iosr-Jm   Volume-19 ~ Issue-2 ~ Mar. – Apr. 2023

Abstract : This paper deals with a linear discriminant function based on the development of a nonparametric statistic. The statistic is defined as a maximum rank sum statistic which maximizes the sum of the ranks associated with the observations from one sample, based on the distances of all observations from two samples to a hyperplane. The optimal hyperplane which gives the maximum rank sum statistic is considered as a discriminant function for the two-population discriminant analysis. Mixed-integer and linear programming
formulations are then derived for obtaining this type of nonparametric statistic. An efficient algorithm for computing this statistic is developed for the special case in which both samples are two-dimensional. Monte Carlo studies are conducted to evaluate the performance of the discriminant function derived from the maximum rank sum statistic in comparison with some statistical discriminant functions. The results show that the new discriminant function is competitive in various noncontaminated situations and performs better in some
contaminated situations..

Key Word: Derivation of the Maximum Rank Sum Statistic,Monte Carlo studies.

[1]. T.W. Anderson, Introduction to Multivariate Statistical Analysis (John Wiley & Sons, New York, 1958) ch. 6.
[2]. J.F. Benders, "Partitioning Procedures for Solving Mixed-Variables Programming Problems", NumerischeMathematik 4 (1962)
238-252.
[3]. M. Goldstein and W.R. Dillion, Discrete Discriminant Analysis (John Wiley & Sons, New York, 1978).
[4]. P.A. Lachenbruch, Discriminant Analysis (Hafner Press, New York, 1975).
[5]. J.M. Liittschwager and C. Wang, "Integer Programming Solution of a Classification Problem", Management Science 24 (1978)
1515-1525.

Abstract : In this article, some analytical methods, viz, the homotopy perturbation method (HPM) and the new iterative method (NIM) are proposed with reliable algorithms to solve linear and nonlinear fuzzy integro-differential equations in parametric form. Numerical examples are solved and finally comparison between the results obtained by the two methods which confirm efficiency and power of these methods in solving linear and nonlinear fuzzy integro-differential equations.

Key Word: Fuzzy integro-differential equation; Homotopy perturbation method; New iterative method

[1]. D. Dubois and H. Prade, Operations on fuzzy numbers, J. Syst. Sci., 9(1978), 613-626.
[2]. B. Asady, S. Abbasbandy and M. Alavi, Fuzzy general linear systems, Appl. Math. Comput., 169(2005), 34-40.
[3]. M. S. Hashemi, M. K. Mirnia and S. Shahmorad, Solving fuzzy linear systems by using Schur complement when coefficient matrix is an M-matrix, Iranian J. of fuzzy systems, 5(3)(2008), 15-29.
[4]. S. Abbasbandy, T. allah Viranloo, O. Lopez-Pouso and J. J. Nieto, Numerical methods for fuzzy differential inclusions, Comput. Math. Appl., 48(2004), 1633-1641.
[5]. S. Abbasbandy, J. J. Nieto and M. Alavi, Tuning of reachable set in one dimensional fuzzy differential inclusions, Chaos, Solitons and Fractals, 26(2005), 1337-1341..

Abstract : In this paper, by considering the Boolean matrix on binary Boolean algebra, the definition of inverse-preserving incidence mapping of Boolean matrix is proposed, and the Boolean representations of Ockham algebra and finite De Morgan algebra are obtained.

Key Word: Boolean matrix; row column space lattice; De Morgan algebra; Ockham algebra;

[1]. K.H. Kim, Boolean matrix theory and applications. Marcel Dekker, New York, 1982.
[2]. T.S. Blyth, J. C. Varlet. Ockham Algebras. Oxford University Press, 1994.
[3]. Congwen Luo. De Morgan algebra. Beijing Institute of Technology Press, 2005..

Abstract : In this paper, we define the γ-connectedness by using of γ-separated sets in L-fuzzy topological spaces. We study the characterization and several properties of γ-connectedness. We have proved some equivalent conditions for γ-connectedness.

