An optimization technique for national income determination model with stability analysis of differential equation in discrete and continuous process under the uncertain environment

¹ Department of Industrial & Management Engineering, Hanyang University, 155 88 Ansan, Gyeonggi-do, South Korea
² Department of Natural Science, Maulana Abul Kalam Azad University of Technology, Haringhata, Nadia 741249 West Bengal, India
³ Institute for Mathematical Research (INSPEM), University Putra, Malaysia 434 00 UPM Serdang, Selangor, Malaysia
⁴ Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran
⁵ Department of Mathematics & Statistics, Banasthali Vidyapith, 304 002 Rajasthan, India

^* Corresponding author: hursun@hanyang.ac.kr

Received: 4 September 2018
Accepted: 16 September 2017

Abstract

The paper represents a variation of the national income determination model with discrete and continuous process in fuzzy environment, a significant implication in economics planning, by means of fuzzy assumptions. This model is re-recognized and deliberated with fuzzy numbers to estimate its uncertain parameters whose values are not precisely known. Exhibition of imprecise solutions of the concerned model is carried out by using the proposed two methods: generalized Hukuhara difference and generalized Hukuhara derivative (gH-derivative) approaches. Moreover, the stability analysis of the model in two different systems in fuzzy environment is illustrated. Additionally, different illustrative examples for optimization of national income determination model are undertaken with the constructive graph and table for convenience for clarity of the projected approaches.