Volume-5 , Issue-4 , Aug 2018, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Optimal Decision Model under Mixture Inventory System

  P.K. Tripathy, N.K. Sahoo

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.179-191, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.179191

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this paper, the behavior of an inventory model in a production system with Weibull demand and time dependent deterioration is depicted. Holding cost is changed per unit time. Mathematical model of both crisp and fuzzy models have been developed to determine the optimal cycle time and optimal inventory cost. Fuzzy set theory is primarily concerned with imprecision and uncertainty. It provides the decision maker as a mixture inventory system which is used in modeling real-world problems as compared to the classical deterministic and probabilistic mathematical tools. The demand, deterioration rate, holding cost, unit cost and shortage cost are taken mixture and subsequently as pentagonal fuzzy numbers. Both graded mean integration and signed distance method are used to defuzzify the total cost function. Numerical illustrations are provided to illustrate the applications of the model with useful graphs and tables to validate the developed model. Sensitivity analysis is carried out to analyze the variability in the optimal solution with respect to change in various parameters.

  Key-Words / Index Term
  EOQ Model, Weibull Demand, Pentagonal Fuzzy Number, Graded Mean Integration, Signed Distance

  References
  [1] N.P. Behera, P.K. Tripathy, “Fuzzy EOQ Model for Time-Deteriorating Items Using Penalty Cost”, American Journal of Operational Research, Vol.6, No.1, pp. 1-8, 2016.
  [2] S.C. Chang, J.S. Yao, H. M. Lee, “Economic reorder point for fuzzy backorder quantity”, European Journal of Operational Research, Vol.109, pp.183-202, 1998.
  [3] M.A. Hariga, “Optimal EOQ models for deteriorating items with time-varying demand”, The Journal of the Operational Research Society, Vol.47, pp.1228-1246, 1996.
  [4] C.H. Hsieh, “Optimization of fuzzy production inventory models”, Information Sciences, Vol.146, pp.29-40, 2002.
  [5] C.K. Jaggi, K.K. Aggarwal, S.K. Goel, “Optimal order policy for deteriorating items with inflation induced demand”, International Journal of Production Economics, Vol.103, pp.707-714, 2006.
  [6] C.K. Jaggi, S. Pareek, A. Sharma, Nidhi, “Fuzzy Inventory Model for Deteriorating Items with Time-varying Demand and Shortages’’ American Journal of Operational Research, Vol.2, No.6, pp.81-92, 2012.
  [7] C. Kao, W.K. Hsu, “Lot size-reorder point inventory model with fuzzy demands”, Computers and mathematics with applications, Vol.43, pp.1291-1302, 2002.
  [8] S.P. Modal, M. Mandal, “Pentagonal fuzzy number, its properties and application in fuzzy equation”, Future Computing and Informatics Journal, Vol.2, pp.110-117, 2017.
  [9] B.S. Mohanty, P.K. Tripathy, “Fuzzy inventory model for deteriorating items with exponentially decreasing demand under fuzzified cost and partial backlogging”, International Journal of Mathematics Trends and Technology, Vol.51, No.3, pp.182-189, 2017.
  [10] H. Nagar, P. Surana, “Fuzzy Inventory Model for Deteriorating Items with Fluctuating Demand and Using Inventory Parameters as Pentagonal Fuzzy Numbers”, Journal of Computer and Mathematical Sciences, Vol.6, No.2, pp.55-66, 2015.
  [11] A. Panda, A. Pal, “A study on pentagonal fuzzy number and its corresponding matrices”, Pacific Science Review B: Humanities and Social Sciences, Vol.1, pp.1-9, 2016.
  [12] K.S. Park, “Fuzzy set theoretic interpretation of economic order quantity”, IIIE Transactions on Systems, Man and Cybernetics, Vol.17, pp.1082-1084, 1987.
  [13] P.M. Pu, Y.M Liu, “Fuzzy Topology 1, neighborhood structure of a fuzzy point and Moore-Smith Convergence”, Journal of Mathematical Analysis and Application, Vol.76, pp.571-599, 1980.
  [14] N.K. Sahoo, B.S. Mohanty, P.K. Tripathy, “Fuzzy inventory model with exponential demand and time-varying deterioration”, Global Journal of Pure and Applied Mathematics, Vol.12, No.3, pp.2573-2589, 2016.
  [15] N.K. Sahoo, P.K. Tripathy, “An EOQ Model for Quadratic Demand Rate, Parabolic Deterioration, Time Dependent Holding Cost with Partial Backlogging”, International Journal of Mathematics and its Applications, Vol.6, No.1-B, pp.325-332, 2018.
  [16] N.K. Sahoo, P.K. Tripathy, “An EOQ model with three-parameter Weibull deterioration, trended demand and time varying holding cost with salvage”, International Journal of Mathematics Trends and Technology, Vol.51, No.5, pp.25-29, 2017.
  [17] P.K. Tripathy, W.M.Wee, P.R. Majhi, “An EOQ model with process reliability considerations”, Journal of the Operational Research Society, Vol.54, pp.549-554, 2003.
  [18] J.S. Yao, J. Chiang, “Inventory without backorder with fuzzy total cost and fuzzy storing cost defuzzified by centroid and signed distance”, European Journal of Operation Research, Vol.148, pp.401-409, 2003.
  [19] J.S. Yao, H.M. Lee, “Fuzzy inventory with or without backorder for fuzzy order quantity with trapezoidal fuzzy number”, Fuzzy sets and Systems, Vol.105, pp.311-337, 1999.
  [20] L.A. Zadeh, “Fuzzy Sets”, Information and Control, Vol.8, pp.338-353, 1965.
  

