Multi-Objective De Novo Programming with Type-2 Fuzzy Objective for Optimal System Design

Umarusman, Nurullah

doi:https://doi.org/10.17093/alphanumeric.1254288

Multi-Objective De Novo Programming with Type-2 Fuzzy Objective for Optimal System Design

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Nurullah Umarusman, Ph.D.

Abstract

De Novo Programming, which is also known as Optimal System Design, regulates the resource amount of constraints depending upon the budget. Mostly, this process is managed using traditional methods, fuzzy methods and hybrid methods. When considered from this point of view, there is no certain method for the solution of De Novo Programming problems. An approach for solving the Multi-Objective De Novo Programming has been recommended using Type-2 Fuzzy Sets in this research. Without exceeding the budget in the recommended approach, Type-2 membership function for each objective function has been defined applying positive and negative ideal solutions. The solution phase of this approach, called Multi-Objective De Novo Programming with Type-2 Fuzzy Objective, has been shown step by step on the illustrative problem. Then, this illustrative problem has been solved with regards to five different approaches in the literature and the results have been compared.

Keywords: De Novo Programming, Fuzzy Sets Theory, Type-2 Fuzzy Sets

Jel Classification: C46

Suggested citation

Umarusman, N. (2023). Multi-Objective De Novo Programming with Type-2 Fuzzy Objective for Optimal System Design. Alphanumeric Journal, 11(2), 101-124. https://doi.org/10.17093/alphanumeric.1254288

