Journal Vol – 9 No -2, January 2015

Fault Detection in Engineering Application using Fuzzy Petri net and Abduction Technique


Sudipta Ghosh, Nabanita Das, Debasish Kunduand, Gopal Paul



This paper addresses onengineering application using fuzzy abductionandPetrinettechnique. The problems are introduced informallyabout the fault finding technique ofelectronic networks with different illustrations,so that anyone without any background inthe specific domain easily understands them.and easily find out the fault of thecomplicatedelectronic circuit.The problems require either a mathematical formulation ora computer simulation for their solutions. The detail outlineofthe solution of theengineering problem is illustrated here.


Fuzzy abduction ,Petri net,Relational matrix,Abductive Reasoning,


I.Bugarin, A. J. and Barro, S., “Fuzzy reasoning supported by Petri nets”,IEEE Trans. on Fuzzy Systems,vol. 2, no.2, pp 135-150,1994.

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VI.Cardoso, J., Valette, R., and Dubois, D., “Petri nets with uncertainmarkings”, in Advances in Petri nets, Lecture Notes in Computer Science,Rozenberg, G., Ed., vol.483, Springer-Verlag, New York, pp. 65-78, 1990.

VII.Chen, S. M., Ke, J. S. and Chang, J. F., “Knowledge representation usingfuzzy Petri nets,”IEEE Trans. on Knowledge and Data Engineering, vol. 2 ,no. 3, pp. 311-319, Sept. 1990.

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XII.Graham, I. and Jones, P. L.,Expert Systems: Knowledge, Uncertainty andDecision, Chapman and Hall, London, 1988.

XIII.Hirota, K. and Pedrycz, W., ” OR-AND neuron in modeling fuzzy setconnectives,”IEEE Trans. on Fuzzy systems, vol. 2 , no. 2 , May 1994.

XIV.Hutchinson, S. A. and Kak, A. C., “Planning sensing strategies in a robotworkcell with multisensor capabilities,”IEEE Trans. Robotics andAutomation, vol. 5, no. 6, pp.765-783, 1989.

XV.Jackson, P.,Introduction to Expert Systems, Addison-Wesley, Reading, MA,1988.

XVI.Konar, A. and Mandal, A. K., “Uncertainty management in expert systemsusing fuzzy Petri nets ,”IEEE Trans. on Knowledge and Data Engineering,vol. 8, no. 1, pp. 96-105, February 1996.

XVII.Konar, A. and Mandal, A. K., “Stability analysis of a non-monotonic Petrinet for diagnostic systems using fuzzy logic,”Proc. of 33rd Midwest Symp.on Circuits, and Systems, Canada, 1991.

XVIII.Konar, A. and Mandal, A. K., “Non-monotonic reasoning inExpertsystems using fuzzy Petri nets,” Advances in Modeling &Analysis, B,AMSE Press, vol. 23, no. 1, pp. 51-63, 1992.

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Some properties of 1-distributive join semilattices


Shiuly Akhter, A.S.A.Noor, M.Ayub Ali



J.C.Varlet introduced the concept of 1-distributive lattices to generalize thenotion ofdualpseudo complemented lattices. A latticeLwith 1 is calleda 1-distributivelattice if for allLc,b,a,caba1imply1)(cba. Of course everydistributive lattice with 1 is 1-distributive. Also everydual pseudo complemented lattice is1-distributive.Recently, Shiuly and Noor extended this concept for directedbelow joinsemi lattices. A joinsemi latticeSis calleddirected belowif for allSb,a, there existsScsuch thatb,ac. Again Y.Rav has extended the concept of 1-distributivity byintroducing the notion ofsemi prime filtersin a lattice. Recently, Noor and Ayubhavestudied the semi prime filters in a directed below joinsemi lattice. In this paper we haveincluded several characterizations and properties of 1-distributive joinsemi lattices.Weproved that for a joinsub semi latticeAofS,Aasomeforax:SxA11is a semi prime filter ofSif and only ifSis 1-distributive.We also showed that a directed below join semi lattice with 1 is 1-distributiveif and only if for allSb,a,111)()()(dbafor someb,ad,Sd.Introducingthe notion of-filters and using different equivalent conditions of 1-distributive joinsemilattices we have given a ‘Separation theorem’ for-filters.


1-distributive joinsemi lattice ,Semi prime filter,Prime ideal,Maximal ideal,-filter,


I.M. Ayub Ali and A. S. A. Noor, Semiprime filters in join semilattices,Submitted in Annals of Pure & Applied Mathematics,India.

II.P. Balasubramani and P. V. Venkatanarasimhan,Characterizations of the 0-Distributive Lattices,Indian J. Pure appl.Math. 32(3) 315-324, (2001).

III.R. M. Hafizur Rahman, M. Ayub Ali and A. S. A. Noor, On Semiprime ideals oflattices, J.Mech. Cont. & Math. Sci. Vol.-7, No.-2, January (2013), pages 1094-1102.

IV.C. Jayaram,0-modular semilattices, Studia Sci. Math. Hung. 22(1987), 189-195.