  Citation
  P.K. Tripathy, N.K. Sahoo, "Optimal Decision Model under Mixture Inventory System," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.179-191, 2018

• Open Access   Article

  Application of Game Theoretical Model for Water Management in Rajkot City, Gujarat, India

  Reema Gupta, B. K. Singh, Gaurav Agarwal

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.192-197, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.192197

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Water is essential for the existence of society and needs in all human activities. In the present study, a game theoretical model developed to encourage the maximization of the public benefits in water distribution management in Rajkot city for different players. The present study concludes that Rajkot city demand-supply gap is 33 MLD and is expected to increase to 119 MLD and 236 MLD by 2035 and 2050 respectively. By 2035, when the population of Rajkot city grows to 21 lakh, the present water capacity would be insufficient to provide almost 50% of the city. This gap is continually increasing day by day as population increases and will become double in the year 2050. In the present study, five user game-theoretical model formulated for five players (industry, public, institutional, domestic and UFW) to minimize water demand supply gap based on current water supply in Rajkot city from all five water sources i.e. Ajii-I, Narmada, Nyari-I, Bhadar, Nyari-II. Asymmetric Nash bargaining approach is used to develop a game-theoretic model for the optimization of the weighted Nash product to obtain the actual solutions. From the study, it concluded that there is no water distribution strategy which satisfies the need of domestic users with current water distribution system. It calls for the establishment of new sources of water supply, their conservation, and optimal utilization.

  Key-Words / Index Term
  Water demand-supply gap, Water management, Game theory, Game theoretic model

  References
  [1] L. J. M. Zbigniew and W. Kundzewicz, “Freshwater resources and their management,” World Water, pp. 173–210, 2007.
  [2] A. Keller, R. Sakthivadivel, and D. Seckler, “Water scarcity and the role of storage in development,” Water Manag., Vol. 39, pp. 1–24, 2000.
  [3] Central Water Commission, “Reassessment of Water Resources Potential of India,” 1999.
  [4] A. Georgakakos et al., “Climate change impacts in the United States,” Third Natl. Clim. …, pp. 69–112, 2014.
  [5] Harinarayan Tiwari, N. Sharma, A. Khan, and S. P. Rai, “Water Resources in India : A view from third eye,” in India Water Week 4-8 April 2016: “Water for All- Striving Together” Water, 2016, pp. 1–13.
  [6] A. McIntosh and J. Pontius, “Global Water Resources,” Case Stud. Integr. Sci. Glob. Environ., pp. 113–254, 2017.
  [7] R. Supalla, B. Klaus, O. Yeboah, and R. Bruins, “A game theory approach to deciding who will supply instream flow water,” J. Am. Water Resour. Assoc., vol. 38, no. 4, pp. 959–966, 2002.
  [8] M. Homayounfar, M. Zomorodian, C. J. Martinez, and S. H. Lai, “Two Monthly Continuous Dynamic Model Based on Nash Bargaining Theory for Conflict Resolution in Reservoir System,” PLoS One, vol. 10, no. 12, p. e0143198, 2015.
  [9] M. Karamouz, M. Akhbari, A. Moridi, and R. Kerachian, “A system dynamics-based conflict resolution model for river water quality management,” J. Environ. Heal. Sci. Eng., vol. 3, no. 3, pp. 147–160, 2006.
  [10] S. Wei and A. Gnauck, “Game theory based water quality models for reservoir management,” Proc. EnviroInfo Warsaw 2007 Environ. Informatics Syst. Res. Vol. 1 Plenary Sess. Pap. Warsaw Pol., pp. 363–370, 2007.
  [11] K. Madani, “Game theory and water resources,” J. Hydrol., vol. 381, no. 3–4, pp. 225–238, 2010.
  [12] N. Mahjouri and M. Ardestani, “A game theoretic approach for interbasin water resources allocation considering the water quality issues,” Environ. Monit. Assess., vol. 167, no. 1–4, pp. 527–544, 2010.
  [13] W. Zhanping and T. Juncang, “Optimal Allocation of Regional Water Resources Based on Genetic Algorithms,” J. Converg. Inf. Technol., vol. 7, no. 13, pp. 437–445, 2012.
  [14] A. Ahmadi, “Water Distribution as a no Cooperative Game,” vol. 13, no. 3, 2013.
  

