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Projection based regret theory on three-way decision model in probabilistic interval-valued q-rung orthopair hesitant fuzzy set and its application to medicine company

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Abstract

Three-way decision (3WD) can be used to handle complexity and uncertainty in decision-making problems, and is compatible with human cognitive systems. For insufficient existing experiences, decision-makers (DMs) can select interval fuzzy information, as the information about medicine company is more hesitation, imprecision, and ambiguity. In the determination process, DMs may not take suitable decisions by choosing membership and non-membership degree of imprecise information. To improve fault-tolerance and validate the plausibility of DMs’ evaluation, the probabilistic interval-valued q-rung orthopair hesitant fuzzy set (PIVq-ROHFS) is introduced. Additionally, distinct psychological behaviours of DMs have an impact on the outcomes of decision-making. For this situation, we first develop a regret theory based 3WD model in PIVq-ROHFS to evaluate the utility value of the objects. The core focus of regret theory is to develop a new regret-rejoice function based on projection theory. Another core focus of this inquisition is to propose a novel multi-criteria decision making (MCDM) method for evaluating conditional probability in 3WD model. The criteria’s weight in MCDM method is evaluated by a newly proposed multi-objective optimization (MOO) problem. To solve the MOO problem, we utilize a hybrid technique by combining particle swarm optimization and multi-choice goal programming with utility function.

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Acknowledgements

The author Binoy Krishna Giri is very much grateful to the University Grant Commission of India for supporting financially to continue this research work under JRF (UGC) scheme: Sanctioned letter number [F.NO. 16-9(June 2019)/2019(NET/CSIR)].

Funding

This work is supported by the University Grant Commission of India to continue this research work under JRF (UGC) scheme: Sanctioned letter number [F.NO. 16-9(June 2019)/2019(NET/CSIR)].

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, 721101, India

    Binoy Krishna Giri & Sankar Kumar Roy

  2. Department of Industrial Engineering, Turkish Naval Academy, National Defence University, 34940, Tuzla, Istanbul, Turkey

    Muhammet Deveci

  3. The Bartlett School of Sustainable Construction, University College London, Gower St, London, WC1E 6BT, UK

    Muhammet Deveci

  4. Department of Electrical and Computer Engineering, Lebanese American University, Byblos, Lebanon

    Muhammet Deveci

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  1. Binoy Krishna Giri
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All authors are equally contributed to this study.

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Correspondence to Sankar Kumar Roy.

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Giri, B.K., Roy, S.K. & Deveci, M. Projection based regret theory on three-way decision model in probabilistic interval-valued q-rung orthopair hesitant fuzzy set and its application to medicine company. Artif Intell Rev 56 (Suppl 3), 3617–3649 (2023). https://doi.org/10.1007/s10462-023-10611-3

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