Frank aggregation operators and analytic hierarchy process based on interval‐valued picture fuzzy sets and their applications

Mahmood, Tahir; Waqas, Muhammad; Ali, Zeeshan; Ullah, Kifayat; Pamučar, Dragan

doi:10.1002/int.22614

Cited by 32 publications

(14 citation statements)

References 38 publications

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“…It is worth noting that Frank t -norm and s -norm [ 22 ] is the only operational form with compatibility characteristics in above operations, which has better generality, flexibility, and robustness in dealing with information aggregation to overcome the defects of AOLs. Since the Frank t -norm and s -norm can be degenerated into Lukasiewicz and Algebraic operations under special conditions, it has been applied to define the operational laws in various fuzzy theories, such as IFSs [ 23 ], Hesitant fuzzy sets [ 24 ], PyFSs [ 25 ], q -ROFSs [ 26 ], PFSs [ 27 ], and single-value neutrosophic sets [ 28 ]. Combined with the previous T-SF AOs review, we find that there is no research on developing new AOs based on Frank operations in the T-SF environment.…”

Section: Literature Reviewmentioning

confidence: 99%

Improved CoCoSo Method Based on Frank Softmax Aggregation Operators for T-Spherical Fuzzy Multiple Attribute Group Decision-Making

Wang

Mahmood

Ullah

2023

Int. J. Fuzzy Syst.

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In this article, a novel CoCoSo (Combined compromise solution) method based on Frank operational laws and softmax function is investigated to handle multiple attribute group decision-making problems for T-spherical fuzzy sets. We extend Frank operations in T-spherical fuzzy environment and develop a series of aggregation operators, including T-spherical fuzzy Frank softmax (T-SFFS) average and geometric operators, and their weighted forms, i.e., T-SFFS weighted averaging (T-SFFSWA) and T-SFFS weighted geometric (T-SFFSWG) operators. Some of their basic properties and particular cases are discussed. Meanwhile, the monotonicity of proposed operators is also analyzed, and it is discussed that how they indicate the decision-makers’ optimistic and pessimistic decision attitudes with risk preference. Furthermore, a novel CoCoSo method based on Hamming distance measure is proposed, which considers both decision-maker’s decision attitude and attribute priority, and a multiple attribute group decision-making framework with two independent and parallel T-spherical fuzzy information processing processes are designed. Lastly, a real case of spent power battery recycling technology (SPBRT) selection is presented to show the practicability of the proposed method. Also sensitivity and comparative analyses are carried out to prove the reliability, effectiveness, and superiority of our proposed method.

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Section: Literature Reviewmentioning

confidence: 99%

Improved CoCoSo Method Based on Frank Softmax Aggregation Operators for T-Spherical Fuzzy Multiple Attribute Group Decision-Making

Wang

Mahmood

Ullah

2023

Int. J. Fuzzy Syst.

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“…In this section, to observe the validity and reliability of our discussed AOs in the form of PFAAWA and PFAAWG operators. For this purpose we compare the experimental results of our proposed AOs with existing AOs given in [11,17,53,54]. We applied all existing AOs on the information given by the decision-maker depicted in Table 1, AOs of PFDWA and PFDWG by Jana et al [17] and IVIFWA and IVIFWG by Xu and Gou [54], are failed to aggregate the given information.…”

Section: Comparative Analysismentioning

confidence: 99%

“…We applied all existing AOs on the information given by the decision-maker depicted in Table 1, AOs of PFDWA and PFDWG by Jana et al [17] and IVIFWA and IVIFWG by Xu and Gou [54], are failed to aggregate the given information. AOs of IVPHFWA and IVPHFWG by Kamacı et al [11], and AOs of IVPFFWA and IVPFFWG by Mahmood et al [53] are also applied on the information given in Table 1. Te consequences of current work and existing AOs are shown in Table 5.…”

Section: Comparative Analysismentioning

confidence: 99%

Interval Valued Picture Fuzzy Aczel–Alsina Aggregation Operators and Their Application by Using the Multiattribute Decision Making Problem

Jabeen

Ullah

Akram

et al. 2023

Journal of Mathematics

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The engineering and construction sector is vital to a country’s economic growth, financial activities, and development. These sectors generate opportunities for the unemployed, unskilled, and skilled workforce. Recently, a lot of researchers worked on the Aczel–Alsina t-norm (TN) and t-conorm (TCN), which are generalizing many other t-norms and producing reliable results. In this article, first, we developed some new aggregation operators (AOs) and fundamental operational laws of Aczel–Alsina operations, including Aczel–Alsina product, sum, and scalar multiplication based on the IVPF information. Furthermore, we introduced an innovative AOs in the form of IVPF Aczel–Alsina weighted averaging (IVPFAAWA) operators with some basic characteristics. Moreover, we also generalized Aczel–Alsina operations in the form of the IVPF Aczel–Alsina weighted geometric (IVPFAAWG) operator. For the solution of daily life problems by utilizing a multiattribute decision-making (MADM) approach, we also established an application under the system of engineering and construction sectors. We illustrated a numerical example to find the suitable construction material for the engineering and construction sectors. To find the validity and flexibility of our proposed AOs, we also studied a comprehensive comparative analysis, in which we compared the results of exiting AOs with the results of our current invented approaches. At the end, we sum up our whole article in a single paragraph.

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“…Unlike IFS, PFS indicates the degree of refusal and brings about better accuracy and granularity in the analysis, which involves a considerable amount of subjectivity and impreciseness in the available information [41]. Due to its potential for superior analysis under uncertainty, PFS has been utilized by various researchers (e.g., [42][43][44][45][46][47][48]) in distinct situations, for multi-criteria decision making (MCDM) related problems. In the following section, we mention some of the basic definitions, operations and properties of PFS [49,50].…”

Section: Pfsmentioning

confidence: 99%

A Cross-Sectional Study on Mental Health of School Students during the COVID-19 Pandemic in India

Deb¹,

Kar

Deb

et al. 2022

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The broad objective of the present study is to assess the levels of anxiety and depression of school students during the COVID-19 lockdown phase and their association with students’ background, stress, concerns and social support. In this regard, the present study follows a novel two stage approach. In the first phase, an empirical survey was carried out, based on multivariate statistical analysis, wherein a group of 273 school students participated in the study voluntarily. In the second phase, a novel Picture Fuzzy FFA (PF-FFA) method was applied for understanding the dynamics of facilitating and prohibiting factors for three categories of focus groups (FG), formulated on the basis of attendance in online classes. Findings revealed a significant impact of anxiety and depression on mental health. Further, PF-FFA examinedthe impact of the driving forces that steered children to attend class as contrasted to the the impact of the restricting forces.

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Frank aggregation operators and analytic hierarchy process based on interval‐valued picture fuzzy sets and their applications

Abstract: To cope with awkward and unreliable information in daily life issues, the theory of interval-valued picture fuzzy set (IVPFS) is a useful idea to manage unpredictable and vague information. An IVPFS contains

Cited by 32 publications

References 38 publications

Improved CoCoSo Method Based on Frank Softmax Aggregation Operators for T-Spherical Fuzzy Multiple Attribute Group Decision-Making

Improved CoCoSo Method Based on Frank Softmax Aggregation Operators for T-Spherical Fuzzy Multiple Attribute Group Decision-Making

Interval Valued Picture Fuzzy Aczel–Alsina Aggregation Operators and Their Application by Using the Multiattribute Decision Making Problem

A Cross-Sectional Study on Mental Health of School Students during the COVID-19 Pandemic in India

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