  Citation
  Reema Gupta, B. K. Singh, Gaurav Agarwal, "Application of Game Theoretical Model for Water Management in Rajkot City, Gujarat, India," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.192-197, 2018

• Open Access   Article

  Autoregressive Order Selection Criteria and their Performances at Different Sizes of Time Series

  P. Kiran Kumar, B. Sarojamma, P. Ramakrishna Reddy

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.198-208, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.198208

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In the present study, the most popular model selection criteria are used as the autoregressive order selection criteria and the performances of time series model selection criteria at different sizes of the same time series are observed. In time series analysis and forecasting, selecting the most suitable model for a given time series and size of available time series plays a vital role. We verified that Final Prediction Error Criterion and Akaike’s Information Criterion are asymptotically equivalent and Akaike’s Information Criterion and Bias-Corrected Akaike’s Information Criterion are asymptotically equivalent when the size of time series is large with respect to the dimension of the parameters of the autoregressive process using empirical study. All the time series model selection criteria presented in the paper are evaluated by log-likelihood function.

  Key-Words / Index Term
  FPE, AIC, AICc, BIC, HQC, and MDL

  References
  [1] Brockwell, P. J. , Davis, R. A., “Introduction to Time Series and Forecasting”, Springer-Verlag New York Publishing, USA, pp.169-171, 1991.
  [2] Allan D R McQuarrie, Chin-Ling Tsai, “Regression and Time Series Model Selection”, World Scientific Publishing, Singapore, pp.89-97, 1998.
  [3] Cavanaugh, J. E., “Unifying the derivations for the Akaike and corrected Akaike information criteria”, Statistics & Probability Letters, Vol. 33, No. 2, pp. 201-208, 1997.
  [4] Schwarz, G., "Estimating the Dimension of a Model ”, Annals of Statistics, Vol. 6, No. 2, pp.461-464, 1978.
  [5] Sadanori Konish.i, Genshiro Kitagawa, “Information Criteria and Statistical Modeling”, Springer-Verlag New York Publishing, USA, pp.211-218, 2008.
  [6] Chang C.Y. Dorea, Catia R. Goncalves, Paulo A.A. Resende, “Simulation Results for Markov Model Seletion : AIC, BIC and EDC”, In the Proceedings of the World Congress on Engineering and Computer Science (Vol II WCECS 2014), San Francisco, USA, pp.22-24 ,2014.
  [7] J. K. Ghosh, M. Delampady, and T. Samanta, “An Introduction to Bayesian Analysis: Theory and Methods”, Springer-Verlag New York Publishing, USA, pp.114-115, 2006.
  [8] Hannan, E. J., and B. G. Quinn, “The Determination of the Order of an Autoregression ”, Journal of the Royal Statistical Society, Series B, Vol. 41, No. 2, pp.190-195, 1979.
  [9] Ritei Shibata, “An Optimal Selection of Regression Variables”, Biometrika, Vol. 68, No. 1, pp.45-54, 1981.
  [10] Rissanen, J, “Modeling by shortest data description ”, Automatica, Vol. 14, Issue.,5, pp.465–471, 1978.
  [11] Baki Billah, Rob J. Hyndman, Anne B. Koehler, “Empirical information criteria for time series forecasting model selection”, Journal of Statistical Computation and Simulation, Vol. 75, No. 10, pp.831-840, 2005.
  

  Citation
  P. Kiran Kumar, B. Sarojamma, P. Ramakrishna Reddy, "Autoregressive Order Selection Criteria and their Performances at Different Sizes of Time Series," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.198-208, 2018

• Open Access   Article

  Economic Lotsize Model for a Price Dependent Demand System under Credit Policy

  P.K. Tripathy, R. Shial, S. Pradhan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.209-217, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.209217

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  The main purpose of this paper is to study an inventory model for time dependent deterioration with selling price dependent demand. Here it is assumed that demand rate is a function of selling price. This model allows shortages, which is partially backlogged. It is also investigated under credit policy. The results are illustrated with the help of numerical examples. The sensitivity analysis for the model is carried out to study the effect of changes on the values of the parameters associated with the model.

  Key-Words / Index Term
  EOQ, Partially Backlogging, Trade Credit, Selling Price Dependent Demand, Deterioration

