2012
9
4
4
158
Cover Special Issue vol. 9, no. 4, October 2012
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CONVERGENCE APPROACH SPACES AND APPROACH
SPACES AS LATTICEVALUED CONVERGENCE SPACES
CONVERGENCE APPROACH SPACES AND APPROACH
SPACES AS LATTICEVALUED CONVERGENCE SPACES
2
2
We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued pretopological spaces and that the category of approach spaces is a coreective subcategory of a category of latticevalued topological convergence spaces
1
We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued pretopological spaces and that the category of approach spaces is a coreective subcategory of a category of latticevalued topological convergence spaces
1
16
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
Lfilter
Llimit space
Approach space
Convergence approach space
Preapproach space
[[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New##York, 1989.##[2] P. Brock and D. C. Kent, Approach spaces, limit tower spaces, and probabilistic convergence##spaces, Applied Categorical Structures, 5 (1997), 99110.##[3] P. V. Flores, R. N. Mohapatra and G. Richardson, Latticevalued spaces: fuzzy convergence,##Fuzzy Sets and Systems, 157 (2006), 2706 2714.##[4] W. Gahler, Monadic convergence structures, In S. E. Rodabaugh and E. P. Klement, Editors,##Topological and Algebraic Structures in Fuzzy Sets. Kluwer Academic Publishers, Dordrecht,##[5] J. Gutierrez Garca, I. Mardones Perez and M. H. Burton, The relationship between various##lter notions on a GLmonoid, J. Math. Anal. Appl., 230 (1999), 291302.##[6] U. Hohle, Commutative, residuated lmonoids, In: Nonclassical Logics and Their Application##to Fuzzy Subsets (U. Hohle, S. E. Rodabaugh and eds.), Kluwer, Dordrecht, (1995), 53106.##[7] U. Hohle, Many valued topology and its applications, Kluwer, Boston/Dordrecht/London,##[8] 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 and##eds.), Kluwer, Boston/Dordrecht/London, (1999), 123272.##[9] G. Jager, A category of Lfuzzy convergence spaces, Quaest. Math., 24 (2001), 501517.##[10] G. Jager, Subcategories of latticevalued convergence spaces, Fuzzy Sets and Systems, 156##(2005), 124. ##[11] G. Jager, Pretopological and topological latticevalued convergence spaces, Fuzzy Sets and##Systems, 158 (2007), 424435.##[12] G. Jager, Fischer's diagonal condition for latticevalued convergence spaces, Quaest. Math.,##31 (2008), 1125.##[13] G. Jager, Latticevalued convergence spaces and regularity, Fuzzy Sets and Systems, 159##(2008), 24882502.##[14] G. Jager, Latticevalued categories of latticevalued convergence spaces, Iranian Journal of##Fuzzy Systems, 8 (2011), 6789.##[15] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Dordrecht, 2000.##[16] H. J. Kowalsky, Limesraume und Komplettierung, Math. Nachrichten, 12 (1954), 301340.##[17] L. Li and Q. Jin, On adjunctions between Lim, SLTop, and SLLim, Fuzzy Sets and Systems,##doi:10.1016/j.fss.2010.10.002, to appear.##[18] E. Lowen and R. Lowen, A quasitopos containing CONV and MET as full subcategories,##Internat. J. Math. and Math. Sci., 11 (1988), 417 438.##[19] R. Lowen, Approach spaces: a common supercategory of TOP and MET, Math. Nachr., 141##(1989), 183226.##[20] R. Lowen, Approach spaces: the missing link in the topologyuniformitymetric triad, Claredon##Press, Oxford, 1997.##[21] D. L. Orpen and G. Jager, Latticevalued convergence spaces: extending the lattice context,##Fuzzy Sets and Systems, 190 (2012), 120.##[22] B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983.##[23] W. Yao, On manyvalued Lfuzzy convergence spaces, Fuzzy Sets and Systems, 159 (2008),##25032519.##[24] W. Yao, On Lfuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6 (2009),##]
EFFICIENCY IN FUZZY PRODUCTION POSSIBILITY SET
EFFICIENCY IN FUZZY PRODUCTION POSSIBILITY SET
2
2
The existing Data Envelopment Analysis models for evaluating the relative eciency of a set of decision making units by using various inputs to produce various outputs are limited to crisp data in crisp production possibility set. In this paper, rst of all the production possibility set is extended to the fuzzy production possibility set by extension principle in constant return to scale, and then the fuzzy model of Charnes, Cooper and Rhodes in input oriented is proposed so that it satis es the initial concepts with crisp data. Finally, the fuzzy model of Charnes, Cooper and Rhodes for evaluating decision making units is illustrated by solving two numerical examples.
1
The existing Data Envelopment Analysis models for evaluating the relative eciency of a set of decision making units by using various inputs to produce various outputs are limited to crisp data in crisp production possibility set. In this paper, rst of all the production possibility set is extended to the fuzzy production possibility set by extension principle in constant return to scale, and then the fuzzy model of Charnes, Cooper and Rhodes in input oriented is proposed so that it satis es the initial concepts with crisp data. Finally, the fuzzy model of Charnes, Cooper and Rhodes for evaluating decision making units is illustrated by solving two numerical examples.
17
30
T.
Allahviranloo
T.
Allahviranloo
Department of Mathematics, Science and Research Branch, Is
lamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research
Iran
tofigh@allahviranloo.com
F.
Hosseinzadeh Lotfi
F.
Hosseinzadeh Lotfi
Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research
Iran
hosseinzadeh lotfi@yahoo.com
M.
AdabitabarFirozja
M.
