.R. China
Department of Mathematics, Hebei University
China
yaowei0516@163.com
Net
(Nettheoretical) Lgeneralized convergence space
(Enriched) Lfuzzy topological space
Cartesianclosed category
[[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New##York, 1990.##[2] U. Hohle, Probabilistic topologies induced by Lfuzzy uniformities, Manuscipta Math., 38##(1982), 289323.##[3] U. Hohle, Many valued topology and its appplications, Kluwer Academic Publishers, 2001.##[4] U. Hohle and A. P. Sostak, Axiomatic foundations of xedbasis fuzzy topology, Chapter##3 In: Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, (U. Hohle, S. E.##Rodabaugh, eds.), Kluwer Academic Publishers, Boston/Dordrecht/London, (1999), 123272.##[5] G. Jager, A category of Lfuzzy convergence spaces, Quaest. Math., 24 (2001), 501517. ##[6] G. Jager, Subcategories of lattice valued convergence spaces, Fuzzy Sets and Systems, 156##(2005), 124.##[7] P. Johnstone, Stone spaces, Cambridge University Press, Cambridge, 1982.##[8] D. C. Kent, Convergence functions and their related topologies, Fund. Math., 54 (1964),##[9] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientic Publishing, Singapore, 1997.##[10] R. Lowen, Convergence in fuzzy topological spaces, Gen. Topol. Appl., 10 (1979), 147160.##[11] G. Preu, Foundations of topology: an approach to convenient topology, Kluwer Academic##Publishers, Dordrecht/Boston/London, 2002.##[12] P. M. Pu and Y. M. Liu, Fuzzy topology: I. neighborhood structure of a fuzzy point and##MooreSmith convergence, J. Math. Anal. Appl., 76 (1980), 571599.##[13] S. E. Rodabaugh, Powerset operator foundations for poslat fuzzy set theories and topologies,##Chapter 2 In: Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, (U. Hohle,##S. E. Rodabaugh, eds.), Kluwer Academic Publishers, Boston/Dordrecht/London, (1999),##[14] W. Yao, On manyvalued stratied Lfuzzy convergence spaces, Fuzzy Sets and Systems, 159##(2008), 25032519.##[15] W. Yao, On Lfuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6 (2009),##[16] Y. L. Yue and J. M. Fang, Fuzzy ideals and fuzzy limit structures, Iranian Journal of Fuzzy##Systems, 5 (2008), 5564.##]
GENERALIZED REGULAR FUZZY MATRICES
GENERALIZED REGULAR FUZZY MATRICES
2
2
In this paper, the concept of kregular fuzzy matrix as a general ization of regular matrix is introduced and some basic properties of a kregular fuzzy matrix are derived. This leads to the characterization of a matrix for which the regularity index and the index are identical. Further the relation between regular, kregular and regularity of powers of fuzzy matrices are dis cussed.
1
In this paper, the concept of kregular fuzzy matrix as a general ization of regular matrix is introduced and some basic properties of a kregular fuzzy matrix are derived. This leads to the characterization of a matrix for which the regularity index and the index are identical. Further the relation between regular, kregular and regularity of powers of fuzzy matrices are dis cussed.
133
141
A. R.
Meenakshi
A. R.
Meenakshi
Department of Mathematics, Karpagam college of Engineering,
Coimbatore 641 032, India
Department of Mathematics, Karpagam college
India
arm meenakshi@yahoo.co.in
P.
Jenita
P.
Jenita
Department of Mathematics, Karpagam college of Engineering, Coimbat
ore 641 032, India
Department of Mathematics, Karpagam college
India
sureshjenita@yahoo.co.in
Fuzzy matrices
Kregular fuzzy matrices
Index
period
[[1] A. BenIsrael and T. N. E. Greville, Generalized inverses, Theory and Applications, Wiley,##Newyork, 1974.##[2] H. H. Cho, Regular fuzzy matrices and fuzzy equations, Fuzzy sets and systems, 105 (1999),##[3] K. H. KIM and F. W. Roush, On generalised fuzzy matrices, Fuzzy Sets and Systems, 4##(1980), 293375.##[4] A. R. Meenakshi, On regularity of block triangular fuzzy matrices, Applied Math & Comput##ing, 15 (2004), 207220.##[5] A. R. Meenakshi and S. Sriram, On regularity of sums of fuzzy matrices, Bulletin of Pure##and Applied sciences., 22E(2) (2003), 395403.##[6] T. J. Ross, Fuzzy logic with engineering applications, McGraw Hill Inc., 1995.##[7] W. Pedrycz, Fuzzy relational calculus, Hand Book of Fuzzy Computations, IOP.4d, 1998.##]
GRADATION OF CONTINUITY IN FUZZY TOPOLOGICAL
SPACES
GRADATION OF CONTINUITY IN FUZZY TOPOLOGICAL
SPACES
2
2
In this paper we introduce a definition of gradation of continuity ingraded fuzzy topological spaces and study its various characteristic properties.The impact of the grade of continuity of mappings over the Ncompactnessgrade is examined. Concept of gradation is also introduced in openness, closedness, homeomorphic properties of mappings and T2 separation axiom. Effectof the grades interrelated with Ncompactness, closedness, T2 separation andhomeomorphism of mappings are studied.
