2008
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Cover Vol.5 No.1, February 2008
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THE pCENTER PROBLEM ON FUZZY NETWORKS AND
REDUCTION OF COST
THE pCENTER PROBLEM ON FUZZY NETWORKS AND REDUCTION OF COST
2
2
Here we consider the
pcenter problem on different types of fuzzy
networks. In particular, we are interested in the networks with interval and
triangular fuzzy arc lengths and vertexweights. A methodology to obtain the
best satisfaction level of the decision maker who wishes to reduce the cost
within the tolerance limits is proposed. Illustrative examples are provided.
1
Here we consider the pcenter problem on different types of fuzzy
networks. In particular, we are interested in the networks with interval and
triangular fuzzy arc lengths and vertexweights. A methodology to obtain the
best satisfaction level of the decision maker who wishes to reduce the cost
within the tolerance limits is proposed. Illustrative examples are provided.
1
26
Sk. Md. Abu
Nayeem
Sk. Md. Abu
Nayeem
Department of Mathematics, Jhargram Raj College, Jhargram,
West Bengal, 721 507, India
Department of Mathematics, Jhargram Raj College,
India
nayeemsma@gmail.com
Madhumangal
Pal
Madhumangal
Pal
Madhumangal Pal, Department of Applied Mathematics with Oceanology and Computer
Programming, Vidyasagar University, Midnapore, West Bengal, 721 102, India
Madhumangal Pal, Department of Applied Mathematic
India
madhumangal@lycos.com
Fuzzy sets
Location
Networks
[[1] A. Alkhedhairi and S. Salhi,Enhancement to two exact algorithms for solving the vertex ##pcenter problem, Journal of Mathematical Modelling and Algorithms, 4(2) (2005), 129147. ##[2] D. Bespamyatnikh, B. Bhattacharya, M. Keil, D. Kirkpatric and D. Segal,Efficient algorithms ##for centers and medians in interval and circulararc graphs, Networks, 39 (1979),144152. ##[3] M. J. Can´os, C. Ivorra and V. Liern,An exact algorithm for the fuzzy pmedian problem, ##European Journal of Operational Research,116 (1999), 8086. ##[4] M. J. Can´os, C. Ivorra and V. Liern,The fuzzy pmedian problem : a global analysis of the ##solutions, European Journal of Operational Research, 130 (2001), 430436. ##[5] S. Chanas, M. Delgado, J. L. Verdegay and M. A. Vila,Fuzzy optimal flow on a imprecise ##structures, European Journal of Operational Research, 83 (1995), 568580. ##[6] S. Chanas and W. Kolodziejczyk,Maximum flow in a network with fuzzy arc capacities, ##Fuzzy Sets and Systems,8 (1982), 165173. ##[7] S. Chanas and W. Kolodziejczyk,Real valued flows in a network with fuzzy arc capacities, ##Fuzzy Sets and Systems,13 (1984), 139151. ##[8] P. T. Chang and E. S. Lee,Ranking fuzzy sets based on the concept of existence, Computers ##and Mathematics with Applications,27 (1994), 121. ##[9] P. T. Chang and E. S. Lee,Fuzzy decision networks and deconvolution, Computers and ##Mathematics with Applications,37 (1999), 5363. ##[10] R. Chandrasekharan and A. Tamir,Polynomial bounded algorithms for locating pcenters on ##a tree, Mathematics in Programming, 22 (1982), 304315. ##[11] M. Daskin,Network and discrete location, Wiley, NewYork, 1995. ##[12] M. Delgado, J. L. Verdegay and M. A. Vila,On fuzzy tree definition, European Journal of ##Operational Research,22 (1985), 243249. ##[13] M. Delgado, J. L. Verdegay and M. A. Vila,A procedure for ranking fuzzy numbers using ##fuzzy relations, Fuzzy Sets and Systems, 26 (1988), 4962. ##[14] M. Delgado, J. L. Verdegay and M. A. Vila,On valuation and problems in fuzzy graphs : a ##general approach and some particular cases, ORSA Journal on Computing, 2 (1990), 7484. ##[15] H. Y. Handler and P. B. Mirchandani,Location on networks : theory and algorithms, MIT ##Press, Cambridge, MA, 1979. ##[16] F. Herrera and