AdabitabarFirozja
Department of Mathematics, Qaemshar Branch, Islamic Azad
University, Qaemshahr, Iran
Department of Mathematics, Qaemshar Branch,
Iran
mohamadsadega@yahoo.com
Data Envelopment Analysis
Extension principle
Fuzzy number
[[1] J. M. Adamo, Fuzzy decision trees, Fuzzy Sets and Systems, 4 (1980), 207219.##[2] T. Allahviranloo, F. Hosseinzadeh Lot, L. Alizadeh and N. Kiani, Degenercy in fuzzy linear##programming problems, In Journal of the Journal of Fuzzy Mathematics (International Fuzzy##Mathematics Institute), 17(2) (2009).##[3] J. F. Baldwin and N. C. F. Guild, Comparison of fuzzy sets on the same decision space,##Fuzzy Sets and Systems, 2 (1979), 213233.##[4] R. D. Banker, A. Charnes and W. W. Cooper, Some models for estimating teachnical and##scale eciencies in data envelopment analysis, Manage. Sci., 30 (1984), 10781092.##[5] R. E. Bellman and L. A. Zadeh, Decisionmaking in a fuzzy environment, Management Sci.,##17 (1970), 141164.##[6] A. Charnes, W. W. Cooper and E. Rhodes, Measuring the eciency of decision making##units, Europian Journal of Operation Research, 2 (1978), 429444.##[7] W. W. Cooper, L. M. Sieford and K. Tone, Data envelopment analysis: a comprehensive text##with models, applications, References and DEA Solver Software, Kluwer Academic Publishers,##[8] W. W. Cooper, K. S. Park and J. T. Pastor, RAM: a range adjusted measure of ineciency##for use with additive models, and relations to other models and measures in DEA, J. Product.##Anal., 11 (1999), 524.##[9] M. J. Farrell, The measurement of productive eciency, Journal of the Royal Statistical##Society A, 120 (1957), 253281.##[10] R. Fuller, Neural fuzzy systems, Donner Visiting Professor Abo Akademi University, ISBN##9516506240, ISSN 03585654, Abo, 1995.##[11] P. Guo and H. Tanaka, Fuzzy DEA: a perceptual evaluation method, Fuzzy Sets and Systems,##119 (2001), 149160.##[12] P. Guo, Fuzzy data envelopment analysis and its aplication to location problems, Information##Sciences, 176(6,1) (2009), 820829.##[13] F. Hosseinzadeh Lot, T. Allahviranloo, M. Alimardani Jondabeh and L. Alizadeh, Solving##a full fuzzy linear programming using lexicography method and fuzzy approximate solution,##Applied Mathematical Modelling, 33(7) (2009), 31513156.##[14] G. R. Jahanshahloo, M. SoleimaniDamaneh and E. Nasrabadi, Measure of eciency in DEA##with fuzzy inputoutput levels: a methodology for assessing, ranking and imposing of weights##restrictions, Applied Mathematics and Computation, 156 (2004), 175187.##[15] N. Javadian, Y. Maali and N. MahdaviAmiri, Fuzzy linear programing with grades of satis##faction in constraints, Iranian Journal of Fuzzy Systems, 6(3) (2009), 1735. ##[16] C. Kao and ShiangTai Liu, Fuzzy eciency measures in data envelopment analysis, Fuzzy##Sets and Systems, 113 (2000), 427437.##[17] C. Kao and S. T. Liu, A mathematical programming approach to fuzzy eciency ranking,##Internat. J. Production Econom, 86 (2003), 45154.##[18] S. Lertworasirikul, S. C. Fang, J. A. Joines and H. L. W. Nuttle, Fuzzy data envelopment##analysis(DEA):a possibility approach, Fuzzy Sets and Systems, 139 (2003), 379394.##[19] T. Leon, V. Lierm, J. L. Ruiz and I. Sirvent, A fuzzy mathematical programing approach to##the assessment eciency with DEA models, Fuzzy Sets and Systems, 139 (2003), 407419.##[20] S. Lertworasirikul, S. C. Fang, J. A. Joines and H. L. W. Nuttle, Fuzzy data envelopment##analysis(DEA): a possibility aporoach, Fuzzy Sets and Systems, 139(2) (2003), 379394.##[21] S. T. Liu and M. Chuang, Fuzzy eciency measures in fuzzy DEA/AR with application to##university libraries, Expert Systems with Applications, 36(2) (2009), 11051113.##[22] S. Ramezanzadeh, M. Memariani and S. Saati, data envelopment analisis with fuzzy random##inputs and outputs: a chance constrained programing approach, Iranian Journal of Fuzzy##Systems, 2(2) (2005), 2129.##[23] M. R. Sa, H. R. Maleki and E. Zaeimazad, A note on the zimmermann method for solving##fuzzy linear programing problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 3145.##[24] Y. M. Wang, R. Greatbanks and J. B. Yang, Interval eciency assessment using data en##velopment analysis, Fuzzy Sets and Systems, 153 (2005), 347370.##[25] Y. M. Wang, Y. Luo and L. Liang, Fuzzy data envelopment analysis based upon fuzzy arith##metic with an aplication to performance assessment of manufacturing enterprises, Expert##Systems with Applications, 363 (2009), 52055211.##[26] M. Wen and H. Li, Fuzzy data envelopment analysis(DEA): model and ranking method,##Journal of Computational and Applied Mathematics, 223(2,15) (2009), 872878.##[27] H. J. Zimmermann, Fuzzy set theory and its applications, Second ed., KluwerNijho, Boston,##]
CLASSIFYING FUZZY SUBGROUPS OF FINITE NONABELIAN
GROUPS
CLASSIFYING FUZZY SUBGROUPS OF FINITE NONABELIAN
GROUPS
2
2
In this paper a rst step in classifying the fuzzy subgroups of a nite nonabelian group is made. We develop a general method to count the number of distinct fuzzy subgroups of such groups. Explicit formulas are obtained in the particular case of dihedral groups.
1
In this paper a rst step in classifying the fuzzy subgroups of a nite nonabelian group is made. We develop a general method to count the number of distinct fuzzy subgroups of such groups. Explicit formulas are obtained in the particular case of dihedral groups.
