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Rouben Ranking Function and parametric approach to quadratically constrained multiobjective quadratic fractional programming with trapezoidal fuzzy number coefficients

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Abstract

The present study proposed a procedure to obtain an efficient solution for a programming model which is multiobjective quadratic fractional with trapezoidal fuzzy numbers as coefficients in all the objective functions and constraints. The proposed approach consists of three stages. In the first stage, defuzzification of the coefficients is carried out using the Rouben Ranking Function. Then, in the second stage, a crisp multiobjective quadratic fractional programming model is reconstructed to obtain a non-fractional model based on an iterative parametric approach. In the final stage, this multiobjective non-fractional model is transformed to get a single objective model by applying \(\varepsilon\)-constraint method. This final model is then solved to get a desired solution . Also, an algorithm and flowchart expressing the methodology is given to present a clear picture of the approach. Finally, a numerical illustration expressing the complete approach is given in the end.

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References

  • Abraham C, Cooper William W (1962) Programming with linear fractional functionals. Naval Res Logist Q 9(3–4):181–186

    MathSciNet  Google Scholar 

  • Aghila R, Prasad JG, Ramachandran A, Subhalakshmi RT, Manju K, Sudan Jha K, Shankar JY (2020) A deep learning model based on multi-objective particle swarm optimization for scene classification in unmanned aerial vehicles. IEEE Access 8:135383–135393

    Article  Google Scholar 

  • Almogy Y, Levin O (1971) A class of fractional programming problems. Oper Res 19(1):57–67

    Article  MathSciNet  Google Scholar 

  • Arti Saxena YM, Kumar DM, Abneesh S (2021) Performance comparison of anfis, fopid-pso and fopid-fuzzy tuning methodology for optimizing response of high-performance drilling machine. IETE J Res 1–14

  • Barbara C, Ferdinando DM (2021) Gis-based hierarchical fuzzy multicriteria decision-making method for urban planning. J Amb Intell Human Comput 12(1):601–615

    Article  Google Scholar 

  • Borza M, Rambely AS, Saraj M (2014) Parametric approach for an absolute value linear fractional programming with interval coefficients in the objective function. AIP Conf Proc 1602(1):415–421

    Article  Google Scholar 

  • Chiclana F, Kumar R, Mittal M, Khari M, Chatterjee JM, Baik SW et al (2018) Arm-amo: an efficient association rule mining algorithm based on animal migration optimization. Knowledge-Based Syst 154:68–80

    Article  Google Scholar 

  • Dinkelbach W (1967) On nonlinear fractional programming. Manag Sci 13(7):492–498

    Article  MathSciNet  Google Scholar 

  • Ehrgott M, Ruzika S (2008) Improved \(\varepsilon\)-constraint method for multiobjective programming. J Optim Theory Appl 138(3):375–396

    Article  MathSciNet  Google Scholar 

  • Emam OE (2013) Interactive approach to bi-level integer multi-objective fractional programming problem. Appl Math Comput 223:17–24

    MathSciNet  MATH  Google Scholar 

  • Emam OE (2011) Interactive bi-level multi-objective integer non-linear programming problem. Appl Math Sci 5(65):3221–3232

    MathSciNet  MATH  Google Scholar 

  • Emmerich Michael TM, Deutz André H (2018) A tutorial on multiobjective optimization: fundamentals and evolutionary methods. Nat comput 17(3):585–609

    Article  MathSciNet  Google Scholar 

  • Falehi AD (2020) Robust and intelligent type-2 fuzzy fractional-order controller-based automatic generation control to enhance thDe damping performance of multi-machine power systems. IETE J Res 1–12

  • Falk JE, Palocsay SW (1992) Optimizing the sum of linear fractional functions. Recent advances in global optimization. Princeton University Press, pp 221–258

  • Goyal V, Namrata R, Deepak G (2021) Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming. OPSEARCH 1–18