J. L. Verdegay,Three models of fuzzy integer linear programming, European ##Journal of Operational Research,83 (1995), 581593. ##[17] O. Kariv and S. L. Hakimi,An algorithmic approach to network location problems, I: the ##pcenters, SIAM Journal of Applied Mathematics, 37 (1979), 513538. ##[18] A. Kaufmann and M. M. Gupta,Introduction to fuzzy arithmetic : theory and applications, ##Van Nostrand Reinhold, New York, 1985. ##[19] P. B. Mirchandani and R. L. Francis,Discrete location theory, Wiley, New York, 1990. ##[20] N. Mledanovic, M. Labb´e and P. Hansen,Solving the pcenter problem with tabu search and ##variable neighborhood search, Networks, 42(1) (2003), 4864. ##[21] R. E. Moore,Method and application of interval analysis, SIAM, Philadelphia, 1979. ##[22] J. N. Mordeson and P. S. Nair,Fuzzy graphs and fuzzy hypergraphs, Studies in fuzzyness and ##soft computing, PhysicaVerlag, Wurzburg, 2000. ##[23] J. A. Moreno P´erez, J. M. Moreno Vega and J. L. Verdegay,Fuzzy location problems on ##networks, Fuzzy Sets and Systems, 142 (2004), 393405. ##[24] S. M. A. Nayeem and M. Pal,Genetic algorithm to solve pcenter and pradius problem on ##a network, International Journal of Computer Mathematics, 82 (2005), 541550. ##[25] S. M. A. Nayeem and M. Pal,Shortest path problem on a network with imprecise edge weight, ##Fuzzy Optimization and Decision Making,4 (2005), 293312. ##[26] S. M. A. Nayeem and M. Pal,PERT on a network with imprecise edge weight, communicated. ##[27] S. Okada and T. Soper,A shortest path problem on a network with fuzzy arc lengths, Fuzzy ##Sets and Systems,109 (2000), 129140. ##[28] F. A. ¨Ozsoy and MC¸ . Pinar,An exact algorithm for the capacitated vertex pcenter problem, ##Computers and Operations Research,33(5) (2006), 14201436. ##[29] A. Rosenfeld,Fuzzy graph, In: L. A. Zadeh, K. S. Fu, K. Tanaka and M. Shimura Eds., ##Fuzzy sets and their application to cognitive and decision processes, Academic Press, New ##York, (1975), 7997. ##[30] A. Sengupta, T. K. Pal,On comparing interval numbers, European Journal of Operational ##127 (2000), 2843. ##[31] J. K. Sengupta,Optimal decision under uncertainty, Springer, New York, 1981. ##[32] A. Tamir,Improved complexity bounds for center location problems on networks by using ##dynamic data structures, SIAM Journal of Discrete Mathematics, 1 (1988), 377396. ##[33] L. A. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338353.##]
INTELLIGENT TECHNIQUE OF CANCELING MATERNAL ECG IN
FECG EXTRACTION
INTELLIGENT TECHNIQUE OF CANCELING MATERNAL ECG IN FECG EXTRACTION
2
2
In this paper, we propose a technique of artificial intelligence called adaptive neuro fuzzy inference system (ANFIS) for canceling maternal electrocardiogram (MECG) in fetal electrocardiogram extraction (FECG).This technique is used to estimate the MECG present in the abdominal signal of a pregnant woman. The FECG is then extracted by subtracting the estimated MECG from the abdominal signal. Performance of the proposed method in terms of mean square error, signal to noise ratio is compared with neural network. Our results show that this method is a simple and powerful means for the extraction of FECG.
1
In this paper, we propose a technique of artificial intelligence called adaptive neuro fuzzy inference system (ANFIS) for canceling maternal electrocardiogram (MECG) in fetal electrocardiogram extraction (FECG).This technique is used to estimate the MECG present in the abdominal signal of a pregnant woman. The FECG is then extracted by subtracting the estimated MECG from the abdominal signal. Performance of the proposed method in terms of mean square error, signal to noise ratio is compared with neural network. Our results show that this method is a simple and powerful means for the extraction of FECG.