31
41
Marius
Tarnauceanu
Marius
Tarnauceanu
Faculty of Mathematics, Al.I. Cuza" University, Iasi, Romania
Faculty of Mathematics, Al.I. Cuza" University,
Romania
tarnauc@uaic.ro
Fuzzy subgroups
Chains of subgroups
Maximal chains of subgroups
Dihedral groups
Recurrence relations
[[1] Y. Alkhamees, Fuzzy cyclic subgroups and fuzzy cyclic psubgroups, J. Fuzzy Math., 3 (1995),##[2] G. Gratzer, General lattice theory, Academic Press, New York, 1978.##[3] T. Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and##Systems, 73 (1995), 349358.##[4] T. Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and##Systems, 79 (1996), 277278.##[5] A. Jain, Fuzzy subgroups and certain equivalence relations, Iranian Journal of Fuzzy Systems,##3 (2006), 7591.##[6] R. Kumar, Fuzzy algebra, I, Univ. of Delhi, Publ. Division, 1993.##[7] M. Mashinchi and M. Mukaidono, A classication of fuzzy subgroups, Ninth Fuzzy System##Symposium, Sapporo, Japan, (1992), 649652.##[8] M. Mashinchi and M. Mukaidono, On fuzzy subgroups classication, Research Report of Meiji##Univ., 9 (1993), 3136.##[9] J. N. Mordeson, Invariants of fuzzy subgroups, Fuzzy Sets and Systems, 63 (1994), 8185.##[10] J. N. Mordeson, N. Kuroki and D. S. Malik, Fuzzy semigroups, Springer Verlag, Berlin, 2003.##[11] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups, I, Fuzzy Sets and##Systems, 123 (2001), 259264.##[12] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups, II, Fuzzy Sets and##Systems, 136 (2003), 93104.##[13] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups, III, Int. J. Math. Sci.,##36 (2003), 23032313.##[14] V. Murali and B. B. Makamba, Counting the number of fuzzy subgroups of an abelian group##of order pnqm, Fuzzy Sets and Systems, 144 (2004), 459470. ##[15] V. Murali and B. B. Makamba, Fuzzy subgroups of nite abelian groups, FJMS, 14 (2004),##[16] S. Ngcibi, V. Murali and B. B. Makamba, Fuzzy subgroups of rank two abelian pgroup,##Iranian Journal of Fuzzy Systems, 7 (2010), 149153.##[17] R. Schmidt, Subgroup lattices of groups, de Gruyter Expositions in Mathematics, de Gruyter,##Berlin, 14 (1994).##[18] R. P. Stanley, Enumerative combinatorics, II, Cambridge University Press, Cambridge, 1999.##[19] M. Suzuki, Group theory, I, II, Springer Verlag, Berlin, (1982, 1986).##[20] M. Stefanescu and M. Tarnauceanu, Counting maximal chains of subgroups of nite nilpotent##groups, Carpathian J. Math., 25 (2009), 119127.##[21] M. Tarnauceanu, Groups determined by posets of subgroups, Ed. Matrix Rom, Bucuresti,##[22] M. Tarnauceanu, The number of fuzzy subgroups of nite cyclic groups and Delannoy num##bers, European J. Combin., doi: 10.1016/j.ejc.2007.12.005, 30 (2009), 283287.##[23] M. Tarnauceanu, Distributivity in lattices of fuzzy subgroups, Information Sciences, doi:##10.1016/j.ins.2008.12.003, 179 (2009), 11631168.##[24] M. Tarnauceanu and L. Bentea, On the number of fuzzy subgroups of nite abelian groups,##Fuzzy Sets and Systems, doi: 10.1016/j.fss.2007.11.014, 159 (2008), 10841096.##[25] M. Tarnauceanu and L. Bentea, A note on the number of fuzzy subgroups of nite groups,##Sci. An. Univ. "Al.I. Cuza" Iasi, Math., 54 (2008), 209220.##[26] I. Tomescu, Introduction to combinatorics, Collet's Publishers Ltd., London, 1975.##[27] A. C. Volf, Counting fuzzy subgroups and chains of subgroups, Fuzzy Systems & Articial##Intelligence, 10 (2004), 191200.##[28] A. Weinberger, Reducing fuzzy algebra to classical algebra, New Math. Natur. Comput., 1##(2005), 2764.##[29] Y. Zhang and K. Zou, A note on an equivalence relation on fuzzy subgroups, Fuzzy Sets and##Systems, 95 (1998), 243247.##]
SOME FIXED POINT THEOREMS IN LOCALLY CONVEX
TOPOLOGY GENERATED BY FUZZY NNORMED SPACES
SOME FIXED POINT THEOREMS IN LOCALLY CONVEX
TOPOLOGY GENERATED BY FUZZY NNORMED SPACES
2
2
The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy nnormed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy nnormed spaces. Also we givesome remarks in locally convex topology generated by fuzzy nnormed spaces.
1
The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy nnormed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy nnormed spaces. Also we givesome remarks in locally convex topology generated by fuzzy nnormed spaces.
43
54
S. K.
Elagan
S. K.
Elagan
Mathematics and statistics Department, Faculty of Science, Taif Uni
versity (P.O.888), Zip Code 21974, Kingdom of Saudi Arabia (KSA) and Department of