Key Word: γ-separated sets, γ-closed sets, γ-open sets, γ-connectedness,L-fuzzy topological spaces

[1]. D. M. Ali, Some other types of fuzzy connectedness, Fuzzy Sets and Systems, 46 (1992) 55-61.
[2]. D. M. Ali and A. K. Srivastava, On fuzzy connectedness, Fuzzy Sets and Systems, 28 (1988) 203-208.
[3]. N. Ajmal and J. K. Kohli, Connectedness in fuzzy topological spaces, Fuzzy Sets and Systems, 31 (1989) 369-388.
[4]. N. Ajmal and J. K. Kohli, Connectedness and local connectedness in fuzzy topological spaces and heyting algebra valued sets, Fuzzy Sets and Systems, 44 (1991) 93-108.
[5]. S. Z. Bai, P-connectedness in L-topological spaces, Soochow Journal of Mathematics, 29 (1) (2003) 35-42.

Abstract : The intent of this paper is to establish sovle linear equations by decomposition method is a numerical technique

Key Word:Decomposition Method , Fuzzy Matrix, Fuzzy Vector , Fuzzy Liner Fractional Programming Problem

[1]. Bharati, SK & Singh, SR 2015, "A note on solving a fully intuitionistic fuzzy linear programming problem based on sign distance‟,
International Journal of Computer Application, vol.119, no.23, pp. 30-35
[2]. Charnes, A & Cooper, WW 1962, "Programs with linear fractional functions‟, Naval Research Logistics Quarterly, vol.9, pp. 181-
196.
[3]. Chanas, S 1983, "The use of parametric programming in fuzzy linear programming‟, Fuzzy Sets and Systems, vol. 11, pp. 243-251.
[4]. Charnes, A & Cooper, WW 1962, "Programs with linear fractional functions‟, Naval Research Logistics Quarterly, vol.9, pp. 181-
196.
[5]. Jayalakshmi, M & Pandian P 2013, "On solving linear fractional programming problems‟, Modern Applied Science, vol. 7, no. 6,
pp. 90-100

Abstract : The assignment problems are a well-studied topic in combinatorial optimization. These problems find numerous applications in production planning, telecommunication VLSI design, economic etc. The assignment problem is a special case of the transportation problem where the supply from every source and the demand at every sink are equal to 1. Such a situation arises naturally in the setting of assigning workers to jobs, or of assigning workers to a time schedule. In this paper we consider the assignment problem as LPP with objective is to assign n persons to n jobs, so as to minimize the total assignment cost and then we solve this problem with the help of two phase &big M method......

Key Word: Assignment problem, Hungarian assignment method (HA) method, Linear Integer Programming, optimization Problem, NWCM,LCM,VAM, Two Phase method , Big M method

[1]. H. Basirzadeh, "Ones Assignment Method for Solving Mathematical formulation of assignment prob-," vol. 6, no. 47, pp. 2345–2355, 2012.
[2]. H. D. Afroz and D. M. A. Hossen, "New Proposed Method for Solving Assignment Problem and Comparative Study with the Existing Methods," IOSR J. Math., vol. 13, no. 02, pp. 84–88, 2017, doi: 10.9790/5728-1302048488.
[3]. A. Rashid, "An Alternative Approach for Solving Unbalanced Assignment Problems," vol. 40, no. 2, pp. 45–56, 2017.
[4]. M. Khalid, M. Sultana, and F. Zaidi, "New improved ones assignment method," Appl. Math. Sci., no. 81–84, pp. 4171–4177, 2014, doi: 10.12988/ams.2014.45327.
[5]. P. Jaskowski, "Assignment problem and its extensions for construction project scheduling" Czas. Tech., vol. 2014, no. January 2014, pp. 241–248, 2014, doi: 10.4467/2353737XCT.14.133.2583

Abstract : In this paper, the relation of Silver Ratio with Pell numbers and Silver Rectangle is discussed. The value (1+√2) is known as silver ratio. It can be expressed as a trigonometric function and also in terms of an infinite continued fraction. A rectangle whose length and breadth are in the ratio (1+√2):1 is known as Silver Rectangle. Silver rectangle can be constructed within a regular octagon. The area of an octagon depends on silver ratio. Silver rectangles of gradually decreasing size can be formed successively within a rectangle whose sides are in the ratio √2:1.The ratio √2:1 is used in the construction of temples and towers in Japan.