27
45
C.
KEZI SELVA VIJIILA
C.
KEZI SELVA VIJIILA
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING KARUNYA
UNIVERSITY, COIMBATORE, INDIA
DEPARTMENT OF ELECTRONICS AND COMMUNICATION
India
vijila_2000@yahoo.com,vijila@karunya.edu
P.
KANAGASABAPATHY
P.
KANAGASABAPATHY
DEAN MIT CAMPUS, ANNA UNIVERSITY, CHENNAL, INDIA
DEAN MIT CAMPUS, ANNA UNIVERSITY, CHENNAL,
India
pks@mail.mitindia.edu
Interference cancellation
Neuro fuzzy logic
Fetal ECG extraction
[[1]K. Assalch and H. AlNashash, A novel technique for the extraction of fetal ECG using ##polynomial networks, IEEE Transactions in Biomedical Engineering, 52 (6) (2005),11481152. ##[2]K. Assaleh, Extraction of fetal electrocardiogram using adaptive neurofuzzy inference ##systems,IEEE Transactions in Biomedical Engineering, 54(1) (2007), 5968. ##[3]M.G. Jafari, and J. A. Chambers, Fetal electrocardiogram extraction by sequential source ##separation in the wavelet domain, IEEE Transactions in Biomedical Engineering, 52( 3)(2005), 390400. ##[4]J. S. R. Jang and N. Gulley, The fuzzy logic toolbox for use with MATLAB, MA: The MathWorks Inc., 1995. ##[5]J. S. R. Jang, ANFIS: adaptive–networkbased fuzzy inference system, IEEE Transactions on Systems, Man and Cybernatics, 23(3) (1993), 665685. ##[6]J. S. R. Jang, C. T. Sun and E. Mizuatani, Neurofuzzy and soft computing, Prentice Hall International Inc., 1997. ##[7]A. Khamene and S. Negahdaripour, A new method for the extraction of fetal ECG from the composite abdominal signal ##, IEEE Transactions in Biomedical Engineering, 47(4)(2000), 507516. ##[8]L. D. Lathauwer, B. D. Moor and J. Vandewalle, Fetal electrocardiogram extraction by blind source subspace separation, IEEE Transactions in Biomedical Engineering, 47(5)(2000), 567572. ##[9]M. Martínez, E. Soria, J. Calpe, J. F. Guerrero and J. R. Magdalena GPDS, Application ##of the adaptive impulse correlated filter for recovering fetal electrocardiogram ##, Computers in Cardiology, Universitat deValència. Valencia, Spain, 2001. ##[10] C. Salustri, G. Barbati, and C. Porcaro, Fetal magnetocardiographic signals extracted ##by‘signal subspace’, blind source separation , IEEE Transactions in Biomedical Engineering, ##52 (6) (2005), 11401142. ##[11]C. K. Selva Vijila, P. Kanagasabapathy and S. Johnson, Fetal ECG extraction using softcomputing technique ##, Journal of Applied Sciences, 6(2) (2006), 251256. ##[12]V. Zarzoso and A. K. Nandi, Noninvasive fetal electrocardiogram extraction: blind separation versus adaptive noise cancellation , IEEE Transactions in Biomedical Engineering,48(1) (2001), 1218.##]
A COMMON FIXED POINT THEOREM FOR $psi$WEAKLY
COMMUTING MAPS IN LFUZZY METRIC SPACES
A COMMON FIXED POINT THEOREM FOR $psi$WEAKLY COMMUTING MAPS IN LFUZZY METRIC SPACES
2
2
In this paper, a common fixed point theorem for $psi$weakly commuting
maps in Lfuzzy metric spaces is proved.
1

47
53
R.
Saadati
R.
Saadati
Faculty of Sciences, University of Shomal, Amol, P.O. Box 731, Iran
Faculty of Sciences, University of Shomal,
Iran
rsaadati@eml.cc
S.
Sedghi
S.
Sedghi
Department of Mathematics, Islamic Azad UniversityGhaemshahr Branch,
Ghaemshar, P.O. Box 163, Iran
Department of Mathematics, Islamic Azad University
Iran
H.