Mathematics, Faculty of Science, Menofiya University, Shebin Elkom, Egypt
Mathematics and statistics Department, Faculty
Egypt
sayed khalil2000@yahoo.com
M. R.
Segi Rahmat
M. R.
Segi Rahmat
School of Applied Mathematics, University of Nottingham Malaysia
Campus, Jalan Broga, 43500, Semenyih, Selangor D.E, Malaysia
School of Applied Mathematics, University
Malaysia
Mohd.Rafi@nottingham.edu.my
Fuzzy nnormed spaces
nseminorm
Fixed points
[[1] C. Alaca, A new perspective to the mazurulamproblem in 2fuzzy 2normed linear spaces,##Iranian Journal of Fuzzy Systems, in press.##[2] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,##11(3) (2003), 687705.##[3] S. Berberian, Lectures in functional analsysis and operator theory, SpringerVerlag, New##York, 1974.##[4] S. C. Chang and J. N. Mordesen, Fuzzy linear operators and fuzzy normed linear spaces,##Bull. Calcutta Math. Soc., 86(5) (1994), 429436.##[5] C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and systems, 48(2)##(1992), 239248.##[6] C. Felbin, The completion of a fuzzy normed linear space, J. Math. Anal. Appl., 174(2)##(1993), 428440.##[7] C. Felbin, Finite dimensional fuzzy normed linear space. II., J. Anal., 7 (1999), 117131.##[8] S. Gahler, Untersuchungen uber verallgemeinerte mmetrische Raume, I, II, III., Math.##Nachr., 40 (1969), 165189.##[9] H. Gunawan and M. Mashadi, On nnormed spaces, Int. J. Math. Math. Sci., 27(10) (2001),##[10] A. K. Katsaras, Fuzzy topological vector spaces. II., Fuzzy Sets and Systems, 12(2) (1984),##[11] S. S. Kim and Y. J. Cho, Strict convexity in linear n normed spaces, Demonstratio Math.,##29(4) (1996), 739744.##[12] S. V. Krish and K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and##Systems, 63(2) (1994), 207217.##[13] R. Malceski, Strong nconvex nnormed spaces, Math. Bilten No., 21 (1997), 81102.##[14] A. Misiak, ninner product spaces, Math. Nachr., 140 (1989), 299319. ##[15] A. Narayanan and S. Vijayabalaji, Fuzzy n normed linear spaces, Int. J. Math. Math. Sci.,##27(24) (2005), 39633977.##[16] R. Rado, A theorem on innite series, J. Lond. Math. Soc., 35 (1960), 273276.##[17] M. R. S. Rahmat, Fixed point theorems on fuzzy inner product spaces, Mohu Xitong yu##Shuxue, Fuzzy Systems and Mathematics. Nat. Univ. Defense Tech., Changsha, 22(3) (2008),##[18] G. S. Rhie, B. M. Choi and D. S. Kim, On the completeness of fuzzy normed linear spaces,##Math. Japon., 45(1) (1997), 3337.##[19] A. Smith, Convergence preserving function: an alternative discussion, Amer. Math. Monthly,##96 (1991), 831833.##[20] S. Vijayabalaji and N. Thilligovindan, Complete fuzzy nnormed space, J. Fund. Sciences,##Available Online at www.ibnusina.utm.my/jfs, 3 (2007), 119126.##[21] G. Wildenberg, Convergence preserving functions, Amer. Math. Monthly, 95 (1988), 542544.##]
Fuzzy $h$ideal of Matrix Hemiring $S_{2}=left(
begin{array}{cc}
R & Gamma
S & L
end{array}
right)$
Fuzzy $h$ideal of Matrix Hemiring $S_{2}=left(
begin{array}{cc}
R & Gamma
S & L
end{array}
right)$
2
2
The purpose of this paper is to study matrix hemiring $S_{2}$ via fuzzy subsets and fuzzy $h$ideals.
1
The purpose of this paper is to study matrix hemiring $S_{2}$ via fuzzy subsets and fuzzy $h$ideals.
55
70
S. K.
Sardar
S. K.
Sardar
Department of Mathematics, Jadavpur University, Kolkata, India
Department of Mathematics, Jadavpur University,
India
sksardarjumath@gmail.com
D.
Mandal
D.
Mandal
Department of Mathematics, Jadavpur University, Kolkata, India
Department of Mathematics, Jadavpur University,
India
dmandaljumath@gmail.com
B.
Davvaz
B.
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University,
India
davvaz@yazduni.ac.ir
$Gamma$hemiring
Fuzzy $h$ideal
$h$hemiregular
Matrix hemiring
Operator hemirings
[bibitem{B} Y. Bingxue, {it Fuzzy semiideal and generalized fuzzy quotient ring}, Iranian Journal of Fuzzy Systems, {bf 5(2)} (2008), 8792. ##bibitem{D1} B. Davvaz and P. Corsini, {it On $(alpha,beta)$fuzzy $Hsb v$ideals of $Hsb v$rings}, Iranian Journal of Fuzzy Systems, {bf5(2)} (2008), 3547. ##bibitem{D2} B. Davvaz, {it Fuzzy hyperideals in ternary semihyperrings}, Iranian Journal of Fuzzy Systems, {bf6(4)} (2009), 2136. ##bibitem{Dudek} W. A. Dudek, M. Shabir and R. Anjum, {it Characterization of hemirings by their $h$ideals}, Computer Mathematics with Applications, {bf 59} (2010), 31673179.##bibitem{re:Dutta} T. K. Dutta and S. K. Sardar, {it On the operator semirings of a##$Gamma$semiring}, Southeast Asian Bull. Math.,##{bf 26} (2002), 203213. ##bibitem{Golan} J. S. Golan, {it Semirings and their applications}, Kluwer Academic##Publishers, 1999. ##bibitem{Henriksen} M. Henriksen, {it Ideals in semirings with commutative addition},##Am. Math. Soc. Notices, {bf6} (1958), 321. ##bibitem{Iizuka} K. Iizuka,{it On the Jacobson radical of semiring}, Tohoku Math. J., {bf 11(2)}##(1959), 409421. ##bibitem{J} I. Jahan, {it Embedding of the lattice of ideals of a ring into its lattice of fuzzy ideals}, Iranian Journal of Fuzzy Systems, {bf 6(3)} (2009), 6571. ##bibitem{YBjun} Y. B. Jun, M. A. "{O}zt"{u}rk and S. Z. Song, {it On Fuzzy $h$ideals in##hemiring}, Information Sciences, {bf 162} (2004), 211226. ##bibitem{LaTorre} D. R. La Torre, {it On $h$ideals and $k$ideals in hemirings}, Publ. Math. Debrecen,##{bf12} (1965), 219226. ##bibitem{Xma2} X. Ma and J. Zhan, {it Fuzzy $h$ideals in $h$hemiregular and $h$simple $Gamma$hemirings}, Neural Comput. Applic., {bf 19} (2010), 477485. ##bibitem{Rao} M. M. K. Rao, {it $Gamma$semirings1}, Southeast Asian Bull. of Math.,##{bf 19} (1995), 4954. ##bibitem{Saha} B. C. Saha and S. K. Sardar, {it On semiring $left(## begin{array}{cc}## R & Gamma ## S & L ## end{array}## right)##$ and morita context}, Int. J. Alg., {bf4} (2010), 303315. ##bibitem{Saha2}S. K. Sardar and B. C. Saha, {it On nobusawa gamma semirings}, Universitatea Din Bacaau Studii Si Cercetari Stiintifice, Seria: Mathematica, {bf 18} (2008), 283306. ##bibitem{Sardar} S. K. Sardar and D. Mandal, {it Fuzzy $h$ideals in $Gamma$hemiring}, Int. J. Pure. Appl.##Math., {bf56} (2009), 439450. ##bibitem{corresponding} S. K. Sardar, D. Mandal and B. Davvaz, {it Fuzzy $h$ideal in $Gamma$hemiring and its operator hemirings}, submitted. ##bibitem{Regularity} S. K. Sardar and D. Mandal, {it On fuzzy $h$ideals in hregular $Gamma$hemirings and hduo $Gamma$hemirings}, General Mathematics Notes, to appear. ##bibitem{Yin} Y. Yin and H. Li, {it The characterization of $h$hemiregular hemirings and $h$intrahemiregular hemirings}, Information Sciences, {bf178} (2008), 34513464.##bibitem{Yin2} Y. Yin, X. Huang, D. Xu and F. Li, {it The characterization of $h$semisimple hemirings}, Int. J. Fuzzy Systems, {bf 11} (2009), 116122.##bibitem{Zhan} J. Zhan and W. A. Dudek, {it Fuzzy $h$ideals of hemirings},##Information sciences, {bf 177} (2007), 876886. ##bibitem{Z} J. Zhan, Y. B. Jun and B. Davvaz, {it On $(in,invee q)$fuzzy ideals of BCIalgebras}, Iranian Journal of Fuzzy Systems, {bf 6(1)} (2009), 8194.##]
ATANASSOV'S INTUITIONISTIC FUZZY GRADE OF I.P.S.
