Type-2 fuzzy differential inclusion for solving type-2 fuzzy differential equation
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this article, we have solved the type-2 fuzzy differential equation. The nonlinear type-2 triangular fuzzy numbers(NT2TFNs) are taken, and their different arithmetic properties are manifested. We have taken the type-2 fuzzy initial and type-2 fuzzy boundary value problem. Type-2 fuzzy differential inclusion concepts solve the differential equations. Numerical examples with solution graphs have also been provided to illustrate the outcomes of the proposed theory.
Abstract
In this article, we have solved the type-2 fuzzy differential equation. The nonlinear type-2 triangular fuzzy numbers(NT2TFNs) are taken, and their different arithmetic properties are manifested. We have taken the type-2 fuzzy initial and type-2 fuzzy boundary value problem. Type-2 fuzzy differential inclusion concepts solve the differential equations. Numerical examples with solution graphs have also been provided to illustrate the outcomes of the proposed theory.
참고문헌 (42)
- Osmo Kaleva, "A note on fuzzy differential equations", Nonlinear Analysis: Theory, Methods &Applications, 64(5), pp.895~900 (2006)
- L. A. Zadeh, "Fuzzy sets", Information and control, 8, pp.338~353 (1965)
- Sheldon SL Chang, "On fuzzy mapping and control, Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by L. A Zadeh", World Scientific, pp.180~184 (1996)
- Madan L. Puri, "Differentials of fuzzy functions", J. Math. Anal. Appl, 98, pp.552~558 (1983)
- Osmo Kaleva, "Fuzzy differential equations", Fuzzy sets and systems, 24, pp.301~317 (1987)
- Osmo Kaleva, "The Cauchy problem for fuzzy differential equations", Fuzzy sets and systems, 35, pp.389~396 (1990)
- Seppo Seikkala, "On the fuzzy initial value problem", Fuzzy sets and systems, 24, pp.319~330 (1987)
- Yurilev Chalco-Cano, "Calculus for interval-valued functions using generalized Hukuhara derivative and applications", Fuzzy Sets and Systems, 219, pp.49~67 (2013)
- Marek T. Malinowski, "Interval Cauchy problem with a second type Hukuhara derivative", Inform. Sci, 213, pp.94~105 (2012)
- A. V. Plotnikov, "Averaging in differential equations with Hukuhara derivative and delay", Journal of Uncertain Systems, 13(1), pp.3~13 (2019)
- Barnab´as Bede, "Generalizations of the differentiability of fuzzy-numbervalued functions with applications to fuzzy differential equations", Fuzzy Sets and Systems, 151, pp.581~599 (2005)
- "A generalization of Hukuhara difference for interval and fuzzy arithmetic, WP-EMS Working Papers Series in Economics, Mathematics and Statistics" (2008)[URL]
- Didier Dubois, "Towards fuzzy differential calculus part 3 : Differentiation", Fuzzy sets and systems, 8, pp.225~233 (1982)
- Phil Diamond, "Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations", IEEE Transactions on Fuzzy Systems, 7(6), pp.734~740 (1999)
- Eyke H¨ullermeier, "An approach to modelling and simulation of uncertain dynamical systems", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5(02), pp.117~137 (1997)
- Chao Min, "Existence of solutions for implicit fuzzy differential inclusions", Applied Mathematics and Mechanics, 36(3), pp.401~416 (2015)
- Mostafijur Rahaman, "The solution techniques for linear and quadratic equations with coefficients as Cauchy neutrosphic numbers", Granular Computing, 7(2), pp.421~439 (2022)[DOI]
- Pinki Majumder, "Application of generalized Hukuhara derivative approach in an economic production quantity model with partial trade credit policy under fuzzy environment", Operations Research Perspectives, 3, pp.77~91 (2016)[DOI]
- Mostafijur Rahaman, "An estimation of effects of memory and learning experience on the EOQ model with price dependent demand", RAIRO Operations Research, 55(5), pp.2991~3020 (2021)[DOI]