  References
  [1] P.L. ABAD (2001), “Optimal price and order size for a reseller under partial backordering”, Computational Operational Research. Vol. 28, pp. 53-65.
  [2] P.L. ABAD, and C.K. JAGGI, (2003), “A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive.” International Journal of Production Economic, Vol. 83, pp. 115-122.
  [3] H.J. CHANG, and C.Y. DYE (2001), “An inventory model for deteriorating items with partial backlogging and permissible delay in payment,” International Journal of system Science. Vol. 32, pp. 345-352.
  [4] K.J. CHUNG, and C.K. HUANG, (2009), “An ordering policy with allowable shortage and permissible delay in payments.” Applied Mathematical modelling, Vol. 33, pp. 2518-2525.
  [5] C.Y. DYE, (2007), “Joint pricing and ordering policy for a deteriorating inventory with partial backlogging”, Omega. Vol. 35, pp. 184-189.
  [6] S.K. GOYAL, and B.C. GIRI, (2001). “Recent trends in modelling of deteriorating inventory.” European Journal of operational Research. Vol. 134, pp. 1-16.
  [7] A.K. JALAN, B.C. GIRI and K.S. CHADHURI, (2001),“EOQ model for items with weibull distribution deterioration, shortages and ramp type demand” ,Recent Development in Operations Research. pp. 207-223.
  [8] B. KARMAKAR, and K.D. CHOUDHURY, (2014), “Inventory models with ramp-type demand rate for deteriorating items with partial backlogging and time varying holding cost”, Yugoslav Journal of Operations Research. Vol. 24, pp. 249-266.
  [9] A. ROY, (2008), “An inventory model for deteriorating items with price dependent demand and time varying holding cost” ,Advanced Modelling and Optimization, Vol. 10, pp. 25-37.
  [10] K. SKOURI, and I. KONSTANTARAS, (2009),“Order level inventory models for deteriorating seasonable products with time dependent demand and shortages”, Hyundai publishing corporation mathematical problem in engineering article, Vol. ID679736.
  [11] G. SRIDEVI, K. NIRUPAMA DEVI, and K. SRINIVAS RAO, (2010). “Inventory model for deteriorating items with weibull rate of replenishment and selling price dependent demand.” International Journal of Operational Research. Vol. 9, pp. 329-349.
  [12] G.P. SAMANTA, and A. ROY, (2004), “A production inventory model with deteriorating items and shortages”, Yugoslav Journal of Operation Research. Vol. 14, pp. 219-230.
  [13] R.P. TRIPATHY, (2013). “Inventory model with cash flow oriented and time dependent holding cost under permissible delay in payments.” Yugoslav Journal of Operations Research. Vol. 23, pp. 419-429.
  [14] P.K. TRIPATHY, and S. PRADHAN (2012), “Inventory model for ramp type items with Trade credit under extra ordinary purchase.” IOSR Journal of Mathematics, Vol. 2, pp. 2278-5728.
  [15] J.T. TENG (2005), “Optimal pricing and ordering policy under permissible delay in payments.” International Journal of Production Economics, Vol. 97, pp. 121-129.
  [16] K.S. WU, and L.Y. OUYANG (2000), “A replacement policy for deteriorating items with ramp-type demand rate.” Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering, Vol. 24 , pp. 279–286.
  

  Citation
  P.K. Tripathy, R. Shial, S. Pradhan, "Economic Lotsize Model for a Price Dependent Demand System under Credit Policy," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.209-217, 2018

• Open Access   Article

  Generalized Common Fixed Point Theorem for Four Self Mappings in b- Metric Space

  Akash singhal, Rajesh kumar Sharma, Anil Agrawal

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.5 , Issue.4 , pp.218-225, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.218225

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this paper we have tried to prove a common fixed point theorem of four self-mappings satisfying a generalized contractive condition in b-metric space. Our result extend several comparable pre-existing results in literature. We have also given an example that shows the applicability and validity of our result.

  Key-Words / Index Term
  Fixed point; Common Fixed point; Cauchy Sequence; compatible mapping; b-Metric space

  References
  [1]. Akkouchi M., Common fixed point theorems for two self-mapping of a b-metric space
  under an implicit relation , Hacettepe Journal of mathematics and statistics , 40 (6),805- 810
  ,2011
  [2]. Aydi ,H.Bota ,M.Karapinar,E.and Moradi,S.A ,fixed point for weak ? –contractions on b-
  metric spaces, Fixed point theory, 13 (2) , 337- 346, 2012.
  [3] . Bakhtin, I.A. , Contraction mapping principle in almost metric spaces ,Funct. Anal.30,
  26–37,1989.
  [4] Boriceanu, M.,Fixed point theory for multivalued generalized contraction on a set with two
  b-metric, Studia, Univ Babes, Bolya: Math, Liv(3) ,1-14 ,2009.
  [5].Bota, M., Molnar, A. and Varga, C.S , On ekeland`s variational principle in b-metric spaces,
  Fixed Point Theory 12( 2) ,21-28 ,2011.
  [6]. Bourbaki, N., Topologie Generale; Herman: Paris, France, 1974.
  [7]. Ciric , L.B.,A generalization of Banach’s contraction principle,proceedings of the American
  Mathematical Society, 45 , 267-273 ,1974.
  [8]. Czerwik S, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostra., 1,
  5–11, 1993.
  [9].Czerwik, S., Non-linear set valued contraction mappings in b-metric spaces, Atti sem math fiq
  Univ. Modena, 46 (2 ),263-276 ,1998.
  [10]. J R. Roshan , N.shobkolaei , S.sedghiand M.abbas, Common fixed point of four maps in b-
  Metric spaces , Hacettepe Journal of Mathematics and Statistics , 4(4 ),613-624 ,2014 .
  [11] .Kir, Mehmet, Kiziltune, Hukmi, On some well-known fixed point theorems in b-metric
  space, Turkish journal of analysis and number theory, 1( 1) , 13-16 , 2013.
  [12]. Pacurar, M.Sequences of almost contractions and fixed points in b-metric spaces, Analele
  Universit?? de Vest, Timisoara, Seria Matematic? Informatic?, 3 ,125-137 , 2010.
  [13]. Shah, M.H.and Hussain , N. Nonlinear contractions in partially ordered quasi b-metric
  spaces, Commun. Korean Math. Soc. 27(1) , 117-128 ,2012.
  