HYPERGROUPS OF ORDER LESS THAN OR EQUAL TO 6
ATANASSOV'S INTUITIONISTIC FUZZY GRADE OF I.P.S.
HYPERGROUPS OF ORDER LESS THAN OR EQUAL TO 6
2
2
In this paper we determine the sequences of join spaces and Atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.
1
In this paper we determine the sequences of join spaces and Atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.
71
97
B.
Davvaz
B.
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University,
Iran
davvaz@yazduni.ac.ir
E.
Hassani Sadrabadi
E.
Hassani Sadrabadi
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University,
Iran
hassanipma@yahoo.com
I.
Cristea
I.
Cristea
University of Udine, Via delle Scienze 206, 33100 Udine, Italy
University of Udine, Via delle Scienze 206,
Italy
irinacri@yahoo.co.uk
Fuzzy set
Atanassov's intuitionistic fuzzy set
i.p.s. hypergroup
Fuzzy grade
Join space
[[1] R. Ameri and H. Hedayati, Fuzzy isomorphism and quotient of fuzzy subpolygroups, Quasi##groups and Related Systems, 13 (2005), 175184.##[2] R. Ameri and H. Hedayati, On fuzzy closed, invertible and re##exive subsets of hypergroups,##Italian J. Pure Appl. Math., 22 (2007), 95114.##[3] R. Ameri and M. M. Zahedi, Hypergroup and join space induced by a fuzzy subset, Pure##Math. App., 8 (1997), 155168.##[4] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 8796.##[5] G. Chowdhury, Fuzzy transposition hypergroups, Iranian Journal of Fuzzy Systems, 6(3)##(2009), 3752.##[6] P. Corsini, Prolegomena of hypergroups theory, Aviani Editore, 1993.##[7] P. Corsini, Sugli ipergruppi canonici niti con identita parziali scalari, Rend. Circolo Mat.##di Palermo, Serie II, Tomo, XXXVI (1987), 205219.##[8] P. Corsini, (i:p:s:) Ipergruppi di ordine 6, Ann. Sc. de I'Univ. Blaise Pascal, ClermontFerrand##II, 24 (1987), 81104.##[9] P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull.##Math., 27 (2003), 221229.##[10] P. Corsini, Join spaces, power sets, fuzzy sets, In: Proc. Fifth International Congress on##A.H.A. 1993, Iasi, Romania, Hadronic Press, (1994), 4552.##[11] P. Corsini and I. Cristea, Fuzzy grade of i:p:s: hypergroups of order less or equal to 6, Pure##Math Appl., 14(4) (2003), 275288.##[12] P. Corsini and I. Cristea, Fuzzy grade of i:p:s: hypergroups of order 7, Iranian Journal of##Fuzzy Systems, 1 (2004), 1532.##[13] P. Corsini and V. Leoreanu, Join spaces associated with fuzzy sets, J. Combin. Inform. Syst.##Sci., 20 (1995), 293303.##[14] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics,##Kluwer Academic Publishers, Dordercht, 2003.##[15] P. Corsini and V. LeoreanuFotea, On the grade of a sequence of fuzzy sets and join spaces##determined by a hypergraph, Southeast Asian Bull. Math., 34 (2010), 231242.##[16] P. Corsini, V. LeoreanuFotea and A. Iranmanesh, On the sequence of hypergroups and mem##bership functions determined by a hypergraph, J. Mult.Valued Logic Soft Comput., 14 (2008)##[17] I. Cristea, About the fuzzy grade of the direct product of two hypergroupoids, Iranian Journal##of Fuzzy Systems, 7 (2010), 95108.##[18] I. Cristea and B. Davvaz, Atanassov's intuitionistic fuzzy grade of hypergroups, Information##Sciences, 180 (2010), 15061517. ##[19] B. Davvaz, Fuzzy hyperideals in ternary semihyperrings, Iranian Journal of Fuzzy Systems,##6(4) (2009), 2136.##[20] B. Davvaz, Fuzzy Hvgroups, Fuzzy Sets and Systems, 101 (1999), 191195.##[21] B. Davvaz and P. Corsini, On (; )fuzzy Hvideals of Hvrings, Iranian Journal of Fuzzy##Systems, 5(2) (2008), 3547.##[22] B. Davvaz and V. LeoreanuFotea, Hyperring theory and applications, Hadronic Press, Inc,##115, Palm Harber, USA, 2007.##[23] B. Davvaz, P. Corsini and V. LeoreanuFotea, Atanassov's intuitionistic (S; T)fuzzy nary##subhypergroups and their properties, Information Sciences, 179 (2009), 654666.##[24] M. Horry and M. M. Zahedi, Hypergroups and general fuzzy automata, Iranian Journal of##Fuzzy Systems, 6(2) (2009), 6174.##[25] O. Kazanc, S. Yamak and B. Davvaz, On nary hypergroups and fuzzy nary homomorphism,##Iranian Journal of Fuzzy Systems, 8(1) (2011), 117.##[26] J. Mittas, Hypergroupes canoniques, values et hypervalues. Hypergroupes fortement et su##perieurement canoniques, Bull. Soc. Math. Greece, 23 (1982), 5588.##[27] F. Marty, Sur une generalization de la notion de group, 8th Congress Math. Scandenaves,##Stockholm, (1934), 4549.##[28] W. Prenowitz and J. Jantosciak, Geometries and join spaces, J. Reine und Angew Math.,##257 (1972), 100128.##[29] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512517.##[30] M. Stefanescu and I. Cristea, On the fuzzy grade of hypergroups, Fuzzy Sets and Systems,##159 (2008), 10971106.##[31] T. Vougiouklis, Hyperstructures and their Representations, Hadronic Press, Inc, 115, Palm##Harber, USA, 1994.##[32] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##]
More General Forms of $(alpha, beta )$fuzzy Ideals of Ordered Semigroups
More General Forms of $(alpha, beta )$fuzzy Ideals of Ordered Semigroups
2
2
This paper consider the general forms of $(alpha,beta)$fuzzyleft ideals (right ideals, biideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$left ideals (right ideals, biideals, interiorideals) and some related properties are investigated. Thecharacterization of regular ordered semigroups in terms of$(in_{gamma},ivq)$fuzzy left (right) ideals,$(in_{gamma},ivq)$fuzzy biideals and$(in_{gamma},ivq)$fuzzy interior ideals is also investigated.