  • Harold Robinson Y, Vimal S, Golden Julie E, Manju K, Christopher E-I, Javier M (2021) Hybrid optimization routing management for autonomous underwater vehicle in the internet of underwater things. Earth Sci Inf 14(1):441–456

    Article  Google Scholar 

  • Heesterman, A. R. G.: Parametric methods in quadratic programming. In In Matrices and Simplex Algorithms, pp 516–555. (1983)

  • Khari M, Sinha A, Verdu E, Crespo RG (2019) Performance analysis of six meta-heuristic algorithms over automated test suite generation for path coverage-based optimization. Soft Comput 1–18

  • Klaus T, Christiane T, Evelin O (2005) Multicriterial fractional optimization. Humboldt-Universitat zu Berlin, Mathematisch-Naturwissenschaftliche FakultatII Institut fur Mathematik

    MATH  Google Scholar 

  • Kumar P, Khari, M (2017) An investigating approach for optimization of software test suite. Recent Advances in Communications and Networking Technology (Formerly Recent Patents on Telecommunication)(Discontinued), 6(1):41–54,

  • Malhotra R, Khari M (2014) Test suite optimization using mutated artificial bee colony. In: Proceedings of International Conference on Advances in Communication, Network, and Computing, CNC, Elsevier

  • Manju K (2020) Empirical evaluation of automated test suite generation and optimization. Arab J Sci Eng 45(4):2407–2423

    Article  Google Scholar 

  • Manju K, Prabhat K (2017) An effective meta-heuristic cuckoo search algorithm for test suite optimization. Informatica 41(3)

  • Manju K, Prabhat K, Daniel B, González CR (2018) Optimized test suites for automated testing using different optimization techniques. Soft Comput 22(24):8341–8352

    Article  Google Scholar 

  • Manju K, Prabhat K, Gulshan S (2019) Enhanced approach for test suite optimisation using genetic algorithm. Int J Comput Aided Eng Technol 11(6):653–668

    Article  Google Scholar 

  • Manju K, Prabhat K, Gulshan S (2020) Test optimisation: an approach based on modified algorithm for software network. Int J Adv Intell Paradig 17(3–4):208–237

    Google Scholar 

  • Martos B, Whinston V (1964) Hyperbolic programming. Naval Res Logist Q 11(2):135–155

    Article  MathSciNet  Google Scholar 

  • Maziar S, Saeed F (2016) Parametric approach for solving quadratic fractional optimization with a linear and a quadratic constraint. Comput Appl Math 35(2):439–446

    Article  MathSciNet  Google Scholar 

  • Namrata R, Vandana G, Deepak G (2021) Algorithm for bi-level multi-objective fully quadratic fractional optimization model with fuzzy parameters. J Amb Intell Human Comput 1–13

  • Namrata R, Vandana G, Deepak G (2021) Multi-level multi-objective fully quadratic fractional optimization model with trapezoidal fuzzy numbers using rouben ranking function and fuzzy goal programming. Materials Today: Proceedings

  • Nayak S, Ojha AK (2015) Generating pareto optimal solutions of multi-objective lfpp with interval coefficients using \(\varepsilon\)-constraint method. Math Modell Anal 20(3):329–345

    Article  MathSciNet  Google Scholar 

  • Nayak S, Ojha AK (2019) Solution approach to multi-objective linear fractional programming problem using parametric functions. OPSEARCH 56(1):174–190

    Article  MathSciNet  Google Scholar 

  • Nikas A, Fountoulakis A, Forouli A, Doukas H (2020) A robust augmented \(varepsilon\)-constraint method (augmecon-r) for finding exact solutions of multi-objective linear programming problems. Oper Res 1–42

  • Ojha AK, Biswal KK (2014) Multi-objective geometric programming problem with \(\varepsilon\)-constraint method. Appl Math Modell 38(2):747–758

    Article  MathSciNet  Google Scholar 

  • Pareto V et al. (1971) Manual of political economy

  • Philippe F, Marc R (1996) Ranking and defuzzification methods based on area compensation. Fuzzy Sets Syst 82(3):319–330