  Citation
  Akash singhal, Rajesh kumar Sharma, Anil Agrawal, "Generalized Common Fixed Point Theorem for Four Self Mappings in b- Metric Space," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.218-225, 2018

• Open Access   Article

  Designing Single Sampling Plan using Generalized Poisson Distribution

  V. Kaviyarasu, V. Devika

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.226-232, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.226232

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  This paper introduces a new two-parameter discrete probability distribution through an attribute acceptance sampling plan to develop a sampling plan through the Generalized Poisson Distribution (GPD) called as single sampling plan. The performance measures of the sampling plan are studied through its Operating Characteristic (OC) curve, Operating Characteristic function and its Operating Ratio (OR) values. Designing methods were developed to study the various quality levels namely AQL, LTPD and IQL values and are given for the distribution to protect both the producer and consumer simultaneously. The proposed plan is to support the design of attribute acceptance single sampling plan for lot acceptance with the fraction of non-conforming item modeled by GPD. This distribution is compared with conventional Poisson distribution through its plan parameters. Necessary tables and procedures are constructed with suitable examples to meet the needs of manufacturing industries to study the feasibility of the sampling plan.

  Key-Words / Index Term
  Acceptance Sampling, Single Sampling Plan, Generalized Poisson Distribution,Operating Characteristic Function

  References
  [1] H.F. Dodge, H.G. Romig, “Sampling Inspection Tables”, 2nd Edition, New York, Wiley, 1969.
  [2] P.C. Consul, G.C. Jain, “A Generalization of the Poisson Distribution”, Technometrics, Vol. 15, pp. 791-799, 1973.
  [3] J.M. Cameron, “Tables for constructing and for computing the operating characteristics of single sampling plans”, Industrial Quality Control, Vol. 9, pp. 37-39, 1952.
  [4] H.C. Hamaker, “Some Basic Principles of Sampling Inspection by Attributes”, Journal of Applied Statistics, Vol. 17, No.3 pp. 149-159, 1958.
  [5] A. Hald, “On the theory of single sampling inspection by attributes based on two quality levels”, Review of the International Statistical Institute, Vol. 35, No. 1, pp. 1–29, 1967.
  [6] V. Soundararajan, “Single Sampling Attributes Plan Indexed by AQL and AOQL”, Journal of Quality Technology, Vol. 13, No. 3, pp. 195-200, 1981.
  [7] K. Govindaraju, “Design of Minimum Average Total Inspection Sampling Plans”, Communications in Statistics- Simulation and Computations, Vol. 34, No. 2, pp. 485-493, 2005.
  [8] R. Radhakrishnan, L. Mohanapriya, “Selection of Single Sampling Plan Using Conditional Weighted Poisson Distribution”, Journal of Contemporary Research in Management, pp. 75-79, 2008.
  [9] Fangyu Liu, Lirong Cui, “A Design of Attributes Single Sampling Plans for Three-Class Products”, Quality Technology and Quantitative Management, Vol.10, No.4, pp. 369-387, 2011.
  [10] K. Pradeepa Veerakumari, S. Azarudheen, “Evaluation of Single Sampling Plan under the Conditions of Intervened Poisson distribution”, Communications in Statistics - Simulation and Computation, issue available at http://dx.doi.org/10.1080/03610918.2016.1193196.
  [11] V. Kaviyarasu, Asif T. Thottathil, “Designing Special Type Double Sampling Plan for Zero Inflated Poisson Distribution through Various Quality Levels”, International Journal of Statistics and Applied Mathematics, Vol.3(4), pp. 44-53, 2018.
  [12] P.C. Consul, “Generalized Poisson Distribution: Properties and Applications”, Marcel Dekker, New York, 1989.
  [13] E.G. Schilling, D.V. Neubauer, “Acceptance Sampling in Quality Control”, Boca Raton, CRC Press, 2009.
  

  Citation
  V. Kaviyarasu, V. Devika, "Designing Single Sampling Plan using Generalized Poisson Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.226-232, 2018

• Open Access   Article

  Alpha Weakly Semi Closed Sets in Topological Spaces

  R.S. Suriyaand, T. Shyla Issac Mary

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.233-242, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.233242

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  N. Levine introduced the concept of generalized closed (briefly g-closed) sets in topology. Researches in topology studied several versions of generalized closed sets and they characterized that sets. In this paper, we introduce a new class of closed sets which is called Alpha weakly semi closed sets in topological spaces and we study the relationships of this set with some other generalized closed sets. Also we study some of its basic properties.

