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...

Full description

Saved in:
Bibliographic Details
Main Authors: Qasim Noor, Dalal Awadh Alrowaili, Tabasam Rashid, Syed Muhammad Husnine
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2021/2906854
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849306607706439680
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
collection DOAJ
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
id doaj-art-317c71c58cf2415c8f64b7194e12fde0
institution Kabale University
issn 1099-0526
language English
publishDate 2021-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-317c71c58cf2415c8f64b7194e12fde02025-08-20T03:55:01ZengWileyComplexity1099-05262021-01-01202110.1155/2021/2906854Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality EvaluationQasim Noor0Dalal Awadh Alrowaili1Tabasam Rashid2Syed Muhammad Husnine3Department of Science and HumanitiesMathematics DepartmentUniversity of Management and TechnologyDepartment of Science and HumanitiesAs 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.http://dx.doi.org/10.1155/2021/2906854
spellingShingle Qasim Noor
Dalal Awadh Alrowaili
Tabasam Rashid
Syed Muhammad Husnine
Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation
Complexity
title 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_short Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation
title_sort normal wiggly probabilistic hesitant fuzzy information for environmental quality evaluation
url http://dx.doi.org/10.1155/2021/2906854
work_keys_str_mv AT qasimnoor normalwigglyprobabilistichesitantfuzzyinformationforenvironmentalqualityevaluation
AT dalalawadhalrowaili normalwigglyprobabilistichesitantfuzzyinformationforenvironmentalqualityevaluation
AT tabasamrashid normalwigglyprobabilistichesitantfuzzyinformationforenvironmentalqualityevaluation
AT syedmuhammadhusnine normalwigglyprobabilistichesitantfuzzyinformationforenvironmentalqualityevaluation