Zhou
H.
Zhou
Department of Mathematics, Shijiazhuang Mechnical Engineering University,
Shijiazhuang 050003, People’s Republic of China
Department of Mathematics, Shijiazhuang Mechnical
Iran
LFuzzy contractive mapping
Complete Lfuzzy metric space
Common fixed point theorem
$psi$weakly commuting maps
[[1] H. Adibi, Y. J. Cho, D. O’Regan and R. Saadati, Common fixed point theorems in Lfuzzy ##metric spaces , Appl. Math. Comput., 182 (2006), 820828. ##[2] A. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 8796. ##[3] S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung and S. M. Kang, Coincidence point and minimization ##theorems in fuzzy metric spaces , Fuzzy Sets and Systems, 88 (1997), 119128. ##[4] Y. J. Cho, H. K. Pathak, S. M. Kang and J. S. Jung, Common fixed points of compatible ##maps of type (B) on fuzzy metric spaces, Fuzzy Sets and Systems, 93 (1998), 99111. ##[5] G. Deschrijver , C. Cornelis and E. E. Kerre,On the representation of intuitionistic fuzzy ##tnorms and tconorms , IEEE Transactions on Fuzzy Systems, 12 (2004), 4561. ##[6] G. Deschrijver and E. E Kerre,On the relationship between some extensions of fuzzy set ##theory , Fuzzy Sets and Systems, 33 (2003), 227235. ##[7] Z. K. Deng,Fuzzy pseduometric spaces, J. Math. Anal. Appl., 86 (1982), 7495. ##[8] M. A. Erceg,Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69 (1979), 205230. ##[9] A. George and P. Veeramani,On some results in fuzzy metric spaces, Fuzzy Sets and Systems, ##64(1994), 395399. ##[10] J. Goguen,Lfuzzy sets, J. Math. Anal. Appl., 18 (1967), 145174. ##[11] V. Gregori and A. Sapena,On fixed point theorem in fuzzy metric spaces, Fuzzy Sets and ##Systems,125 (2002), 245252. ##[12] O. Hadˇzi´c and E. Pap,Fixed point theory in PM spaces, Kluwer Academic Publishers, Dordrecht, ##[13] O. Hadˇzi´c and E. Pap,New classes of probabilistic contractions and applications to random ##operators, in: Y. J. Cho, J. K. Kim and S. M. Kong (Eds.), Fixed point theory and application, ##Nova Science Publishers, Hauppauge, NewYork,4 (2003), 97119. ##[14] O. Kaleva and S. Seikkala,On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), ##[15] I. Kramosil and J. Michalek,Fuzzy metric and statistical metric spaces, Kybernetica, 11 ##(1975), 326334. ##[16] D. Miheot, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, ##144(2004), 431439. ##[17] S. B. Hosseini, D. O’Regan and R. Saadati,Some results on intuitionistic fuzzy spaces, Iranian ##J. Fuzzy Systems,4 (2007), 5364. ##[18] E. Pap, O. Hadzic and R. Mesiar,A fixed point theorem in probabilistic metric spaces and ##an application, J. Math. Anal. Appl., 202 (1996), 433449. ##[19] A. Razani and M. Shirdaryazdi,Some results on fixed points in the fuzzy metric space, J. ##Appl. Math. and Computing,20 (2006), 401408. ##[20] J. Rodr´ıguez L´opez and S. Ramaguera,The Hausdorff fuzzy metric on compact sets, Fuzzy ##Sets and Systems,147 (2004), 273283. ##[21] R. Saadati,Notes to the paper “Fixed points in intuitionistic fuzzy metric spaces” and its ##generalization to Lfuzzy metric spaces, Chaos, Solitons and Fractals, 35(2008), 176180. ##[22] R. Saadati, A. Razani and H. Adibi,A Common fixed point theorem in Lfuzzy metric spaces, ##Chaos, Solitons and Fractals,33 (2007), 358363. ##[23] R. Saadati and J. H. Park,On the intuitionistic fuzzy topological spaces, Chaos, Solitons and ##Fractals,27 (2006), 331344. ##[24] R. Saadati and J. H. Park,Intuitionistic fuzzy Euclidean normed spaces, Commun. Math. ##Anal.,1(2) (2006), 8690. ##[25] S. Sessa and B. Fisher,On common fixed points of weakly commuting mappings and set ##valued mappings, Internat. J. Math. Math. Sci., 9(2) (1986), 323329. ##[26] L. A. Zadeh,Fuzzy sets, Inform. and control, 8 (1965), 338353.##]
FUZZY IDEALS AND FUZZY LIMIT STRUCTURES
FUZZY IDEALS AND FUZZY LIMIT STRUCTURES
2
2
In this paper, we establish the theory of fuzzy ideal convergence on
completely distributive lattices and give characterizations of some topological
notions. We also study fuzzy limit structures and discuss the relationship
between fuzzy cotopologies and fuzzy limit structures.