  Key-Words / Index Term
  αws-closed, ws-open, α-closure

  References
  [1] N. Levine, “Generalized closed sets in topology”, Rend. Circ. Mat. Palermo, 19 (2), 89 - 96, 1970.
  [2] M. Sheik John, “On w-closed sets in topology”, Acta Ciencia Indica, 4, 389 - 392, 2000.
  [3] Basavaraj M. Ittanagi and Veeresha A Sajjanar, “On weakly semi closed sets in topological
  Spaces”, Int. J. of Mathematical Archive- 8(9), 126 - 134, 2017.
  [4] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, “On pre-continious and weak pre-
  continious mappings”, Proc. Math and Phys. Soc. Egypt 53, 47- 53, 1982.
  [5] N. Levine, “Semi-open sets and semi-continuity in topological spaces”, Amer. Math.
  monthly, 70, 36 - 41, 1963.
  [6] D. Andrijevic, “Semi-preopen sets”, Mat. Vesnik 38, 24 - 32, 1986.
  [7] O. Njastad, “On some classes of nearly open sets”, Pacific J. Math., 15, 961 - 970, 1965.
  [8] M.Stone, “Application of the theory of Boolean rings to general topology,” Trans. Amer.
  Maths. Soc., 41, 374 - 481, 1937.
  [9] D.Andrijevic, “On b-open sets”, Mat.Vesnik 48, 59 - 64, 1996.
  [10] V. Zaitsav, “On certain classes of topological spaces and their bicompactifications”, Dokl.
  Akad. Nauk SSSR, 178, 778 -779, 1968.
  [11] N. Palaniappan and Rao.K.C, “Regular generalized closed sets”, Kyungpook Math.J., 33
  (2), 211 - 219, 1993.
  [12] H. Maki, R. Devi and K. Balachandran, “Associated topologies of generalized α-closed sets
  and α-generalized closed sets”, Mem. Fac. sci. Kochi.Univ. Ser. A. Math., 15, 51 - 63,1994. [13] H. Maki, R. Devi and K. Balachandran, “Generalized α -closed sets in topology”, Bull.
  Fukuo Univ. Ed. Part III, 42, 13 - 21, 1993.
  [14] M.K.R.S.Veerakumar, “Pre-semi-closed sets”, Indian J. Math., 44 (2), 165-181, 2002.
  [15] S. P. Arya and T. M. Nour, “Characterizations of s-normal spaces”, Indian J. Pure. Appl.
  Math., 21 (8), 717 - 719, 1990.
  [16] H. Maki., J. Umehara and T. Noiri, “Generalized pre closed sets”, Mem. Fac. Sci. Kochi
  Univ. Ser. A. Math, 17, 33 - 42, 1996.
  [17] Sharmistha Bhattacharya (Halder), “On Generalized Regular Closed Sets”, Int. J. Contemp.
  Math. Sciences, Vol. 6, no. 3, 145-152, 2011.
  [18] J. Dontchev, “On generalizing semi-pre-open sets”, Mem. Fac. Sci. Kochi Univ. ser. A.
  Math., 16, 35 - 48, (1995).
  [19] J. Dontchev, and T. Noiri, “Quasi-normal spaces and πg-closed sets”, Acta Math. Hungar.,
  89 (3), 211 - 219, 2000.
  [20] N.Nagaveni, “Studies on generalizations of homeomorphisms in topological spaces”, Ph.D
  Thesis., Bharathiar University, Coimbatore, India.
  [21] M.K.R.S .Veerakumar, “g#-closed sets in topological spaces”, Mem. Fac. Sci. Kochi. Univ.
  Ser. A, Math, 24, 1 - 13, 2003.
  [22] K. A. Alli, A. Subramanian and S. Pious Missier, “g#p#-closed sets in topological spaces”, Int. J. of
  Math. And soft Computing, Vol. 3, No.3, 55 - 60, 2013.
  [23] Ahmad-Al-Omari and Mohd. Salmi Md Noorani, “On generalized b-closed sets”, Bulletin
  of Mathematical Sciences Society, 32, 19 - 30, 2009.
  [24] L. Vinayagamoorthi and N. Nagaveni, “On generalized αb-closed sets”, Proceeding ICMD-
  Allahabad, Puspha Publication vol. 1, 2010 - 11.
  [25] K. Mariappa and S. Sekar, “On regular generalized b-closed set”, Int. Journal of Math.
  Analysis, 7 (13), 613 - 624, 2013.
  [26] M.K.R.S . Veerakumar, “Between g*- closed sets and g-closed sets”, Mem. Fac. Sci. Kochi.
  Univ. Ser. A, Math, 21, 1-19, 2000.
  [27] P. Bhattacharya & B.K. Lahiri, “semi-generalized Closed Sets on topology”, Indian. J.
  Maths 29 (3), 375 - 382, (1987).
  [28] M. Pauline Mary Helen & A.Kulandhai Therese, “(gsp)*- closed sets in topological
  Spaces”, Int. J. of Math. Trends & Technology - vol 6, 75-86, 2014.
  [29] Y. Gnanambal, “On generalized pre regular closed sets in topological spaces”, Indian J.
  Pure. Appl. Math., 28 (3).
  [30] M.K.R.S. Veerakumar, “On α-generalized regular closed sets”, Indian .J. of Math, 44 (2),
  165 - 181 (2002).
  [31] D. Iyappan and N. Nagaveni, “On semi generalized b-closed set”, Nat. Sem. On Mat &
  Comp. sci, proc.6, jan 2010.
  [32] H. Maki, R. Devi and K. Balachandran, “Generalized α-continuous maps and α-generalized
  closed maps”, Indian .J. Pure. Appl. Math., 29(1), 37- 49, 1998.
  [33] Julian Dontchev, “On door spaces”, Indian J. Pure Appl. Math., 26(9), 873 - 881,1995.
  [34] M. Anitha and P. Thangavelu, “Generalized closed sets in sub maximal spaces”, Antarctica
  J.Math., 4 (1), 99 - 108,2007.
  [35] Saeid Jaifari, M. Lellis Thivagar and Nirmala Rebecca Paw, “Remarks on gα -closed sets in
  topological spaces”, Int. mathematical forums, 5, no.24, 1167 -1178, 2010.
  [36] A. Vadivel and K. Vairamanickam, “rgα-closed sets and rgα-open sets in topological
  Spaces”, Int. J. of Math. Analysis,Vol. 3, no.37, 1803 - 1819,2009.
  [37] D. Jankovic and,I. L. Reilly, “On semi-separation properties”, Indian. J. Pure and appl.
  math., 16, 957 - 964, 1985.
  [38] Luay A. Al-Swidi, M. Basim Mohammed , “New characterization of kernel set in
  Topological Spaces”, Archives Des science, vol. 65, No.9, 244 - 249, Sep 2012.
  

