Abstract
This chapter aims to introduce the parametric representation of the Type-2 interval and its ranking. This chapter also wishes to derive the optimality criteria of the imprecise unconstrained optimization problem in a Type-2 interval environment with these concepts. For this purpose, at first, by recapitulating the idea of Type-2 interval introduced by Rahman et al. (Rahman MS, Shaikh AA, Bhunia AK (2020d)), the parametric representation of Type-2 interval is proposed. Then an order relation on the set of Type-2 intervals is introduced. Using this order relation, the maximizer and minimizer of an unconstrained Type-2 interval-valued optimization problem are defined. Then the optimality conditions (both necessary and sufficient) for the said optimization problem are derived. Finally, the obtained optimality results are illustrated by some numerical examples.
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Das, S., Rahman, M.S., Mahato, S.K., Shaikh, A.A., Bhunia, A.K. (2022). On the Parametric Representation of Type-2 Interval and Ranking: Its Application in the Unconstrained Non-linear Programming Problem Under Type-2 Interval Uncertainty. In: Ali, I., Chatterjee, P., Shaikh, A.A., Gupta, N., AlArjani, A. (eds) Computational Modelling in Industry 4.0. Springer, Singapore. https://doi.org/10.1007/978-981-16-7723-6_15
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DOI: https://doi.org/10.1007/978-981-16-7723-6_15
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