References

Afli, F., Hasbiyati, I., & Gamal, M.D.H. (2019). Modification goal programming for solving multi-objective de novo programming problems. Int. J. of Management and Fuzzy Systems 5(4), 64-69.
Babic,Z., & Pavic,I. (1996). Multicriterial production planning by de novo programming approach, International journal of Production Economics, 43(1), 59-66.
Babic, Z., Veza, I., Balic, A., & Crnjac, M., (2018). Application of de novo programming approach for optimizing the business process, International Journal of Industrial and Systems Engineering, 12(5), 590-595.
Banik, S., & Bhattacharya, S. (2018). Weighted goal programming approach for solving multi-objective de novo programming problems. International Journal of Engineering Research in Computer Science and Engineering (IJERCSE), 5(2), 316-322.
Banik, S., & Bhattacharya, D.(2019) One-step approach for solving general multi-objective de novo programming problem involving fuzzy parameters. Hacettepe Journal of Mathematics and Statistics 48(6), 1824-1837.
Banik, S., & Bhattacharya, D. (2022). General method for solving multi-objective de novo programming problem. Optimization, 1-18.
Bare, B. B., & Mendoza, G. A. (1990). Designing forest plans with conflicting objectives using de Novo programming. Journal of environmental management, 31(3), 237-246.
Bellman, R.E., & Zadeh, L.A. (1970), Decision-making in a fuzzy environment. Management Science B.17, 141-164.
Bhattacharya, D., & Chakraborty, S. (2018). Solution of the general multi-objective De-Novo programming problem using compensatory operator under fuzzy environment. In Journal of Physics: Conference Series 1039(1), 012012. http://i:10.1088/1742-6596/1039/1/012012.
Bigdeli, H., & Hassanpour, H. (2015). Interactive Type-2 Fuzzy Multıobjective Linear Programming. International Conference of the Iranian Soceity of Operations Research 2014, Ferdowsi University of Mashhad, Iran, May 21-22, pp.1-3,2015.
Chanas, S. (1983). The use of parametric programming in fuzzy linear programming. Fuzzy Sets and Systems 11(1), 243-251.
Chakraborty, S., & Bhattacharya, D. (2012). A new approach for solution of multi-stage and multi-objective decision-making problem using de novo programming. Eur J Sci Res, 79(3), 393-417.
Chen, J.K. (2014). Adopting De Novo programming approach on IC design service firms resources integration. Mathematical Problems in Engineering,1-13. http://dx.doi.org/10.1155/2014/903056
Chen, Y.W., &. Hsieh, H.E. (2006). Fuzzy multi-stage de-novo programming problem. Applied Mathematics and Computation 181(2), 1139-1147.
Dinagar,D.S., & Anbalagan, A. (2011). Two-phase approach for solving type-2 fuzzy linear programmig problem. International Journal of Pure and Applied Mathematics 70(6), 873-888.
Fiala, F. (2011). Multiobjective de novo linear programming. Acta universitatis palackianae olomucensis. Facultas rerum naturalium, Mathematica 50(2), 29-36.
Gao, P. P., Li, Y. P., Sun, J., & Huang, G. H. (2018). A Monte-Carlo-based interval de novo programming method for optimal system design under uncertainty. Engineering Applications of Artificial Intelligence, 72, 30-42.
Gao, P. P., Li, Y. P., Gong, J. W., & Huang, G. H. (2021). Urban land-use planning under multi-uncertainty and multiobjective considering ecosystem service value and economic benefit-A case study of Guangzhou, China. Ecological Complexity, 45, 100886.
García, J.C.F. (2009). Solving fuzzy linear programming problems with interval type-2 RHS. In 2009 IEEE International Conference on Systems, Man and Cybernetics, San Antonio, Texas, USA, October 11-14, (2009), 262-267.
García, J.C.F. (2011). Interval type-2 fuzzy linear programming: Uncertain constraints. In 2011 IEEE Symposium on Advances in Type-2 Fuzzy Logic Systems (T2FUZZ), Paris, France, April 11-15, pp. 94-101.
Hassan, N.R.S. (2021). The literature review of de novo programming. Journal of University of Shanghai for Science and Technology, 23(1), 360-371.
Huang, J.-D., & M. H. Hu. (2013). Two-Stage Solution Approach for Supplier Selection: A Case Study in A Taiwan Automotive İndustry. International Journal of Computer Integrated Manufacturing 26 (3): 237–251.
Javanmard, M., & Nehi, H.M. (2017). Solving interval type-2 fuzzy linear programming problem with a new ranking function method.2017 5th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), Qazvin, Iran, Mar. 07-09 2017, pp. 4-6.
Javanmard, M., & Nehi, H.M. (2019). A solving method for fuzzy linear programming problem with interval type-2 fuzzy numbers, International Journal of Fuzzy Systems, 21(3), 882-891.
John, R. (1998). Type 2 fuzzy sets: an appraisal of theory and applications. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 6(06), 563-576.
Khalifa, H.A. (2018). On solving fully fuzzy multi-criteria de novo programming via fuzzy goal programming approach, Journal of Applied Research on Industrial Engineering 5(3), 239-252.
Khalifa, H. (2019). On solving possibilistic multi-objective De Novo linear programming. Iranian Journal of Optimization, 11(2), 277-284.
Kim, H., Ida, K., & Gen, M. (1993). A de Novo approach for bicriteria 0-1 linear programming with interval coefficients under gub structure. Comput. Ind. Eng., 25(1-4), 17-20
Kundu,P., Majumder,S., Kar, S. & Maiti, M. (2019). A method to solve linear programming problem with interval type-2 fuzzy parameters, Fuzzy optimization and decision making 18(1),103-130.
Lai Y.J., & Hwang, C.L.(1992). Fuzzy Mathematical Programming Springer-Verlag Berlin.
Lee E.S., &Li, R.J.(1993). Fuzzy multiple objective programming and compromise programming with pareto optimum, Fuzzy Sets and Systems 53(3), 275-288.
Li R.J., & Lee, E.S. (1990a). Fuzzy approaches to multicriteria de novo programs, Journal of Mathematical Analysis and Applications 153(1), 97-111.