  Citation
  R.S. Suriyaand, T. Shyla Issac Mary, "Alpha Weakly Semi Closed Sets in Topological Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.233-242, 2018

• Open Access   Article

  A Bivariate Discrete Distribution from Freund Bivariate Exponential Distribution

  S. R. Supanekar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.243-246, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.243246

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  A bivariate discrete distribution is introduced by transforming a bivariate continuous random vector. Continuous random vector has been transformed to a discrete random vector by considering integer part of the components of continuous random vector. Freund bivariate exponential distribution is considered and corresponding bivariate discrete distribution is obtained. The methodology used is simple and can be applied to generate variety of bivariate/multivariate discrete distributions.

  Key-Words / Index Term
  Bivariate discrete distribution; Freund bivariate exponential distribution; Transformation of random variables

  References
  [1] E. Gomez-Deniz, F. J. Vazquez-Polo and V. Garcia-Garcia, “A discrete version of the half- normal distribution and its generalization with applications”, Stat Papers, Vol.55, pp.497-511, 2014
  [2] P. Holgate, “Estimation for the bivariate Poisson distribution”, Biometrika, Vol.51, pp.241-245, 1964.
  [3] H. Teicher, “On the multivariate Poisson distribution”, Skandinavisk Aktuarietidskrift, Vol.37, pp.1-9, 1954
  [4] M. A. Hamdan, “Estimation in the truncated bivariate Poisson distribution”, Technometrics, Vol.14, pp.33-45, 1972.
  [5] R. C. Dahiya, “Estimation in a truncated bivariate Poisson distribution”, Communications in Statistics Theory and Methods, Vol.6, pp.113-120, 1977.
  [6] S. Kocherlakota, K. Kocherlakota, “Bivariate Discrete Distributions”, Marcel Dekker, New York, 1992
  [7] N. L. Johnson, S. Kotz, and N. Balakrishnan, “Discrete multivariate distributions”, John Wiley and Sons, New York, 1997.
  [8] J. Lakshminarayana, S. N. N. Pandit, K. Rao, Srinivasa, “On Bivariate Poisson distribution”, Commun. Statistics-Theory Methods, Vol.28(2), pp.267-276, 1999
  [9] S. R. Supanekar and D. T. Shirke, “A new bivariate generalized power series distributiion”, Int. J. Agricult. Stat. Sci., Vol. 10(2), pp.343-349, 2014
  [10] K.Vanitha, M. Suresh Kumar, Sk. Althaf Rahaman, "An Effective Segmentation Approach of Medical Images Based on Beta Mixture Model", International Journal of Computer Sciences and Engineering, Vol.6 (3), pp.225-229, 2018.
  [11] J. E. Freund, “A bivariate extension of the exponential distribution”, J. Amer. Statist. Assoc., Vol.56, pp.971-977, 1961.
  

  Citation
  S. R. Supanekar, "A Bivariate Discrete Distribution from Freund Bivariate Exponential Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.243-246, 2018

• Open Access   Article

  On Almost Gβ closed mapping and Contra Gβ closed mapping in Intuitionistic Fuzzy Topological Spaces

  S. Jothimani, T. Jenitha Premalatha

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.247-257, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.247257

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this paper we introduce intuitionistic fuzzy almost pi generalized beta closed mappings intuitionistic fuzzy contra pi generalized beta continuous mappings and intuitionistic fuzzy almost contra pi generalized beta continuous mappings.