1
In this paper we introduce a definition of gradation of continuity ingraded fuzzy topological spaces and study its various characteristic properties.The impact of the grade of continuity of mappings over the Ncompactnessgrade is examined. Concept of gradation is also introduced in openness, closedness, homeomorphic properties of mappings and T2 separation axiomEffectof the grades interrelated with Ncompactness, closedness, T2 separation andhomeomorphism of mappings are studied.
143
159
Ramkrishna
Thakur
Ramkrishna
Thakur
Department of Mathematics, VisvaBharati, Santiniketan731235,
West Bengal, India
Department of Mathematics, VisvaBharati,
India
thakurram06@gmail.com
S. K.
Samanta
S. K.
Samanta
Department of Mathematics, VisvaBharati, Santiniketan731235,
West Bengal, India
Department of Mathematics, VisvaBharati,
India
syamal 123@yahoo.co.in
K. K.
Mondal
K. K.
Mondal
Department of Mathematics, Kurseong College, Kurseong734203,
West Bengal, India
Department of Mathematics, Kurseong College,
India
krishnakmondal@yahoo.co.in
Fuzzy belongingness
Fuzzy quasicoincidence
Gradation of openness
Gradation of neighborhoodness
Fuzzy topological spaces
Fuzzy filters
Graded continuity
[[1] M. E. Abd ElMonsef, S. N. ElDeep, F. M. Zeyada and I. M. Hanafy, On fuzzy continuity##and fuzzy closed graph, Periodica Mathematica Hungarica, 26(1) (1993), 4353.##[2] M. H. Burton, M. Muraleetharan and J. Gutierrez Garcia, Generalized lters 1, Fuzzy Sets##and Systems, 106 (1999), 275284.##[3] M. Caldas, S. Jafari, T. Noiri and M. Simoes, A new generalization of contracontinuity via##Levine's gclosed sets, Chaos, Solitons & Fractals, 32(4) (2007), 15971603.##[4] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182190.##[5] K. C. Chattopadhyay, R. N. Hazra and S. K. Samanta, Gradation of openness : fuzzy topology,##Fuzzy Sets and Systems, 49 (1992), 237242.##[6] M. Demirci, On the convergence structure of Ltopological spaces and the graded continuity in##Ltopological spaces, part III, International Conference on Applicable and General Topology,##August: 1218, 2001.##[7] E. Ekici, Generalization of weakly clopen ansd strongly bcontinuous functions, Chaos,##Solitons & Fractals, 38(1) (2008), 7988.##[8] M. S. El. Naschie, Superstring, knots and noncommutative geometry in space, Int. J Theor##Phys, 37(12) (1998), 293551.##[9] M. S. El. Naschie, Topics in the mathematical physics of Einnity theory, Chaos, Solitons##& Fractals, 30 (2006), 65663.##[10] M. S. El. Naschie, Quantum gravity, Cliford algebras, fuzzy set theory and fundamental##constants of nature, Chaos, Solitons & Fractals, 20 (2004), 43750.##[11] M. S. El. Naschie, Topics of mathematical physics of Einnity theory, Chaos, Solitons &##Fractals, 30 (2006), 65663.##[12] M. S. El. Naschie, A review of Einnity theory and mass spectrum of high energy particle##physics, Chaos, Solitons & Fractals, 19 (2004), 20936.##[13] F. Jinming, MVquasicoincident neighborhood systems in Itopology, Preprint.##[14] T. Kubiak, On fuzzy topologies, Ph. D. Thesis, A. Mickiewiez, Poznan, 1985.##[15] K. K. Mondal and S. K. Samanta, Fuzzy convergence theory I, Journal of the Korea Society##of Mathematical Education Series B: PAM, 12(1) (2005), 7591.##[16] K. K. Mondal and S. K. Samanta, Fuzzy convergence theory II, Journal of the Korea Society##of Mathematical Education Series B: PAM, 12(2) (2005), 105124.##[17] K. K. Mondal and S. K. Samanta, Fuzzy belongingness, fuzzy quasicoincidence and conver##gence of generalized fuzzy lters, The Journal of Fuzzy Mathematics, 15(4) (2007).##[18] T. Noiri and V. Popa, Faintly mcontinuous functions, Chaos, Solitons & Fractals, 19 (2004),##[19] P. PaoMing and L. Ying Ming, Fuzzy topology I, neighborhood structure of a fuzzy point and##MoorSmith convergence, J. Math. Anal. Appl., 76 (1980), 571599.##[20] D. W. Rosen and T. J. Peters, The role of toplogy in engineering design research, Res Eng##Des, 2 (1996), 8198##[21] A. P. Sostak, On a fuzzy topological structure, Supp. Rend. Circ. Math. Palermo (Ser. II) II,##(1985), 89103.##[22] G. Werner, The general fuzzy lter approach to fuzzy topology, I, Fuzzy Sets and Systems,##76 (1995), 205224. ##[23] C. H. Yan and J. X. Fang, Lfuzzy bilinear operator and its continuity, Iranian Journal of##Fuzzy Systems, 4(1) (2007), 6573.##[24] M. S. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39 (1991),##[25] M. S. Ying, On the method of neighborhood systems in fuzzy topology, Fuzzy Sets and Systems,##68 (1994), 227238.##[26] L. YingMing and L. MaoKang, Fuzzy topology, World Scientic.##[27] A. M. Zahran, O. R. Sayed and A. K. Mousa, Completely continuous functions and Rmap##in fuzzifying topological space, Fuzzy Sets and Systems, 158 (2007), 40923.##]
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