- Mostafijur Rahaman, "A study of a lock fuzzy EPQ model with deterioration and stock and unit selling price dependent demand using Preservation Technology", Soft Computing, 26, pp.2721~2740 (2022)[DOI]
- Animesh Mahata, "Mathematical model for diabetes in fuzzy environment with stability analysis", Journal of Intelligent and Fuzzy Systems, 36(3), pp.2923~2932 (2019)[DOI]
- Animesh Mahata, "Application of ordinary differential equation in glucose-insulin regulatory system modeling in fuzzy environment", Ecological Genetics and Genomics, 36(3), pp.60~66 (2017)[DOI]
- Sankar Prasad Mondal, "Solution of second order linear fuzzy ordinary differential equation by Lagrange multiplier method with application in mechanics", Opsearch, 54(4), pp.766~798 (2017)[DOI]
- Sankar Prasad Mondal, "Adaptive strategies for system of fuzzy differential equation : Application of arms race model", Journal of Mathematics and Computer Science, 18, pp.192~205 (2018)
- Suklal Tudu, "Different solution strategy for solving type-2 fuzzy system of differential equations with application in arms race model", International Journal of Applied and Computational Mathematics, 7(5), pp.1~33 (2021)[DOI]
- Susmita Paul, "Discussion on proportional harvesting model in fuzzy environment : Fuzzy differential equation approach", International Journal of Applied and Computational Mathematics, 3(4), pp.3067~3090 (2017)[DOI]
- Najeeb Alam Khan, "Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment", Advances in Difference Equations, 1, pp.1~34 (2019)[DOI]
- Animesh Mahata, "Linear fuzzy delay differential equation and its application in biological model with fuzzy stability analysis", International Conference on Soft Computing and Data Mining, 978, pp.231~240 (2020)
- Sankar Prasad Mondal, "Classical modeling of HIV virus infected population in imprecise environments", Fuzzy Differential Equation and its Application, 6(1), pp.17~55 (2015)
- Susmita Paul, "Discussion on fuzzy quota harvesting model in fuzzy environment : Fuzzy differential equation approach", Modeling Earth Systems and Environment, 2(2), pp.1~15 (2016)
- Luciana Takata Gomes, "Fuzzy differential equations in various approaches" (2015), Springer
- Kausik Kumar Majumdar, "Fuzzy differential inclusions in atmospheric and medical cybernetics", IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 34(2), pp.877~887 (2004)
- C. J. Himmelberg, "A note on the solution sets of differential inclusions", The Rocky Mountain Journal of Mathematics, 12(4), pp.621~625 (1982)
- V. A. Baidosov, "Fuzzy differential inclusions", Journal of Applied Mathematics and Mechanics, 54(1), pp.8~13 (1990)
- Vangipuram Lakshmikantham, "Theory of fuzzy differential equations and inclusions" (2004), CRC Press
- Saeid Abbasbandy, "Numerical methods for fuzzy differential inclusions", Computers & mathematics with applications, 48(10-11), pp.1633~1641 (2004)
- Chao Min, "On the implicit fuzzy differential inclusions", 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery IEEE, pp.117~119 (2012)
- Zarife Zararsiz, "A contribution to the algebraic structure of fuzzy numbers", Ann. Fuzzy Math. Inform, 12(2), pp.205~219 (2016)
- Mehmet Senol, "Approximate solution of time-fractional fuzzy partial differential equations", Computational and Applied Mathematics, 38(1) (2019), Springer[DOI]
- Mehran Mazandarani, "Type-2 fuzzy fractional derivatives", Communications in Nonlinear Science and Numerical Simulation, 19(7), pp.2354~2372 (2014)
- Abhirup Bandyopadhyay, "System of type-2 fuzzy differential equations and its applications", Neural Computing and Applications, 31(9), pp.5563~5593 (2019)
- Jerry M. Mendel, "α-plane representation for type-2 fuzzy sets : Theory and applications", IEEE Transactions on Fuzzy Systems, 17(5), pp.1189~1207 (2009)