1
This paper consider the general forms of $(alpha,beta)$fuzzyleft ideals (right ideals, biideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$left ideals (right ideals, biideals, interiorideals) and some related properties are investigated. Thecharacterization of regular ordered semigroups in terms of$(in_{gamma},ivq)$fuzzy left (right) ideals,$(in_{gamma},ivq)$fuzzy biideals and$(in_{gamma},ivq)$fuzzy interior ideals is also investigated.
99
113
Yunqiang
Yin
Yunqiang
Yin
State Key Laboratory, Breeding Base of Nuclear Resources and
Environment, East China Institute of Technology, Nanchang, 330013, China
State Key Laboratory, Breeding Base of Nuclear
China
yunqiangyin@gmail.com
Young Bae
Jun
Young Bae
Jun
Department of Mathematics Education (and RINS), Gyeongsang Na
tional University, Chinju 660701, Korea
Department of Mathematics Education (and
Korea
skywine@gmail.com
Zhihui
Yang
Zhihui
Yang
School of Mathematics and Information Sciences, East China Institute
of Technology, Fuzhou, Jiangxi 344000, China
School of Mathematics and Information Sciences,
Korea
zhhyang75@gmail.com
Ordered semigroups
$(alpha
beta)$fuzzy left (right) ideals
$(in_{gamma}
ivq)$fuzzy biideals
ivq)$fuzzy interior ideals
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LFUZZIFYING TOPOLOGICAL GROUPS
LFUZZIFYING TOPOLOGICAL GROUPS
2
2
The main purpose of this paper is to introduce a concept of$L$fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$fuzzifying neighborhood structure of the unit is given. It isshown that the category of $L$fuzzifying topological groups$L${bf FYTPG} is topological over the category of groups {bf GRP}with respect to the forgetful functor. As an application, theconclusion that the product of $L$fuzzifying topological groups isalso an $L$fuzzifying topological group is proved. Finally, it isproved the forgetful functor preserves the product.
1
The main purpose of this paper is to introduce a concept of$L$fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$fuzzifying neighborhood structure of the unit is given. It isshown that the category of $L$fuzzifying topological groups$L${bf FYTPG} is topological over the category of groups {bf GRP}with respect to the forgetful functor. As an application, theconclusion that the product of $L$fuzzifying topological groups isalso an $L$fuzzifying topological group is proved. Finally, it isproved the forgetful functor preserves the product.
115
132
Shaiyan
Zhang
Shaiyan
Zhang
School of Science, Southern Yangtze University, Wuxi, Jiangsu
214122, People0 s Republic of China
School of Science, Southern Yangtze University,
China
syzhang79@126.com
Conghua
Yan
Conghua
Yan
school of Math. Sciences, Nanjing Normal Uni
versity, Nanjing Jiangsu 210046, People0 s Republic of China
school of Math. Sciences, Nanjing Normal
China
chyan@njnu.edu.cn
Lfuzzifying topological groups
Lfuzzifying topology
Lfuzzifying neighborhood structure
Category
[[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, John Wiley &##Sons, 1990.##[2] D. H. Foster, Fuzzy topological groups, J. Math. Anal. Appl., 67 (1979), 549564.##[3] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, A##compendium of continuous lattices, Springer, Berlin, 1980.##[4] E. Hewitt and K. Stromberg, Real and abstract analysis, Springer, Berlin, 1975.##[5] U. Hohle, Characterization of Ltopologies by Lvalued neighborhoods, In S. E. Rodabaugh,##E. P. Klement, U. Hohle, eds., Applications of Category Theory to Fuzzy Subsets, Kluwer##Academic Publishers, (1999), 389432.##[6] X. Luo and J. Fang, Fuzzifying closure systems and closure operators, Iranian Journal of##Fuzzy Systems, 8(1) (2011), 7794.##[7] J. L. Ma and C. H. Yu, Fuzzy topological groups, Fuzzy Sets and Systems, 12 (1984), 289299.##[8] S. E. Rodabaugh, Powerset operator foundations for pointset latticetheoretic (POSLAT)##fuzzy set theories and topologies, Questions Mathematicae, 20 (1997), 463530.##[9] J. Z. Shen, Fuzzifying topological groups based on completely distributive residuated lattice##valued logic (I), Proceedings of IEEE 22th International Symposium on MultipleValued##Logic, Sendai, (1992), 198205.##[10] J. Z. Shen, Topological groups based on continuous valued logic [0,1], Journal of Engineering##Math., 114 (1994), 5264.##[11] J. Z. Shen, Fuzzifying topological groups(II), [J]. J. Jiangxi Normal Univ., in Chinese, 1##(1994), 7280.##[12] J. Z. Shen, Fuzzifying topological groups based on completely distributive residuated lattice##valued logic (II), Information Sciences, 80 (1994), 319339.##[13] F. G. Shi and H. Y. Li, Almost S{Compactness in Ltoplogical Spaces, Iranian Journal of##Fuzzy Systems, 5(3) (2008), 3144.##[14] W. Yao, On Lfuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6(1) (2009),##[15] M. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39 (1991), 303321.##[16] M. Ying, A new approach for fuzzy topology (III), Fuzzy Sets and Systems, 55 (1993),##[17] C. H. Yu and J. L. Ma, Fuzzy topological groups I, J. Northeastern Normal Univ., in Chinese,##3 (1982), 1318.##[18] C. H. Yu and J. L. Ma, Lfuzzy topological groups, Fuzzy Sets and Systems, 47 (1992),##[19] D. Zhang, On the re##ectivity and core##ectivity of Lfuzzifying topological spaces in L##topological spaces, Acta Math. Sin. (Engl.Ser), 18(1) (2002), 5568.##[20] D. Zhang, Lfuzzifying topologies as Ltopologies, Fuzzy Sets and Systems, 125 (2002),##]
