Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation

As a valuable tool for representing uncertain information, probabilistic hesitant fuzzy sets (PHFS) have gained considerable recognition and in-depth discussion in recent years to increase the flexibility and manifest hesitant information in decision-making problems. However, decision-makers (DMs) c...

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Autores principales:	Qasim Noor, Dalal Awadh Alrowaili, Tabasam Rashid, Syed Muhammad Husnine
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi-Wiley 2021
Materias:	Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/317c71c58cf2415c8f64b7194e12fde0
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id	oai:doaj.org-article:317c71c58cf2415c8f64b7194e12fde0
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spelling	oai:doaj.org-article:317c71c58cf2415c8f64b7194e12fde02021-11-29T00:56:38ZNormal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation1099-052610.1155/2021/2906854https://doaj.org/article/317c71c58cf2415c8f64b7194e12fde02021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/2906854https://doaj.org/toc/1099-0526As a valuable tool for representing uncertain information, probabilistic hesitant fuzzy sets (PHFS) have gained considerable recognition and in-depth discussion in recent years to increase the flexibility and manifest hesitant information in decision-making problems. However, decision-makers (DMs) cannot express all preferences only through a few probabilistic terms in actual decision-making. Much critical information is hidden behind the original information provided by the DMs. Keeping that in mind, we are interested in mining deeper uncertain information from the original probabilistic hesitant fuzzy evaluation data. To achieve the target, we put forward a novel representation tool called the normal wiggly probabilistic hesitant fuzzy set (NWPHFS) to extract deeper uncertain preferences from original probabilistic information. NWPHFS retains the original evaluation information and carries and assesses the potential uncertain details for increasing the rationality of decision-making outcomes. Herein, we propose some fundamental concepts of NWPHFS, for instance, some elementary operational laws, distance measures between two NWPHFSs, and score function. We also suggest two new aggregation operators, that is, the normal wiggly probabilistic hesitant fuzzy weighted averaging (NWPHFWA) and normal wiggly probabilistic hesitant fuzzy weighted geometric (NWPHFWG). A novel mechanism is proposed here to work out multiattribute decision-making (MADM) in solving normal wiggly probabilistic decision-making problems. Through a practical example of environmental quality assessment, the specific calculation steps of this method are epitomized. Finally, we have demonstrated the feasibility and advancement of the proposed approach via a comprehensive comparative study.Qasim NoorDalal Awadh AlrowailiTabasam RashidSyed Muhammad HusnineHindawi-WileyarticleElectronic computers. Computer scienceQA75.5-76.95ENComplexity, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Electronic computers. Computer science QA75.5-76.95
spellingShingle	Electronic computers. Computer science QA75.5-76.95 Qasim Noor Dalal Awadh Alrowaili Tabasam Rashid Syed Muhammad Husnine Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation
description	As a valuable tool for representing uncertain information, probabilistic hesitant fuzzy sets (PHFS) have gained considerable recognition and in-depth discussion in recent years to increase the flexibility and manifest hesitant information in decision-making problems. However, decision-makers (DMs) cannot express all preferences only through a few probabilistic terms in actual decision-making. Much critical information is hidden behind the original information provided by the DMs. Keeping that in mind, we are interested in mining deeper uncertain information from the original probabilistic hesitant fuzzy evaluation data. To achieve the target, we put forward a novel representation tool called the normal wiggly probabilistic hesitant fuzzy set (NWPHFS) to extract deeper uncertain preferences from original probabilistic information. NWPHFS retains the original evaluation information and carries and assesses the potential uncertain details for increasing the rationality of decision-making outcomes. Herein, we propose some fundamental concepts of NWPHFS, for instance, some elementary operational laws, distance measures between two NWPHFSs, and score function. We also suggest two new aggregation operators, that is, the normal wiggly probabilistic hesitant fuzzy weighted averaging (NWPHFWA) and normal wiggly probabilistic hesitant fuzzy weighted geometric (NWPHFWG). A novel mechanism is proposed here to work out multiattribute decision-making (MADM) in solving normal wiggly probabilistic decision-making problems. Through a practical example of environmental quality assessment, the specific calculation steps of this method are epitomized. Finally, we have demonstrated the feasibility and advancement of the proposed approach via a comprehensive comparative study.
format	article
author	Qasim Noor Dalal Awadh Alrowaili Tabasam Rashid Syed Muhammad Husnine
author_facet	Qasim Noor Dalal Awadh Alrowaili Tabasam Rashid Syed Muhammad Husnine
author_sort	Qasim Noor
title	Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation
title_short	Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation
title_full	Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation
title_fullStr	Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation
title_full_unstemmed	Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation
title_sort	normal wiggly probabilistic hesitant fuzzy information for environmental quality evaluation
publisher	Hindawi-Wiley
publishDate	2021
url	https://doaj.org/article/317c71c58cf2415c8f64b7194e12fde0
work_keys_str_mv	AT qasimnoor normalwigglyprobabilistichesitantfuzzyinformationforenvironmentalqualityevaluation AT dalalawadhalrowaili normalwigglyprobabilistichesitantfuzzyinformationforenvironmentalqualityevaluation AT tabasamrashid normalwigglyprobabilistichesitantfuzzyinformationforenvironmentalqualityevaluation AT syedmuhammadhusnine normalwigglyprobabilistichesitantfuzzyinformationforenvironmentalqualityevaluation
_version_	1718407696096428032

Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation

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