Main Article Content
Abstract
Enterprises and industrial centers need current decision for making products in fast changing market. Uncertainty and yield defined goals make decision making more difficult. In this situation fuzzy logic is used for coping surrounding environment. This paper deals with a fuzzy linear programming model for a problem of food industry. The different types of achievement function such as compensatory and weighted compensatory form
Keywords
Fuzzy Linear Programming
Membership Function
Compensatory Operator
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How to Cite
Sinha, M. K., Burnwal, A. P., & Singh, C. (2018). FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING APPROACH FOR SOLVING PROBLEM OF FOOD INDUSTRY. International Journal of Students’ Research in Technology & Management, 6(2), 13–19. https://doi.org/10.18510/ijsrtm.2018.623
References
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[1] Zimmermann, H.J., 1978. Fuzzy programming and linear programming with general objective functions. Fuzzy sets and systems, 1. P. 45.
[2] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of fuzzy set theory in different paradigm,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 16-22.
[3] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “On soft computing techniques in various areas,†Computer Science & Information Technology (CS & IT), 2013, vol. 3, pp. 59-68, DOI : 10.5121/csit.2013.3206.
[4] S. K. Das, S. Tripathi, and A. Burnwal, “Some relevance fields of soft computing methodology,†International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, pp. 1-6.
[5] Bellman, R.E. and Zadeh, L.A. 1970 Management science 17 P.141.
[6] Hannan, E.L.,1979. On the efficiency of the product operator in fuzzy programming with multiple objectives. Fuzzy sets and systems, 2. P. 259.
[7] Tanaka, H. and K.Asai, 1981a. Fuzzy linear programming with fuzzy parameters. International conference or policy analysis and information systems. August 19-22, Taiwan.
[8] Tanaka, H. and K.Asai, 1981b. Fuzzy linear programming based on fuzzy functions. International federation of automatic control, 8th Triennial world congress, Aug. 24-28, Kyoto.
[9] Liena, J., 1985. On Fuzzy linear programming. European journal of operational research, 22, P. 216.
[10] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of Mathematical Modeling in Different Areas,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 23-26.
[11] S. K. Das and S. Tripathi, “Adaptive and intelligent energy efficient routing for transparent heterogeneous ad-hoc network by fusion of game theory and linear programming,†Applied Intelligence, 2017, pp. 1-21, https://doi.org/10.1007/s10489-017-1061-6.
[12] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “Ethics of reducing power consumption in wireless sensor networks using soft computing techniques,†International Journal of Advanced Computer Research, 2013, vol. 3, no. 1, pp. 301-304.
[13] S. K. Das, B. Das, and A. Burnwal, “Intelligent energy competency routing scheme for wireless sensor networksâ€, International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, no. 3, pp. 79-84.
[14] Chanas ,S., 1989. Fuzzy programming in multiple objective linear programming a parametric approach. Fuzzy sets and systems, 29, P.303.
[15] S. K. Das, S. Tripathi, and A. Burnwal, “Intelligent energy competency multipath routing in wanet,†in Information Systems Design and Intelligent Applications, Springer, 2015, pp. 535-543, DOI: 10.1007/978-81-322-2250-7_53.
[16] S. K. Das, S. Tripathi, and A. Burnwal, “Fuzzy based energy efficient multicast routing for ad-hoc network,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-5, DOI: 10.1109/C3IT.2015.7060126.
[17] S. K. Das, S. Tripathi, and A. Burnwal, “Design of fuzzy based intelligent energy efficient routing protocol for WANET,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-4, DOI: 10.1109/C3IT.2015.7060201.
[18] S. K. Das and S. Tripathi, “Energy efficient routing protocol for manet based on vague set measurement technique,†Procedia Computer Science, 2015, vol. 58, pp. 348-355, doi:10.1016/j.procs.2015.08.030.
[19] Rommelfanger, H, R.Hanuscheck and J.Wolf, 1989. Linear programming with fuzzy objectives. Fuzzy sets and systems, P. 29.
[20] Inuiguchi, M., H. Ichihashi and Y. Kume, 1990. A solution algorithm for fuzzy linear programming with piecewise linear membership function. Fuzzy sets and systems, 34. P. 15.
[21] Dipti and Aparna 2011. Linear programming with triangular Intuitionistic Fuzzy number. EUSFLAT-LFA 2011. Aix-les bains, France. P. 563.