FUZZY INTEGRAL OF MEASURABLE MULTIFUNCTIONS
FUZZY INTEGRAL OF MEASURABLE MULTIFUNCTIONS
2
2
We study a fuzzy type integral for measurable multifunctions with respect to a fuzzy measure. Some classical properties and convergence theorems are presented.
1
We study a fuzzy type integral for measurable multifunctions with respect to a fuzzy measure. Some classical properties and convergence theorems are presented.
133
140
Anca
Croitoru
Anca
Croitoru
"Al.I. Cuza" University, Faculty of Mathematics, Bd. Carol I, No.
11, Iasi, 700506, Romania
"Al.I. Cuza" University, Faculty of Mathematics,
Romania
croitoru@uaic.ro
Fuzzy integral
Fuzzy measure
Measurable multifunction
[[1] R. J. Aumann, Integrals of setvalued maps, J. Math. Anal. Appl., 12 (1965), 112.##[2] G. Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble), 5 (19531954), 131292.##[3] A. Croitoru, Setnorm continuity of set multifunctions, ROMAI Journal, 6 (2010), 4756 .##[4] A. Croitoru, A. Gavrilut, N. E. Mastorakis and G. Gavrilut, On dierent types of nonadditive##set multifunctions, WSEAS Transactions on Mathematics, 8 (2009), 246257.##[5] G. Debreu, Integration of correspondences, Proc. 5th Berkely Symposium on Math. Stat.##Prob. II, Part. I, (1967), 351372.##[6] L. Drewnowski, Topological rings of sets, continuous set functions. Integration, I, II, III,##Bull. Acad. Polon. Sci. Ser. Math. Astron. Phys., 20 (1972), 269286.##[7] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Academic Press,##New York, 1980. ##[8] N. Dunford and J. Schwartz, Linear operators I. general theory, Interscience, New York,##[9] A. Gavrilut, A Gould type integral with respect to a multisubmeasure, Math. Slovaca, 58##(2008), 120.##[10] A. Gavrilut, The general Gould type integral with respect to a multisubmeasure, Math. Slovaca,##60(3) (2010), 289318.##[11] A. Gavrilut and A. Croitoru, Nonatomicity for fuzzy and nonfuzzy set multifunctions, Fuzzy##Sets and Systems, 160 (2009), 21062116.##[12] C. Guo and D. Zhang, On setvalued fuzzy measures, Information Sciences, 160 (2004), 1325.##[13] S. Hu and N. S. Papageorgiou, Handbook of multivalued analysis, Kluwer Acad. Publ., Dordrecht,##[14] L. C. Jang and J. S. Kwon, On the representation of Choquet integrals of setvalued functions##and null sets, Fuzzy Sets and Systems, 112 (2000), 233239.##[15] F. Merghadi and A. Aliouche, A related xed point theorem in n fuzzy metric spaces, Iranian##Journal of Fuzzy Systems, 7(3) (2010), 7386.##[16] E. Pap, Nulladditive set functions, Kluwer Academic Publishers, Dordrecht, 1995.##[17] A. M. Precupanu, On the set valued additive and subadditive set functions, An. St. Univ.##"Al.I. Cuza" Iasi, 29 (1984), 4148.##[18] A. Precupanu and A. Croitoru, A Gould type integral with respect to a multimeasure. I, An.##St. Univ. "Al.I. Cuza" Iasi, 48 (2002), 165200.##[19] A. Precupanu, A. Gavrilut and A. Croitoru, A fuzzy Gould type integral, Fuzzy Sets and##Systems, 161 (2010), 661680.##[20] H. Radstrom, An embedding theorem for spaces of convex sets, Proc. A.M.S., 3 (1952), 151##[21] D. A. Ralescu and M. Sugeno, Fuzzy integral representation, Fuzzy Sets and Systems, 84##(1996), 127133.##[22] H. RomanFlores, A. FloresFranulic and Y. ChalcoCano, The fuzzy integral for monotone##functions, Applied Mathematics and Computation, 185 (2007), 492498.##[23] C. Stamate, Vector fuzzy integral, Recent Advances in Neural Network, Fuzzy Systems and##Evolutionary Computing, Proceeding of the 11th WSEAS International Conference on Fuzzy##Systems (FS'10), Iasi, Romania, June 1315, (2010), 221224.##[24] M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of##Technology, 1974.##[25] H. Suzuki, Atoms of fuzzy measures and fuzzy integrals, Fuzzy Sets and Systems, 41 (1991),##[26] S. M. Vaezpour and F. Karini, tBest approximation in fuzzy normed spaces, Iranian Journal##of Fuzzy Systems, 5(2) (2008), 9399.##[27] Z. Wang and G. J. Klir, Fuzzy measure theory, Plenum Press, New York, 1992.##[28] G. F. Wen, F. G. Shi and H. Y. Li, Almost Scompactness in Ltopological spaces, Iranian##Journal of Fuzzy Systems, 5(3) (2008), 3144.##[29] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##[30] D. Zhang and C. Guo, Fuzzy integrals of setvalued mappings and fuzzy mappings, Fuzzy##Sets and Systems, 75 (1995), 103109.##]
ON THE FUZZY DIMENSIONS OF FUZZY VECTOR SPACES
ON THE FUZZY DIMENSIONS OF FUZZY VECTOR SPACES
2
2
In this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by Shi and Huang, is equivalent to the family of its bases de ned by P. Lubczonok. Secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however, the converse is not true. Finally, fuzzy dimension of direct sum is considered, for a nite number of fuzzy vector spaces and it is proved that fuzzy dimension of their direct sum is equal to the sum of fuzzy dimensions of fuzzy vector spaces.
