iosr-Jm   Volume-3 ~ Issue-5

Abstract :In this paper, fuzzy L-open sets due to Abd El-Monsef et al. [4] are used to introduce a new separation axiom and new type of function in fuzzy topological ideals spaces . Some the basic properties of fuzzy L-irresolute functions, as well as the connections between them, are investigated. Possible application to superstrings and   space–time are touched upon.

1] M.E. Abd El-Monsef and M.H. Ghanim , On semi open fuzzy sets, Delta , J. Sci.5 (1981) 30-40.
[2] M.E. Abd El-Monsef; A.A. Nasef and A. A. Salama, Extensions of Fuzzy Ideals, Bull.Cal.Maths.Soc., 92, (3) ( 2000 ) 181 –188
[3] M.E. Abd El-Monsef; A.A.Nasef and A.A.Salama, Some Fuzzy Topological operators via Fuzzy ideales Chaos, Solitons &
Fractals.(12)(13),(2001) , 2509-2515.
[4] M.E. Abd El-Monsef; A.A. Nasef and A.A.Salama, Fuzzy L-open Sets and Fuzzy L-continuous Functions, Analele Universitatii
din Timisoara .XL,fasc.Seria Matematica - Informatica(2),(2002),3-12
[5] K.K. Azad, On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal App. 82 (1981) 1432.
[6] C.L. Chang, Fuzzy Topology Spaces, J. Moths. Anal – Apple 24 (1968) 128-189.
[7] R.A.Mahmoud, Fuzzy Ideals, fuzzy local functions and *-fuzzy topology, the Journal of Fuzzy Mathematics Vol.5, No.1, 1997
Los Angeles.
[8] Pu Pao – Ming and Liu Yang, Fuzzy Topology .1. Neighbour – hood structure of fuzzy point and Moore smith convergence, J.
Math Anal. App. 76 (1980) 571-599.
[9] A.A.salama, Fuzzy Ideals on fuzzy topological spaces, Ph.D in Topology ,Tanta Univ., Egypt( 2002).
[10] D.Sarkar,Fuzzy ideal theory, Fuzzy local function and generated fuzzy topology , Fuzzy Sets and Systems 87 (1997) 117 – 123

Abstract :This paper presents a non parametric measure of association between k populations, and a method of testing for its significance. Analysis of variance technique is employed to developa test statistic for the measure of the association. An illustrative example is provided and the method compares equally well with the Friedman's two way analysis of variance by rank.

[1] Gerald, K. and Warrack , B. (2003): Statistics for Management and Economics, Curt Hinrichs, USA
[2] Gibbons, J.D. (1971): Non Parametric Statistical Inference, McGraw Hill, New York
[3] Legendre, P. (2005): Species Associations: The Kendall Coefficient Revisited, American Statistical Association and International
Biometric Society, Journal of Agricultural, Biological, and Environmental Statistics, Vol 10, 2
[4] Oyeka, C.A. (2009): An Introduction to Applied Statistical Methods (5theds), Nobern Avocation Pub. Coy., Enugu
[5] Scheaffer, R.L. and McClave, J.T. (1982): Statistics for Engineers, PWS, Publishers, USA
[6] Sheskin, D.J (1997): Handbook of Parametric Statistical Procedures, CRC Press, Inc, Boca Raton, New York
[7] Zar, J.H (1999), Biostatistical Analysis (4theds), Prentice Hall, Upper Saddle River, New Jersey

Abstract :This paper developed a Ties adjusted non parametric statistical method for the analysis of ordered repeated measures that are related in time, space or condition that takes account of all possible pairwise combinations of treatment levels. A test statistic is developed to determine whether subjects are increasingly performing better or worse over time or space. The proposed method also enables the researcher to have a bird's eye view of the proportions of subject who are successively improving, experiencing no change or worsening overtime, space or condition to guide the introduction of any desired interventionist measures. The method is illustrated with some data and shown to be more powerful than Friedman test and shown to beeasier to use than the Bartholomew procedure.

[1] Bartholomew DJ (1959a): A Test of Homogeneity for Ordered Alternatives. Biometrika, 46, 36-48
[2] Bartholomew DJ (1959b): A Test of Homogeneity for Ordered Alternatives 11. Biometrika, 46, 328-335
[3] Freidlin B and Gastwirth JL.(): Should the Median Test be Retired from general Use? American Statistician, 54, 161-164
[4] Gibbons JD(1971): Non- Parametric Statistical Inference. McGraw Hill, New York,
[5] Gibbons JD(1993): Non- Parametric Statistical. An Introduction; Newbury Park: Sage Publication
[6] Oyeka, C. A., Ebuh, G.U., Nwankwo, C.C., Obiora- Ilouno, H. Ibeakuzie, P. O., Utazi, C.(2010) : A Statistical Comparison of Test
Scores: A Non- Parametric Approach. Journal of Mathematical Sciences, 21(1) 77-87
[7] Siegel S() : Non- Parametric Statistics for the Behavioural Sciences. McGraw- Hill, Tokyo
[8] Hollander, M. and Wolfe, D.A.(1999): Non-Parametric Statistical Methods (2nd Edition). Wiley Interscience, New York