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55
64
Yueli
Yue
Yueli
Yue
Department of Mathematics, Ocean University of China, Qingdao, 266071,
P. R. China
Department of Mathematics, Ocean University
China
yueliyue@163.com
Jinming
Fang
Jinming
Fang
Department of Mathematics, Ocean University of China, Qingdao,
266071, P. R. China
Department of Mathematics, Ocean University
China
jinmingfang@163.com
Fuzzy cotopology
Fuzzy ideal
Fuzzy limit structure
Fuzzy remote neighborhood system
[[1] J. Ad´amek, H. Herrlich and G. E. Strecker,Abstract and concrete categories, J. Wiley & ##Sons, New York, 1990. ##[2] C. L. Chang,Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182193. ##[3] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott,A compendium ##of continuous lattice, Springer Verlag, Berlin/Heidelberg/New York. ##[4] U. H¨ohle,Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl., 78 (1980), ##[5] U. H¨ohle and A. P. ˇSostak,Axiomatic foundations of fixedbasis fuzzy topology, Chapter 3 in: ##H¨ohle U., Rodabaugh S. E.(Eds), Mathematics of Fuzzy SetsLogic, Topology and Measure ##Theory, Kluwer Academic Publishers (Boston/Dordrecht/London), (1999), 123272. ##[6] K. C. Min,Fuzzy limit spaces, Fuzzy Sets and Systems, 32 (1989), 343357. ##[7] T. Kubiak,On fuzzy topologies, (PhD Thesis, Adam Mickiewicz, Poznan, Poland, 1985. ##[8] Y. M. Li,Limit structures over completely distributive lattices, Fuzzy Sets and Systems, 132 ##(2002), 125134. ##[9] S. E. Rodabaugh,Powerset operator foundations for poslat fuzzy set theories and topologies, ##Chapter 2 in [5]: (1999), 91116. ##[10] S. E. Rodabaugh,Categorical foundations of variablebasis fuzzy topology, Chapter 4 in [5], ##[11] A. P. ˇSostak,On a fuzzy topological structure, Rendiconti Ciecolo Matematico Palermo ##(Suppl. Ser. II),11 (1985), 89103. ##[12] G. J. Wang,Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992), ##[13] L. S. Xu,Characterizations of fuzzifying topologies by some limit structures, Fuzzy Sets and ##Systems,123 (2001), 169176. ##[14] Z. Q. Yang,Ideals in topological molecular lattices, Acta Math.Sinica, 2 (1986), 276279 (in ##[15] M. Ying ,A new approach to fuzzy topology (I), Fuzzy Sets and Systems, 39 (1991), 303321. ##[16] Y. Yue and J. Fang,Categories isomorphic to the KubiakˇSostak extension of TML, Fuzzy ##Sets and Systems,157 (2006), 832842.##]
SOME RESULTS OF INTUITIONISTIC FUZZY WEAK DUAL
HYPER KIDEALS
SOME RESULTS OF INTUITIONISTIC FUZZY WEAK DUAL HYPER KIDEALS
2
2
In this note we consider the notion of intuitionistic fuzzy (weak) dual hyper Kideals and obtain related results. Then we classify this notion according to level sets. After that we determine the relationships between intuitionistic fuzzy (weak) dual hyper Kideals and intuitionistic fuzzy (weak) hyper Kideals. Finally, we define the notion of the product of two intuitionistic fuzzy (weak) dual hyper Kideals and prove several Decomposition Theorems.