Li R.J., & Lee, E.S. (1990b)., Multi-criteria de novo programming with fuzzy parameters, Computers Math. Applic. 19(5), 13-20.
Jin, L., Huang, G. H., Cong, D., & Fan, Y. R. (2014). A robust inexact joint-optimal α cut interval type-2 fuzzy boundary linear programming (RIJ-IT2FBLP) for energy systems planning under uncertainty. International Journal of Electrical Power & Energy Systems, 56, 19-32.
Maali, Y.& Mahdavi-Amiri, N.(20144). A triangular type-2 multi-objective linear programming model and a solution strategy, Information Sciences, 279, 816-826.
Mendel J.M., & John, R.B. (2002). Type-2 fuzzy sets made simple. IEEE Transactions on fuzzy systems, 10(2), 117-127.
Mendel, J. M., John, R. I., & Liu, F. (2006). Interval type-2 fuzzy logic systems made simple. IEEE transactions on fuzzy systems, 14(6), 808-821.
Miao, D.Y., Huang , W.W., Li Y.P., & Yang Z.F. (2014).Planning water resources systems under uncertainty using an ınterval-fuzzy de novo programming method, Journal of Environmental Informatics, 24(1), 11-23.
Mizumoto, M., & Tanaka, K. (1976). Some properties of fuzzy sets of type 2. Information and control, 31(4), 312-340.
Namvar, H., & Bamdad, S. (2021). Resilience-based efficiency measurement of process industries with type-2 fuzzy sets. International Journal of Fuzzy Systems, 23, 1122-1136.
Saeid, N.R., Ahmed I.H.,&. Mahmoud, M.A. (2018). Design an optimal system with fuzzy multiple objective de novo programming approach. In The 53 rd Annual Conference on Statistics, Computer Sciences and Operations Research, 3-5 Dec 2018, Cairo University, Egypt,pp. 1-8.
Sarah, J., & Khalili-Damghani, K. (2019). Fuzzy type-II de-novo programming for resource allocation and target setting in network data envelopment analysis: a natural gas supply chain. Expert Systems with Applications 117, 312-329.
Sasaki, M., Gen, M.& Yamashiro, M.(1995). A method for solving fuzzy de novo programming problem by genetic algorithms, Computers & Industrial Engineering 29(1-4), 507-511.
Shi, Y. (1995).Studuies on optimum-path ratios in multicriteria de novo programming problems. Computers Math. Applic. 29(5),43-50.
Solomon, M., & Mokhtar, A. (2021). An Approach for Solving RoughMulti-Objective De Novo Programming Problems. Design Engineering, 1633-1648.
Srinivasan A., & Geetharamani, G. (2016).Linear programming problem with interval type 2 fuzzy coefficients and an interpretation for ITS constraints. Journal of Applied Mathematics,1-11. doi:http://dx.doi.org/10.1155/2016/8496812.
Tabucanon, M.T. (1988). Multiple Criteria Decision Making In Industry, Elsevier, New York.
Umarusman, N. (2013). Min-max goal programming approach for solving multi-objective de novo programming problems. International journal of operations research, 10(2), 92-99.
Umarusman, N. (2019). Using global criterion method to define priorities in Lexicographic goal programming and an application for optimal system design. MANAS Sosyal Araştırmalar Dergisi, 8(1), 326-341.
Umarusman, N. (2020). A new fuzzy de novo programming approach for optimal system design, In: Soft Computing: Techniques in Engineering Sciences, M. Ram and S. B. Singh, De Gruyter, Boston, pp. 13-32. https://doi.org/10.1515/9783110628616-002.
Wu, D., & Mendel, J. M. (2007). Uncertainty measures for interval type-2 fuzzy sets. Information sciences, 177(23), 5378-5393.
Zadeh, L.A. (1965). Fuzzy Sets. Information and Control, 8(3), 338-353.
Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning-III. Information sciences, 9(1), 43-80.
Zeleny, M. (1976). Multi-objective design of high-productivity systems. Joint Automatic Control Conference-Paper APPL9-4, ASME, Newyork, 13, 297–300.
Zeleny, M. (1981). On the squandering of resources and profits via linear programming. Interfaces 11(5), 101-107.
Zeleny, M.(1984). Multicriterion Design Of High-Productivity Systems: Extension and Application, Decision Making With Multiple Objective s. 308- 321. Y.Haimes and V. Chankong, Eds. Springer-Verlag, New York.
Zeleny, M.(1986). Optimal system design with multiple criteria: de novo programming approach. Engineering Costs and Production Economics 10(1), 89-94.
Zeleny, M. (1987). Systems approach to multiple criteria decision making: metaoptimum. In Toward Interactive and Intelligent Decision Support Systems: Volume 1 Proceedings of the Seventh International Conference on Multiple Criteria Decision Making, Held at Kyoto, Japan, August 18–22, 1986 (pp. 28-37). Springer Berlin Heidelberg.
Zeleny, M. (1990). Optimizing given systems vs. Designing optimal systems: the de novo programming approach. Int. J. General System 17 (4), 295-307.
Zhang, Y.M., Huang, G.H., & Zhang, X.D. (2009). Inexact de Novo programming for water resources systems planning. Eur. J. Oper. Res., 199(2), 531-541. http://dx.doi.org/10.1016/j.ejor.2008.11.019
Zhuang, Z. Y., & Hocine, A. (2018). Meta goal programing approach for solving multi-criteria de Novo programing problem. European journal of operational research, 265(1), 228-238.
Zimmermann, H. J. (1975). Description and optimization of fuzzy systems. International journal of general System, 2(1), 209-215.
Zimmermann, H.J. (1976). Description and optimization of fuzzy systems. International Journal Of General Systems 2(4), 209-215.
Zimmermann, H.J. (1978). Fuzzy programming and linear programming with several functions. Fuzzy Sets and Systems 1(1), 45-55.
Zimmermann, H.J. (1987). Fuzzy Sets Decision Making and Expert Systems, Kluwer Academic Publishers Boston.

2023.11.02.OR.01

alphanumeric journal

Volume 11, Issue 2, 2023

Pages 101-124

Received: Feb. 21, 2023

Accepted: Nov. 23, 2023

Published: Dec. 31, 2023

Full Text [1.1 MB]

2023 Umarusman, N.

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Multi-Objective De Novo Programming with Type-2 Fuzzy Objective for Optimal System Design

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