1
In this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by Shi and Huang, is equivalent to the family of its bases de ned by P. Lubczonok. Secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however, the converse is not true. Finally, fuzzy dimension of direct sum is considered, for a nite number of fuzzy vector spaces and it is proved that fuzzy dimension of their direct sum is equal to the sum of fuzzy dimensions of fuzzy vector spaces.
141
150
ChunE
Huang
ChunE
Huang
Biochemical engineering college, Beijing Union University, Beijing
100023, P. R. China
Biochemical engineering college, Beijing
China
hce 137@163.com, hchune@yahoo.com
FuGui
Shi
FuGui
Shi
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing 100081, P. R. China
Department of Mathematics, School of Science,
China
fuguishi@bit.edu.cn, f.g.shi@263.net
Fuzzy vector space
Fuzzy basis
Fuzzy dimension
Direct sum
[[1] K. S. Abdulkhalikov, The dual of a fuzzy subspace, Fuzzy Sets and Systems, 82 (1996),##[2] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J.##Math. Anal. Appl., 58 (1977), 135146.##[3] R. Kumar, On the dimension of a fuzzy subspace, Fuzzy Sets and Systems, 54 (1993), 229##[4] R. Lowen, Convex fuzzy sets, Fuzzy Sets and Systems, 3 (1980), 291310.##[5] G. Lubczonok and V. Murali, On ##ags and fuzzy subspaces of vector spaces, Fuzzy Sets and##Systems, 125 (2002), 201207.##[6] P. Lubczonok, Fuzzy vector spaces, Fuzzy Sets and Systems, 38 (1990), 329343.##[7] F. G. Shi, A new approach to the fuzzication of matroids, Fuzzy Sets and Systems, 160##(2009), 696705.##[8] F. G. Shi and C. E. Huang, Fuzzy bases and the fuzzy dimension of fuzzy vector spaces,##Mathematical Communications, 15(2) (2010), 303310.##[9] L. Wang and F. G. Shi, Characterization of Lfuzzifying matroids by Lfuzzifying closure##operators, Iranian Journal of Fuzzy Systems, 7(1) (2010), 4758.##[10] L. A. Zadeh, A computational approach to fuzzy quantiers in natural languages, Comput.##Math. Appl., 9 (1983), 149184.##]
ON COMPACTNESS AND GCOMPLETENESS IN FUZZY
METRIC SPACES
ON COMPACTNESS AND GCOMPLETENESS IN FUZZY
METRIC SPACES
2
2
In [Fuzzy Sets and Systems 27 (1988) 385389], M. Grabiec in troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case, for which we present an example of a compact fuzzy metric space that is not complete in Grabiecs sense. On the other hand, Grabiec used a notion of compactness to obtain a fuzzy version of Edelstein s contraction principle. We present here a generalized version of Grabiecs version of the Edelstein xed point theorem and dierent interesting facts on the topology of fuzzy metric spaces.
1
In [Fuzzy Sets and Systems 27 (1988) 385389], M. Grabiec in troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case, for which we present an example of a compact fuzzy metric space that is not complete in Grabiecs sense. On the other hand, Grabiec used a notion of compactness to obtain a fuzzy version of Edelstein s contraction principle. We present here a generalized version of Grabiecs version of the Edelstein xed point theorem and dierent interesting facts on the topology of fuzzy metric spaces.
151
158
Pedro
Tirado
Pedro
Tirado
Instituto Universitario de Matematica Pura y Aplicada, Universidad
Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Instituto Universitario de Matematica Pura
Spain
pedtipe@mat.upv.es
Fuzzy metric space
Cauchy sequence
Gcompleteness
Compactness
Fixed point theorem
[[1] I. Altun, Some xed point theorems for single and multi valued mappings on ordered non##archimedean fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 7(1) (2010), 9196.##[2] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,##64 (1994), 395399.##[3] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385389.##[4] V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Sys##tems, 115 (2000), 485489.##[5] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11##(1975), 336344.##[6] D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems,##144 (2004), 431439.##[7] D. Mihet, Fuzzy quasimetric versions of a theorem of Gregori and Sapena, Iranian Journal##of Fuzzy Systems, 7(1) (2010), 5964. ##[8] S. Romaguera, A. Sapena and P. Tirado, The Banach xed point theorem in fuzzy quasi##metric spaces with application to the domain of words, Topology Appl., 154 (2007), 2196##[9] R. Saadati, S. Sedghi and H. Zhou, A common xed point theorem for weakly commuting##maps in Lfuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(1) (2008), 4754.##[10] A. Sapena, A contribution to the study of fuzzy metric spaces, Appl. Gen. Topology, 2 (2001),##[11] B. Schweizer and A. Sklar, Statistical metric spaces, Pacic J. Math., 10 (1960), 314334.##[12] R. Vasuki and P. Veeramani, Fixed point theorems and Cauchy sequences in fuzzy metric##spaces, Fuzzy Sets and Systems, 135 (2003), 415417.##]
Persiantranslation vol. 9, no. 4, October 2012
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