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65
78
L.
Torkzadeh
L.
Torkzadeh
Department Of Mathematics, Islamic Azad University
of Kerman, Kerman, Iran
Department Of Mathematics, Islamic Azad University
Iran
ltorkzadeh@yahoo.com
M.
Abbasi
M.
Abbasi
Department Of Mathematics, Islamic Azad University
of Kerman, Kerman, Iran
Department Of Mathematics, Islamic Azad University
Iran
M. M.
Zahedi
M. M. Zahedi
Zahedi
Department Of Mathematics, Shahid Bahonar University Of Kerman,
Kerman, Iran
Department Of Mathematics, Shahid Bahonar
Iran
zahedi mm@mail.uk.ac.ir
Dual hyper Kideal
Intuitionistic fuzzy dual hyper Kideal
[[1] K. Atanassov,Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 8796. ##[2] R. A. Borzooei and M. M. Zahedi,Positive implicative hyper Kideals, Scientiae Mathematicae ##Japonicae,53(3) (2001), 525533. ##[3] R. A. Borzooei, A. Hasankhani, M. M. Zahedi and Y. B. Jun,On hyper Kalgebras, Math. ##Japon.,52(1) (2000), 113121. ##[4] P. Corsini and V. Leoreanu,Applications of hyper structure theory, Kluwer Academic Publishers, ##[5] Y. Imai and K. Iseki,On axiom systems of propositional calculi, XIV Proc. Japan Academy, ##42(1966), 1922. ##[6] K. Iseki and S. Tanaka,An introduction to the theory of BCKalgebras, Math. Japon, 23 ##(1978), 126. ##[7] F. Marty,Sur une generalization de la notion de groups, 8th congress Math. Scandinaves, ##Stockholm, (1934), 4549. ##[8] J. Meng and Y. B. Jun,BCKalgebras, Kyung Moonsa, Seoul, Korea, 1994. ##[9] L. Torkzadeh and M. M. Zahedi,Dual positive implicative hyper Kideals of type 4, J. Quasigroups ##and Related Systems,9 (2002), 85106. ##[10] L. Torkzadeh and M. M. Zahedi,(Weak) dual hyper Kideals , Soft Computing, to appear. ##[11] L. Torkzadeh and M. M. Zahedi,(Anti) fuzzy dual positive implicative hyper Kideals, Italian ##Journal of Pure and Applied Mathematics,17 (2005), 6982. ##[12] L. Torkzadeh and M. M. Zahedi,Intuitionistic fuzzy commutative hyper Kideals, J. Appl. ##Math. & Computing, to appear. ##[13] L. A. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338353.##]
GENERALIZATION OF ($epsilon $, $epsilon $ $vee$ q)−FUZZY SUBNEARRINGS AND
IDEALS
GENERALIZATION OF ($epsilon $, $epsilon $ $vee$ q)−FUZZY SUBNEARRINGS AND
IDEALS
2
2
In this paper, we introduce the notion of ($epsilon $, $epsilon $ $vee$ q_{k})− fuzzy subnearring which is a generalization of ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnearring. We have given examples which are ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy ideals but they are not ($epsilon $, $epsilon $ $vee$ q)−fuzzy ideals. We have also introduced the notions of ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzyquasiideals and ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy biideals of nearring. We have characterized($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy quasiideals and ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy biideals of nearrings.
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79
97
P.
Dheena
P.
Dheena
Department of Mathematics, Annamalai University, Annamalainagar
608002, India
Department of Mathematics, Annamalai University,
India
dheenap@yahoo.com
S.
Coumaressane
S.