[22] Negoita, C.V. and M. Saluria, 1976. Fuzzy linear programming tolerance in planning. Econom. Comp. Econom. Cybernet. Studies, 1, P. 3.
[23] Lahandjula, M.K., 1982. Compensatory operators in fuzzy linear programming with multiple objectives. Fuzzy sets and systems, 8, P. 245.
[24] Luhandjula, M.K., 1993. Linear programming under randomness and fuzziness, Fuzzy sets and systems, 10, P. 57.
[25] S. K. Das and S. Tripathi, “Energy Efficient Routing Protocol for MANET Using Vague Set,†in Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Springer, 2016, pp. 235-245, DOI: 10.1007/978-981-10-0448-3_19.
[26] A. Burnwal, A. Kumar, and S. K. Das, “Survey on application of artificial intelligence techniques,†International Journal of Engineering Research & Management, 2014, vol. 1, no. 5, pp. 215-219.
[27] Cagatay Teke and Baha Guney, Fuzzy linear programming approach for determining the production amounts in poultry industry. ICLTET 2016, Dubai (UAE). P. 42
[28] Santosh Kumar Das and Sachin Tripathi. “Energy efficient routing formation algorithm for hybrid ad-hoc network: A geometric programming approachâ€, Peer-to-Peer Networking and Applications, Springer, 2018, pp. 1-27, https://doi.org/10.1007/s12083-018-0643-3.
[29] T. Allahviranloo, F.H. Lofti, M.K. Kiasary, N.A. Kiani, L. Alizadeh, 2008, Solving fully fuzzy linear programming problemby the ranking function, Applied Mathematical Sciences 2, P. 19-32.
[30] T. Allahviranloo, K.H. Shamsolkotabi, N.A. Kiani, L. Alizadeh, 2007, Fuzzy integer linear programming problems, International Journal of Contemporary Mathematical Sciences 2, P. 167-181.
[31] A.Kumar, J. Kaur, P. Singh, 2010 Fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints, International Journal of Applied Mathematics and Computer Sciences 6, P. 37-41.
[32] A. Kumar, J. Kaur, P. Singh, 2011, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling 35, P. 817-823.
[33] Santosh Kumar Das and Sachin Tripathi, “Energy Efficient Routing Formation Technique for Hybrid Ad-Hoc Network using Fusion of Artificial Intelligence Techniquesâ€, International Journal of Communication Systems, Wiley, DOI:10.1002/dac.3340, Vol. 30, No. 16, 10 November 2017.
[34] S. K. Das and S. Tripathi, “Intelligent energy-aware efficient routing for MANET,†Wireless Networks, 2016, pp. 1-21, DOI 10.1007/s11276-016-1388-7.
[35] S. K. Das, A. K. Yadav and S. Tripathi, “IE2M: Design of intellectual energy efficient multicast routing protocol for ad-hoc network,†Peer-to-Peer Networking and Applications, 2016, vol. 10, no. 3, pp. 670-687, DOI 10.1007/s12083-016-0532-6.
[36] A. K. Yadav, S. K. Das and S. Tripathi, “EFMMRP: Design of efficient fuzzy based multi-constraint multicast routing protocol for wireless ad-hoc network,†Computer Networks, 2017, vol. 118, pp. 15-23, https://doi.org/10.1016/j.comnet.2017.03.001.
[37] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “Ethics of E-Commerce in Information and Communications Technologies,†International Journal of Advanced Computer Research, 2013, vol. 3, no. 1, pp. 122-124, doi=10.1.1.300.9397.
[38] H.R. Maleki, 2002, Ranking functions and their applications to fuzzy linear programming, Far East Journal of Mathematical Sciences 4, P. 283-301.
[39] J. Ramik, 2005, Duality in fuzzy linear programming: some new concepts and results, Fuzzy optimization and decision making 4, P. 25-39.
[40] B. Werners, 1987, An interactive fuzzy programming systems, Fuzzy sets and systems 23, P. 131-147.
[41] H. Rommelfanger, 2007, A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values, Fuzzy sets and systems 158, P. 1892-1904.
[42] H.M. Nehi, H.R. Maleki, M. Mashinchi, 2004, Solving fuzzy number linear programming problems by lexicographic ranking function, Italian journal of Pure and Applied mathematics 15, P. 9-20.
[43] X. Liu, 2001, Measuring the satisfaction of constraints in fuzzy linear programming, Fuzzy set and systems 22, P. 263-275.