V.Y. S. Powar and N. K. Thakare,0-Distributive semilattices, Canad. Math. Bull.Vol. 21(4) (1978), 469-475.

VI.Y. Rav,Semi prime ideals in general lattices,Journal of pure and AppliedAlgebra, 56(1989) 105-118.

VII.Shiuly Akhter and A.S.A.Noor,1-distributive join semilattice, J. Mech.Cont. & Math. Sci. Vol.-7,No.-2,January (2013) pages 1067-1076.

VIII.J. C. Varlet,A generalization of the notion of pseudo-complementedness,Bull.Soc.Sci.Liege, 37(1968), 149-158.

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Effect on Probabilistic Continuous EOQ Review Model after Applying Third Party Logistics


Shirajul Islam Ukil, Mollah Mesbahuddin Ahmed, Shirin Sultana, Md. Sharif Uddin



This article explains how a company manages itsbusiness to gain minimuminventorycostandreaches itsbusiness success by usingThird Party Logistics.Applying Third Party Logisticsthe company may put its eyes on its production process and marketing smoothly.Thereby, the inventory cost might be reduced substantially.By applying this technique, mainlyit can reduce the clerical cost, security staff cost and depreciation costamong the variouscosts mentioned in the paper subsequently.And to get the optimum level the party usesits fewtools likedatabase software. Italso expressesamathematical framework to understand the performance of the company and put the argumentsthat inventory cost minimization methodis an approach that helps itto be competitive and success fulin the business arena.Toestablish a new modelin this paper,Probabilistic Continuous Economic Order Quantity(EOQ) Model isused as a baseline.


Inventory,Probabilistic Continuous EconomicOrder Quantity(EOQ),Review Model,fixed cost,variable cost,holding cost,Third Party Logistics,


I.Ahuja K. K., Production Management, New Delhi, 2006.

II.Taha H. A., Operations Research: An Introduction, Fifth Edition.

III.Zipkin P. H., Foundations of Inventory Management, InternationalEdition, 2000.

IV.Bin L., “Study on Modeling of Container Terminal Logistics SystemUsing Agent–Based Computing and Knowledge Discovery,”International journal of Distributed Sensor Networks, Volume 5 (2009),Issue 1, page 36-36, 2009.

V.Erkayman B.,Gundogar E. and Yilmaz A., “An Integrated FuzzyApproach for Strategic Alliance Partner Selection in Third PartyLogistics,” The Scientific World Journal, Volume 2012, 6 pages, 2012.

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VIII.Gupta P. K. and Hira D. S., Introduction to Operations Research, 1995.

IX.Akman G. and Baynal K. “Logistic Service Provider Selection through anIntegrated Fuzzy Multi criteria Decision Making Approach,” Journal ofIndustrial Engineering, Volume 2014, 16 pages, 2014.

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XI.Cheng L., Tsou C. S., Lee M. C., Huang L. H., Song D., and Teng W. S.,“Tradeoff Analysis for Optimal Multiobjective Inventory Model,”Journalof Applied Mathematics Volume 2013, 8 pages, 2013.

XII.Hadley G. and Wahitin T., Analysis of Inventory Systems, Prentice Hall,Engle-wood Cliffs, 1963.

XIII.Narayan P. and Subramanian J., Inventory Management, First Edition,New Delhi, 2008.

XIV.NahmiaS., Production and Operation Analysis, 1997.

XV.Muller M., Essentials of Inventory Management, 2003.

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Experimental Study on Shape and Rise Velocity of Small Bubbles in Stagnant Water


A Mitra, P Bhattacharya, S Mukhopadhyay, K K Dhar



This paper presents the results of an experimental study on the shape andrise velocityof small bubbles risingin stagnant water. Bubbles, generated at the bottom of the chamberholding water, rise through it.A high speed camera (1000 fps, Kodak, Model 1000 HRC)together with a 90 mm Macro lens is placed at a height of 60 cm from the bottom of thechamber. It is linked with a PC. The commercial software Sigma Scan Pro 5.0 and AdobePhotoshop are used for image capturing and processing.Bubbles(diametersin the range0.0245-5.903 cm)aregenerated at the bottom of the chamber holding the water. We find thatbubbles have threesteady shapes, a sphere,an ellipsoidandspherical capin this diameterrange.The experimentally determined rise velocity of bubble in the present investigationagrees well with the data available in the literature


Bubble,Rise Velocity,Stagnant Water,Shape,


I.Arnold, K. and M. Stewart, Surface production operations. 3rd ed. Vol. 1. 2008,Amsterdam: Elsevier.768p.

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IV.Bybee, K., Production of heavy crude oil: Topside experiences on Grane, Journalof petroleum technology, 2007. 59(4): p. 86-89.