Coumaressane
Department of Mathematics, Annamalai University, Annamalainagar
608002, India
Department of Mathematics, Annamalai University,
India
coumaressane_s@yahoo.com
Near ring
Fuzzy subnearring
Fuzzy ideal
Fuzzy quasiideal
Fuzzy biideal ($epsilon $
$epsilon $ $vee$ q)−fuzzy subnearring
($epsilon $
$epsilon $ $vee$ q)−fuzzy ideal
($epsilon $
$epsilon $ $vee$ q)−fuzzy quasiideal
($epsilon $
$epsilon $ $vee$ q)−fuzzy biideal
($epsilon $
$epsilon $ $vee$ q_{k})−fuzzy subnearring
($epsilon $
$epsilon $ $vee$ q_{k})− fuzzy ideal
($epsilon $
$epsilon $ $vee$ q_{k})− fuzzy quasiideal
($epsilon $
$epsilon $ $vee$ q_{k})− fuzzy biideal
[[1] S. AbouZaid,On fuzzy subnearrings and ideals, Fuzzy Sets and Systems, 44 (1991), 139146. ##[2] S. K. Bhakat and P. Das, On the definition of a fuzzy subgroup, Fuzzy Sets and Systems, 51 ##(1992), 235241. ##[3] S. K. Bhakat and P. Das, ($epsilon $, $epsilon $ $vee$ q)−fuzzy subgroup, Fuzzy Sets and Systems, 80 (1996),359368. ##[4] S. K. Bhakat and P. Das,Fuzzy subrings and ideals redefined, Fuzzy Sets and Systems, 81(1996), 383393. ##[5] S. K. Bhakat, ($epsilon $, $epsilon $ $vee$ q)−fuzzy normal, quasinormal and maximal subgroups, Fuzzy Sets and Systems, 112 (2000), 299312. ##[6] P. S. Das,Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264269. ##[7] V. N. Dixit, R. Kumar and A. Ajmal,Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy ##Sets and Systems,4 (1991), 127138. ##[8] T. K. Dutta and B. K. Biswas,Fuzzy ideal of a nearring, Bull. Cal. Math. Soc., 89 (1997),447456. ##[9] S. D. Kim and H. S. Kim,On fuzzy ideals of nearrings, Bull. Korean. Math. Soc., 33 (1996),593601. ##[10] R. Kumar,Fuzzy algebra, University of Delhi Publication Division, Delhi, Vol. I, 1993. ##[11] N. Kuroki,Regular fuzzy duo rings, Inform. Sci., 94 (1996), 119139. ##[12] W. J. Liu,Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982), ##[13] P. P Ming and L. Y. Ming,Fuzzy topology. I. neighborhood structure of a fuzzy point and ##mooresmith convergence, J. Math. Anal. Appl., 76 (1980), 571599. ##[14] T. K. Mukherjee and M. K. Sen,Prime fuzzy ideals in rings, Fuzzy Sets and Systems, 32 ##(1989), 337341. ##[15] Al. Narayanan and T. Manikantan, ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnearrings and (2, 2 _q)−fuzzy ideals of nearrings, J. Appl. Math. & Computing, 18 (2005), 419430. ##[16] G. Pilz,Nearrings, NorthHollandMathematics Studies, 2nd ed., Vol. 23, NorthHolland, ##Amsterdam,1983. ##[17] A. Rosenfeld,Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512517. ##[18] H. K. Saikia and L. K. Barthakur,On fuzzy N−subgroups and fuzzy ideals of nearrings and ##nearring groups, The Journal of Fuzzy Mathematics, 11 (2003), 567580. ##[19] H. K. Saikia and L. K. Barthakur,Characterization of fuzzy substructures of a nearring and ##a nearring group, The Journal of Fuzzy Mathematics, 13 (2005), 159167. ##[20] U. M. Swamy and K. L. N. Swamy,Fuzzy prime ideals of rings, J. Math. Anal. Appl., 134(1988), 94103. ##[21] T. Tamizh Chelvam and N. Ganesan,On biideals of nearring, Indian J. Pure Appl. Math., ##18(1987), 10021005. ##[22] X. Y. Xie,On prime, quasiprime, weakly quasiprime fuzzy left ideals of semigroups, Fuzzy ##Sets and Systems,123 (2001), 239249. ##[23] Z. Yue,Prime Lfuzzy ideals and primary Lfuzzy ideals, Fuzzy Sets and Systems, 27 (1988), ##[24] L. A. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338353.##]
Persiantranslation Vol.5 No.1, February 2008
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