[44] G. Tsakiris and M. Spiliotis, 2004, Fuzzy linear programming for problems of water allocation under uncertainity, European Water 7/8: P. 25-37.
[45] Amit Kumar & Jagdeep Kaur, 2011, A new method for solving fuzzy linear programs with Trapezoidal fuzzy numbers, Journal of fuzzy set valued analysis, ISPACS. P. 1.
References
[1] Zimmermann, H.J., 1978. Fuzzy programming and linear programming with general objective functions. Fuzzy sets and systems, 1. P. 45.
[2] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of fuzzy set theory in different paradigm,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 16-22.
[3] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “On soft computing techniques in various areas,†Computer Science & Information Technology (CS & IT), 2013, vol. 3, pp. 59-68, DOI : 10.5121/csit.2013.3206.
[4] S. K. Das, S. Tripathi, and A. Burnwal, “Some relevance fields of soft computing methodology,†International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, pp. 1-6.
[5] Bellman, R.E. and Zadeh, L.A. 1970 Management science 17 P.141.
[6] Hannan, E.L.,1979. On the efficiency of the product operator in fuzzy programming with multiple objectives. Fuzzy sets and systems, 2. P. 259.
[7] Tanaka, H. and K.Asai, 1981a. Fuzzy linear programming with fuzzy parameters. International conference or policy analysis and information systems. August 19-22, Taiwan.
[8] Tanaka, H. and K.Asai, 1981b. Fuzzy linear programming based on fuzzy functions. International federation of automatic control, 8th Triennial world congress, Aug. 24-28, Kyoto.
[9] Liena, J., 1985. On Fuzzy linear programming. European journal of operational research, 22, P. 216.
[10] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of Mathematical Modeling in Different Areas,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 23-26.
[11] S. K. Das and S. Tripathi, “Adaptive and intelligent energy efficient routing for transparent heterogeneous ad-hoc network by fusion of game theory and linear programming,†Applied Intelligence, 2017, pp. 1-21, https://doi.org/10.1007/s10489-017-1061-6.
[12] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “Ethics of reducing power consumption in wireless sensor networks using soft computing techniques,†International Journal of Advanced Computer Research, 2013, vol. 3, no. 1, pp. 301-304.
[13] S. K. Das, B. Das, and A. Burnwal, “Intelligent energy competency routing scheme for wireless sensor networksâ€, International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, no. 3, pp. 79-84.
[14] Chanas ,S., 1989. Fuzzy programming in multiple objective linear programming a parametric approach. Fuzzy sets and systems, 29, P.303.
[15] S. K. Das, S. Tripathi, and A. Burnwal, “Intelligent energy competency multipath routing in wanet,†in Information Systems Design and Intelligent Applications, Springer, 2015, pp. 535-543, DOI: 10.1007/978-81-322-2250-7_53.
[16] S. K. Das, S. Tripathi, and A. Burnwal, “Fuzzy based energy efficient multicast routing for ad-hoc network,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-5, DOI: 10.1109/C3IT.2015.7060126.
[17] S. K. Das, S. Tripathi, and A. Burnwal, “Design of fuzzy based intelligent energy efficient routing protocol for WANET,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-4, DOI: 10.1109/C3IT.2015.7060201.
[18] S. K. Das and S. Tripathi, “Energy efficient routing protocol for manet based on vague set measurement technique,†Procedia Computer Science, 2015, vol. 58, pp. 348-355, doi:10.1016/j.procs.2015.08.030.
[19] Rommelfanger, H, R.Hanuscheck and J.Wolf, 1989. Linear programming with fuzzy objectives. Fuzzy sets and systems, P. 29.
[20] Inuiguchi, M., H. Ichihashi and Y. Kume, 1990. A solution algorithm for fuzzy linear programming with piecewise linear membership function. Fuzzy sets and systems, 34. P. 15.
[21] Dipti and Aparna 2011. Linear programming with triangular Intuitionistic Fuzzy number. EUSFLAT-LFA 2011. Aix-les bains, France. P. 563.
[22] Negoita, C.V. and M. Saluria, 1976. Fuzzy linear programming tolerance in planning. Econom. Comp. Econom. Cybernet. Studies, 1, P. 3.
[23] Lahandjula, M.K., 1982. Compensatory operators in fuzzy linear programming with multiple objectives. Fuzzy sets and systems, 8, P. 245.