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XVII.Mitra A, Bhattacharya P, MukhopadhyayS,Dhar K K, “Experimental Study onShape and Path of Small Bubbles using Video-Image Analysis,”2015 ThirdInternational Conf. On Computer, Communication, Control And InformationTechnology, 7–8 February 2015, Academy of Technology, Hooghly, West Bengal,India

XVIII.S.Mukhopadhyay,N.K.Das,A.Pradhan,N.Ghosh,P.K.Panigrahi,”Wavelet andmulti-fractal based analysis on DIC images in epithelium region to detect anddiagnose the cancer progress among different grades of tissues”,SPIE PhotonicsEurope-2014, Belgium.

XIX.S.Mukhopadhyay,N.K.Das,A.Pradhan,N.Ghosh,P.K.Panigrahi,”Pre-cancerDetection by Wavelet Transform and Multi-fractality in various grades of DICStromal Images”, SPIE West Photonics-2014, USA.

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XXII.Zheng, Li and Yapa, P.D., Buoyant Velocity of Spherical and Non sphericalBubbles/Droplets, Journal of Hydraulic Engineering, Vol. 126, No. 11, 2000.

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Numerical study and CFD Simulations of Incompressible Newtonian Flow by Solving steady Navier-stokes equations using Newton’s method


K. M.Helal



Inthis paper, incompressible Newtonian flow is numerically studied byapproximatingthesolutionof the steady Navier-Stokes equationsin two dimensional case.Computational Fluid Dynamics (CFD)simulationsare carriedout byusing thefiniteelement method.Newton’smethodis applied to solvetheNavier-Stokes equationswherethe finite element solutions of Stokes equations is considered as the initial guess to obtainthe convergenceof Newton’s sequence.The numericalsimulations are presentedin termsofthe contours ofvelocity, pressure and streamline. All themeshes andsimulations areimplementedonthegeneralfinite element solver FreeFem++.Atwo-dimensionalbenchmark flow was computedwith posteriori estimates.It hasalsobeen established thatthe free accesssolverFreeFem++ can provide a reasonable good numerical simulationsof complicated flow behavior.


Navier-Stokesequations,CFD simulation,finite elementmethod,Newton-Raphsonmethod,


I.Adams, R.A.,and Fournier,J.F.(2003).Sobolev Spaces,Second Edition,Academic Press, New York.

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VIII.Hecht,F. (2012). FreeFem++, Version 3.23,,S. D., Lee,Y. H. and Shin,B. C.(2006).Newton’s Method for theNavier-StokesEquations with Finite-Element Initial Guess of Stokes Equation,Computers and Mathematics with applications,51, 805-816.

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A Direct Analytical Method for Finding an Optimal Solution for Transportation Problems


M. Wali Ullah, Rizwana Kawser, M. Alhaz Uddin



In this paper a direct analytical method is proposed for finding an optimalsolution for a wide range of transportation problems. A numerical illustration isestablished and the optimality of the result yielded by this method is also checked. Themost attractive feature of this method is that it requires very simple arithmetical andlogical calculations. Themethod will be very worthwhile for those decision makers whoare dealing with logistics and supply chain related issues.One canalsoeasily adopt theproposed method among the existing methods for simplicity of the presented method.


TP=Transportation problem,SS=Stepping Stone ,MODI= Modified Distribution,NCM= North-West Corner Method , LCM= Least Cost Method,VAM= Vogel’sApproximation Method,Numerical Example,


I.Goyal, S.K.-Improving VAM for the Unbalanced Transportation Problem,J.Opl.Res.Soc.35, 1113-1114(1984).

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IX.Sudhakar,V. J.,Arunsankar, N.and Karpagam,T.-A New approach forfinding an Optimal Solution forTransportation Problems,European Journal ofScientific Research, vol.68, 254-257(2012).

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Momtaz Begum



In This paper the author studiesthe Glivenko congruence R in a0-distributive meet semilattice. It isprovedthata meet semilattice S with 0 is0-distributive if and only if the quotient semilattice RS is distributive. Hence S is0-distributive if and only if (0] is the Kernel of some homomorphism ofS onto adistributive meet semilattice with 0.


Glivenko congruence,0-distributive semilattice ,distributive meetsemilattice,


I.P. Balasubramani and P. V. Venkatanarasimhan,Characterizations of the 0-Distributive Lattices,Indian J. Pure appl.Math. 32(3) 315-324, (2001).

II.Momtaz Begum and A.S.A. Noor,Semi prime ideals in meet semilattices,Indian J. Pure appl.Math.Vol.1, No.2, 2012, 149-157.

III.H.S.Chakraborty and M.R.Talukder,Some characterizations of 0-distributivesemilattices,Accepted in the Bulletin of Malaysian Math. Sci.Soc.

IV.Azmal Hossain, Title: A study on meet semilattices directed above, Ph.D.Thesis, RU (2004).

V.Y. S. Powar and N. K. Thakare,0-Distributivesemilattices, Canad. Math. Bull.Vol. 21(4) (1978), 469-475.

VI.Rhodes, J.B. Modular and distributive semilattices. Trans. Amer. Math. Society.Vol.201(1975), P.31-41.

VII.J. C. Varlet,A generalization of the notion of pseudo-complementedness,Bull.Soc.Sci.Liege, 37(1968), 149-158.

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