    Article  MathSciNet  Google Scholar 

  • Priyadarsini R, Dash Rajani B (2016) Solution of fuzzy multi-objective linear programming problems using fuzzy programming techniques based on hyperbolic membership functions. J Comput Math Sci 7(12):653–662

    Google Scholar 

  • Priyadarsini R, Rajani DB (2017) Solution of fuzzy multi objective non-linear programming problem (fmonlpp) using fuzzy programming techniques based on exponential membership functions. Bull Pure Appl Sci Math Stat 36(2):133–142

    Google Scholar 

  • Raj J (1966) On some properties of programming problems in parametric form pertaining to fractional programming. Manag Sci 12(7):609–615

    Article  MathSciNet  Google Scholar 

  • Rajesh J (2020) A new multi-criteria decision-making method based on intuitionistic fuzzy information and its application to fault detection in a machine. J Amb Intell Human Comput 11(2):739–753

    Article  Google Scholar 

  • Rao DS, Kumar MS, Raju MR (2019) Two-degree-of-freedom robust controller design approach for fuzzy parametric uncertain systems using particle swarm optimization. IETE J Res 65(3):397–409

    Article  Google Scholar 

  • Seghir F, Khababa G (2021) Fuzzy teaching learning based optimization approach for solving the qos-aware web service selection problem in uncertain environments. J Amb Intell Human Comput 1–31

  • Shalinie Mercy S (2000) Design of neural network based fuzzy logic model for target identification. IETE J Res 46(5):395–400

    Article  Google Scholar 

  • Sushma K, Laxmi V (2017) Implementation of fuzzy model for maintenance scheduling of vehicles based on monte carlo simulation and geographical information system. IETE J Res 63(2):225–237

    Article  Google Scholar 

  • Takrimi M, Khoei A, Hadidi K (2003) A programmable CMOS fuzzy membership function generator. IETE J Res 49(6):431–438

    Article  Google Scholar 

  • Tantawy SF (2008) A new procedure for solving linear fractional programming problems. Math Comput Modell 48(5–6):969–973

    Article  MathSciNet  Google Scholar 

  • Valipour E, Yaghoobi MA, Mashinchi M (2016) An approximation to the nondominated set of a multiobjective linear fractional programming problem. Optimization 65(8):1539–1552

    Article  MathSciNet  Google Scholar 

  • Vandana G, Namrata R, Deepak G (2020) Iterative parametric approach for quadratically constrained bi-level multiobjective quadratic fractional programming. J Comput Theor Nanosci 17(11):5046–5051

    Article  Google Scholar 

  • Vathsala H, Koolagudi Shashidhar G (2021) Neuro-fuzzy model for quantified rainfall prediction using data mining and soft computing approaches. IETE J Res 1–11

  • Vimal S, Manju K, González CR, Kalaivani L, Nilanjan D, Madasamy K (2020) Energy enhancement using multiobjective ant colony optimization with double q learning algorithm for IoT based cognitive radio networks. Comput Commun 154:481–490

    Article  Google Scholar 

  • Wang G, Zhang G (2019) Matching localization algorithm of nonlinear t-s fuzzy system constructed by the piecewise linear function. J Amb Intell Human Comput 10(2):417–427

    Article  Google Scholar 

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Authors and Affiliations

  1. Maharishi Markandeshwar Engineering College, Mullana, Ambala, Haryana, India

    Vandana Goyal, Namrata Rani & Deepak Gupta

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  1. Vandana Goyal
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  2. Namrata Rani
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  3. Deepak Gupta
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All the authors contributed equally for the study and preparation of the manuscript.

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Correspondence to Deepak Gupta.

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Goyal, V., Rani, N. & Gupta, D. Rouben Ranking Function and parametric approach to quadratically constrained multiobjective quadratic fractional programming with trapezoidal fuzzy number coefficients. Int J Syst Assur Eng Manag 13, 923–932 (2022). https://doi.org/10.1007/s13198-021-01363-w

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  • DOI: https://doi.org/10.1007/s13198-021-01363-w

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