[24] Luhandjula, M.K., 1993. Linear programming under randomness and fuzziness, Fuzzy sets and systems, 10, P. 57.
[25] S. K. Das and S. Tripathi, “Energy Efficient Routing Protocol for MANET Using Vague Set,†in Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Springer, 2016, pp. 235-245, DOI: 10.1007/978-981-10-0448-3_19.
[26] A. Burnwal, A. Kumar, and S. K. Das, “Survey on application of artificial intelligence techniques,†International Journal of Engineering Research & Management, 2014, vol. 1, no. 5, pp. 215-219.
[27] Cagatay Teke and Baha Guney, Fuzzy linear programming approach for determining the production amounts in poultry industry. ICLTET 2016, Dubai (UAE). P. 42
[28] Santosh Kumar Das and Sachin Tripathi. “Energy efficient routing formation algorithm for hybrid ad-hoc network: A geometric programming approachâ€, Peer-to-Peer Networking and Applications, Springer, 2018, pp. 1-27, https://doi.org/10.1007/s12083-018-0643-3.
[29] T. Allahviranloo, F.H. Lofti, M.K. Kiasary, N.A. Kiani, L. Alizadeh, 2008, Solving fully fuzzy linear programming problemby the ranking function, Applied Mathematical Sciences 2, P. 19-32.
[30] T. Allahviranloo, K.H. Shamsolkotabi, N.A. Kiani, L. Alizadeh, 2007, Fuzzy integer linear programming problems, International Journal of Contemporary Mathematical Sciences 2, P. 167-181.
[31] A.Kumar, J. Kaur, P. Singh, 2010 Fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints, International Journal of Applied Mathematics and Computer Sciences 6, P. 37-41.
[32] A. Kumar, J. Kaur, P. Singh, 2011, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling 35, P. 817-823.
[33] Santosh Kumar Das and Sachin Tripathi, “Energy Efficient Routing Formation Technique for Hybrid Ad-Hoc Network using Fusion of Artificial Intelligence Techniquesâ€, International Journal of Communication Systems, Wiley, DOI:10.1002/dac.3340, Vol. 30, No. 16, 10 November 2017.
[34] S. K. Das and S. Tripathi, “Intelligent energy-aware efficient routing for MANET,†Wireless Networks, 2016, pp. 1-21, DOI 10.1007/s11276-016-1388-7.
[35] S. K. Das, A. K. Yadav and S. Tripathi, “IE2M: Design of intellectual energy efficient multicast routing protocol for ad-hoc network,†Peer-to-Peer Networking and Applications, 2016, vol. 10, no. 3, pp. 670-687, DOI 10.1007/s12083-016-0532-6.
[36] A. K. Yadav, S. K. Das and S. Tripathi, “EFMMRP: Design of efficient fuzzy based multi-constraint multicast routing protocol for wireless ad-hoc network,†Computer Networks, 2017, vol. 118, pp. 15-23, https://doi.org/10.1016/j.comnet.2017.03.001.
[37] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “Ethics of E-Commerce in Information and Communications Technologies,†International Journal of Advanced Computer Research, 2013, vol. 3, no. 1, pp. 122-124, doi=10.1.1.300.9397.
[38] H.R. Maleki, 2002, Ranking functions and their applications to fuzzy linear programming, Far East Journal of Mathematical Sciences 4, P. 283-301.
[39] J. Ramik, 2005, Duality in fuzzy linear programming: some new concepts and results, Fuzzy optimization and decision making 4, P. 25-39.
[40] B. Werners, 1987, An interactive fuzzy programming systems, Fuzzy sets and systems 23, P. 131-147.
[41] H. Rommelfanger, 2007, A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values, Fuzzy sets and systems 158, P. 1892-1904.
[42] H.M. Nehi, H.R. Maleki, M. Mashinchi, 2004, Solving fuzzy number linear programming problems by lexicographic ranking function, Italian journal of Pure and Applied mathematics 15, P. 9-20.
[43] X. Liu, 2001, Measuring the satisfaction of constraints in fuzzy linear programming, Fuzzy set and systems 22, P. 263-275.
[44] G. Tsakiris and M. Spiliotis, 2004, Fuzzy linear programming for problems of water allocation under uncertainity, European Water 7/8: P. 25-37.
[45] Amit Kumar & Jagdeep Kaur, 2011, A new method for solving fuzzy linear programs with Trapezoidal fuzzy numbers, Journal of fuzzy set valued analysis, ISPACS. P. 1.