  Key-Words / Index Term
  Intuitionistic fuzzy almost Gβ continuous mappings, intuitionistic fuzzy contra Gβ continuous mappings, intuitionistic fuzzy almost contra Gβ continuous mappings and intuitionistic fuzzy contra Gβ closed mappings

  References
  [1] Atanassov,K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 1986,87-96.
  [2] Chang, C., Fuzzy topological spaces, J. Math. Anal.Appl.,1968,182-190.
  [3] Coker,D., An introduction to intuitionistic fuzzy topological space, Fuzzy sets and systems, 1997,81-89.
  [4] E.Ekici and B.Krsteska, Intuitionistic fuzzy contra strong pre-continuity, Facta Univ. Ser. Math. Inform., 2007, 273-284
  [5] Gurcay,H . ,Coker,D., and Haydar,Es .A., On fuzzy continuity inintuitionistic fuzzy topological spaces, The J.fuzzy mathematics, 1997, 365-378.
  [6] S.Jafari and T.Noiri and– “ Properties of β-Connected Spaces ” , Acta Math. Hung. , 101(2003), pp. 227-236.
  [7] S.Jothimani and T.Jenitha Premalatha., Intuitionistic fuzzy  generalized beta closed mappings –Math . Sci.Lett 6.No1,1-7(2017)
  [8] S.Jothimani and T.Jenitha Premalatha., On Almost and Contra Gβ Continuous Mappings in Intuitionisics fuzzy topological spaces.- submitted .
  [9] Joung Kon Jeon, Young Bae Jun, and Jin Han Park, Intuitionistic fuzzy alpha-continuity and intuitionistic fuzzy pre continuity, International Journal of Mathematics and Mathematical Sciences, 2005, 3091-3101.
  [10] Santhi, R. and Jayanthi, D., Intuitionistic fuzzy generalized semi-pre closed mappings-"Notes on IFS", Volume 16 (2010) Number 3, pages 28—39.
  [11] Thakur, S.S and RekhaChaturvedi, Regular generalized closed sets in intuitionistic fuzzy topological spaces Universitatea Din Bacau Studii Si Cercertar Stiintifice vol 6 pp 257-272.
  [12] Young Bae Jun and Seok-Zun Song, Intuitionistic fuzzy beta open sets and Intuitionistic beta continuous mappings Jour.of Appl. Math & computing,2005,467-474.
  [13] Zadeh, L. A., Fuzzy sets, Information and control, 1965,338-35.
  

  Citation
  S. Jothimani, T. Jenitha Premalatha, "On Almost Gβ closed mapping and Contra Gβ closed mapping in Intuitionistic Fuzzy Topological Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.247-257, 2018

• Open Access   Article

  On friendly index set of graphs

  M. Teffilia, J. Devaraj

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.258-263, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.258263

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  A function f from V(G) to {0,1} where for each edge xy ,f*(xy) = (f(x) +f(y))(mod2), let vi(f) is the number of vertices v with f(v) = i and ei(f) is the number of edges e with f*(e) = i is called friendly if |v0(f) - v1(f)| ≤ 1. The friendly index set of a graph G is FI(G) = {|e0(f) - e1(f)|, where f runs over all friendly labelings f of G}. In this paper we find the friendly index set of the umbrella graph, Spl(K1,n), Globe graph ,P2+mk1 and union of a path and a star sharing a vertex in common.

  Key-Words / Index Term
  Friendly labeling, Friendly index set, Umbrella graph, Spl(K1,n), Globe graph

  References
  [1] J. Devaraj and M. Teffilia, “On Harmonious graphs”, Bulletin of pure and applied sciences, Vol 37E (math and stat), No. 1, p.p. 47-53, 2018.
  [2] G.V. Ghodasara and D.G. Adalja, “Divisor Cordial labeling for vertex switching and duplication of special graphs”, International Journal of mathematics and its applications, Vol 4, Issue 3-B, pp 73-80, 2016.
  [3] F. Harary, Graph theory, Narosa publishing House, 1969.
  [4] Joseph A. Gallian, “A dynamic survey of graph labeling”, The electronic Journal of combinatorics, 2015.
  [5] P. Lawrence Rofario Raj and S. Koilraj graph of some standard graphs, “Cordial labeling for the splitting graph of some standard graphs”, International Journal of Mathematics and self computing, Vol 1, pp. 105 - 114, 2011.
  [6] A. Nellai Murugan and G. Devakiruba “Cycle related Divisor Cordial graphs”, International Journal of Mathematics Trends and technology - Volume 12, Number 1, 2014.
  [7] G. Sankari and S. lavanya, “ Odd -even graceful labeling of Umbrella and tadpole graphs”, International Journal of pure and applied mathematics, Vol 114, No. 6, pp. 139 - 143, 2017.
  [8] Sin - Min Lee, Ho-Kuen Ng and Gee-choon Lau, “On friendly index sets of spiders”, Malaysian Journal of Mathematical sciences, 8(1) : pp. 47-68, 2014.
  [9] Yong - song Ho, Sin-Min Lee, Ho-Kuen Ng, “On friendly index sets of root unions of stars by cycles”, Journal of Combinatorial mathematics and Combinatorial Computing, 62, pp. 97-120, 2007.
  [10] Dr. K. Vaithilingam, “Difference labeling of some graph families”, International Journal of mathematics and statistics Invention, Vol 2, Issue 6, pp 37 - 43, 2014.
  

  Citation
  M. Teffilia, J. Devaraj, "On friendly index set of graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.258-263, 2018