Key Word: Recurrence relation, Pell numbers, Silver ratio, Octagon, Silver rectangle

[1]. A.F.Horadam, Applications of modified Pell numbers to representations, Ulam Quart. , Vol.3, pp. 34-53, 1994.
[2]. N. Bicknell, A primer on the Pell sequence and related sequence, Fibonacci Quart., Vol.13, No.4, pp. 345-349, 1975.
[3]. Ahmet Dasdemir , On the Pell, Pell-Lucas and modified Pell numbers by matrix method, Applied Mathematical Sciences, Vol.5, No.64, pp.3173-3181, 2011.
[4]. Vandana N. Purav, Silver ratio and Pell numbers, Journal of Applied Science and Computations, Vol.5, No.7, pp.8-13, 2018
pp. 90-100

Abstract : Background: Mobile phone service providers operate in an oligopolistic market structure and are experiencing high churn rates. Consequently, the service providers invest heavily in market research trying to develop precise ways of predicting customer churn. Building models to predict customer churn in the mobile phone industry when competing risks are confounded with time-dependent covariates has been the center of focus for many studies recently.........

Key Word: Bayesian; Competing risks; Time-dependent covariates; Churn.

[1]. Brandusoiu, I. B. and Toderean, G. 2013: Predicting Churn in Mobile Telecommunications Industry. ACTA Technica Napocensis Electronics and Telecommunications, p. 54(3).
[2]. Customer Churn Prediction & Prevention Model. (2021, December 22). Optimove. Retrieved January 15, 2022, from https://www.optimove.com/resources/learning-center/customer-churn-prediction-and-prevention#:%7E:text=Churn%20prediction%20modeling%20techniques%20attempt%20to%20understand%20the,to%20the%20success%20of%20any%20proactive%20retention%20efforts.
[3]. Heckerman, D. 1997: Bayesian Networks for Data Mining. Data Mining Knowledge Discovery, p. 1.
[4]. Huang, Y., Huang, B., and Kechadi, M. T. 2011: A rule-based method for customer churn prediction in telecommunication services. In: Advances in Knowledge Discovery and Data Mining, Springer, p. 411–422.
[5]. Idris, A. and Khan, A. 2012: Customer churn prediction for telecommunication: Employing various features selection techniques and tree-based ensemble classifiers. In: Multitopic Conference (INMIC), 2012 15th International, p. 23–27.

Abstract : In recent times, there has been an increasing level of research into quantum algorithms and its uses in order to find more efficient ways of computing. The Grover's Search Algorithm is one such algorithm that has become popular that aims search for a given item in an unsorted database. In the following research experiment, Grover's Algorithm was built using IBM Quantum and its time efficiency was compared against its classical simulator. It was found that the Grover's Algorithm does in fact provide a better time efficiency than its clas-sical simulator, but the correlation between the two times differs from their theoretical prediction.

[1]. Grover, Lov K., "A fast quantum mechanical algorithm for database search", 1996, pp. 212-218
[2]. Shor, P. W. (1994). Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, In: Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, edited by S. Goldwasser, p. 124, Los Alamitos, CA, IEEE Computer Society.
[3]. Sakhi, Z. Kabil, R. Tragha, Abderrahim Bennai, Mohamed. (2012). Quantum cryptography based on Grover's algorithm. 33-37. 10.1109/IN-TECH.2012.6457788.
[4]. Mavroeidis, Vasileios et al. "The Impact Of Quantum Computing On Present Cryptography". International Journal Of Advanced Computer Sci-ence And Applications, vol 9, no. 3, 2018. The Science And Information Organization, https://doi.org/10.14569/ijacsa.2018.090354.
[5]. Mina-Zicu, Mina, and Emil Simion. "Threats To Mod-ern Cryptography: Grover'SAlgorithm". Preprints.Org, 2022,