[2] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of fuzzy set theory in different paradigm,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 16-22.
[3] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “On soft computing techniques in various areas,†Computer Science & Information Technology (CS & IT), 2013, vol. 3, pp. 59-68, DOI : 10.5121/csit.2013.3206.
[4] S. K. Das, S. Tripathi, and A. Burnwal, “Some relevance fields of soft computing methodology,†International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, pp. 1-6.
[5] Bellman, R.E. and Zadeh, L.A. 1970 Management science 17 P.141.
[6] Hannan, E.L.,1979. On the efficiency of the product operator in fuzzy programming with multiple objectives. Fuzzy sets and systems, 2. P. 259.
[7] Tanaka, H. and K.Asai, 1981a. Fuzzy linear programming with fuzzy parameters. International conference or policy analysis and information systems. August 19-22, Taiwan.
[8] Tanaka, H. and K.Asai, 1981b. Fuzzy linear programming based on fuzzy functions. International federation of automatic control, 8th Triennial world congress, Aug. 24-28, Kyoto.
[9] Liena, J., 1985. On Fuzzy linear programming. European journal of operational research, 22, P. 216.
[10] A. Burnwal, A. Kumar, and S. K. Das, “Assessment of Mathematical Modeling in Different Areas,†International Journal of Advanced Technology & Engineering Research, 2013, vol. 3, no. 3, pp. 23-26.
[11] S. K. Das and S. Tripathi, “Adaptive and intelligent energy efficient routing for transparent heterogeneous ad-hoc network by fusion of game theory and linear programming,†Applied Intelligence, 2017, pp. 1-21, https://doi.org/10.1007/s10489-017-1061-6.
[12] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “Ethics of reducing power consumption in wireless sensor networks using soft computing techniques,†International Journal of Advanced Computer Research, 2013, vol. 3, no. 1, pp. 301-304.
[13] S. K. Das, B. Das, and A. Burnwal, “Intelligent energy competency routing scheme for wireless sensor networksâ€, International Journal of Research in Computer Applications and Robotics, 2014, vol. 2, no. 3, pp. 79-84.
[14] Chanas ,S., 1989. Fuzzy programming in multiple objective linear programming a parametric approach. Fuzzy sets and systems, 29, P.303.
[15] S. K. Das, S. Tripathi, and A. Burnwal, “Intelligent energy competency multipath routing in wanet,†in Information Systems Design and Intelligent Applications, Springer, 2015, pp. 535-543, DOI: 10.1007/978-81-322-2250-7_53.
[16] S. K. Das, S. Tripathi, and A. Burnwal, “Fuzzy based energy efficient multicast routing for ad-hoc network,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-5, DOI: 10.1109/C3IT.2015.7060126.
[17] S. K. Das, S. Tripathi, and A. Burnwal, “Design of fuzzy based intelligent energy efficient routing protocol for WANET,†in Computer, Communication, Control and Information Technology (C3IT), 2015 Third International Conference on, IEEE, 2015, pp. 1-4, DOI: 10.1109/C3IT.2015.7060201.
[18] S. K. Das and S. Tripathi, “Energy efficient routing protocol for manet based on vague set measurement technique,†Procedia Computer Science, 2015, vol. 58, pp. 348-355, doi:10.1016/j.procs.2015.08.030.
[19] Rommelfanger, H, R.Hanuscheck and J.Wolf, 1989. Linear programming with fuzzy objectives. Fuzzy sets and systems, P. 29.
[20] Inuiguchi, M., H. Ichihashi and Y. Kume, 1990. A solution algorithm for fuzzy linear programming with piecewise linear membership function. Fuzzy sets and systems, 34. P. 15.
[21] Dipti and Aparna 2011. Linear programming with triangular Intuitionistic Fuzzy number. EUSFLAT-LFA 2011. Aix-les bains, France. P. 563.
[22] Negoita, C.V. and M. Saluria, 1976. Fuzzy linear programming tolerance in planning. Econom. Comp. Econom. Cybernet. Studies, 1, P. 3.
[23] Lahandjula, M.K., 1982. Compensatory operators in fuzzy linear programming with multiple objectives. Fuzzy sets and systems, 8, P. 245.
[24] Luhandjula, M.K., 1993. Linear programming under randomness and fuzziness, Fuzzy sets and systems, 10, P. 57.
[25] S. K. Das and S. Tripathi, “Energy Efficient Routing Protocol for MANET Using Vague Set,†in Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Springer, 2016, pp. 235-245, DOI: 10.1007/978-981-10-0448-3_19.
[26] A. Burnwal, A. Kumar, and S. K. Das, “Survey on application of artificial intelligence techniques,†International Journal of Engineering Research & Management, 2014, vol. 1, no. 5, pp. 215-219.
[27] Cagatay Teke and Baha Guney, Fuzzy linear programming approach for determining the production amounts in poultry industry. ICLTET 2016, Dubai (UAE). P. 42
[28] Santosh Kumar Das and Sachin Tripathi. “Energy efficient routing formation algorithm for hybrid ad-hoc network: A geometric programming approachâ€, Peer-to-Peer Networking and Applications, Springer, 2018, pp. 1-27, https://doi.org/10.1007/s12083-018-0643-3.
[29] T. Allahviranloo, F.H. Lofti, M.K. Kiasary, N.A. Kiani, L. Alizadeh, 2008, Solving fully fuzzy linear programming problemby the ranking function, Applied Mathematical Sciences 2, P. 19-32.
[30] T. Allahviranloo, K.H. Shamsolkotabi, N.A. Kiani, L. Alizadeh, 2007, Fuzzy integer linear programming problems, International Journal of Contemporary Mathematical Sciences 2, P. 167-181.
[31] A.Kumar, J. Kaur, P. Singh, 2010 Fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints, International Journal of Applied Mathematics and Computer Sciences 6, P. 37-41.
[32] A. Kumar, J. Kaur, P. Singh, 2011, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling 35, P. 817-823.
[33] Santosh Kumar Das and Sachin Tripathi, “Energy Efficient Routing Formation Technique for Hybrid Ad-Hoc Network using Fusion of Artificial Intelligence Techniquesâ€, International Journal of Communication Systems, Wiley, DOI:10.1002/dac.3340, Vol. 30, No. 16, 10 November 2017.
[34] S. K. Das and S. Tripathi, “Intelligent energy-aware efficient routing for MANET,†Wireless Networks, 2016, pp. 1-21, DOI 10.1007/s11276-016-1388-7.
[35] S. K. Das, A. K. Yadav and S. Tripathi, “IE2M: Design of intellectual energy efficient multicast routing protocol for ad-hoc network,†Peer-to-Peer Networking and Applications, 2016, vol. 10, no. 3, pp. 670-687, DOI 10.1007/s12083-016-0532-6.
[36] A. K. Yadav, S. K. Das and S. Tripathi, “EFMMRP: Design of efficient fuzzy based multi-constraint multicast routing protocol for wireless ad-hoc network,†Computer Networks, 2017, vol. 118, pp. 15-23, https://doi.org/10.1016/j.comnet.2017.03.001.
[37] S. K. Das, A. Kumar, B. Das, and A. Burnwal, “Ethics of E-Commerce in Information and Communications Technologies,†International Journal of Advanced Computer Research, 2013, vol. 3, no. 1, pp. 122-124, doi=10.1.1.300.9397.
[38] H.R. Maleki, 2002, Ranking functions and their applications to fuzzy linear programming, Far East Journal of Mathematical Sciences 4, P. 283-301.
[39] J. Ramik, 2005, Duality in fuzzy linear programming: some new concepts and results, Fuzzy optimization and decision making 4, P. 25-39.
[40] B. Werners, 1987, An interactive fuzzy programming systems, Fuzzy sets and systems 23, P. 131-147.
[41] H. Rommelfanger, 2007, A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values, Fuzzy sets and systems 158, P. 1892-1904.
[42] H.M. Nehi, H.R. Maleki, M. Mashinchi, 2004, Solving fuzzy number linear programming problems by lexicographic ranking function, Italian journal of Pure and Applied mathematics 15, P. 9-20.
[43] X. Liu, 2001, Measuring the satisfaction of constraints in fuzzy linear programming, Fuzzy set and systems 22, P. 263-275.
[44] G. Tsakiris and M. Spiliotis, 2004, Fuzzy linear programming for problems of water allocation under uncertainity, European Water 7/8: P. 25-37.
[45] Amit Kumar & Jagdeep Kaur, 2011, A new method for solving fuzzy linear programs with Trapezoidal fuzzy numbers, Journal of fuzzy set valued analysis, ISPACS. P. 1.