Some Picture Fuzzy Aggregation Operators based on Frank t-norm and t-conorm: Application to MADM Process

Seikh, Mijanur Rahaman; Mandal, Utpal

doi:10.31449/inf.v45i3.3025

Cited by 43 publications

(14 citation statements)

References 48 publications

(49 reference statements)

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“…Definition 6 [57]: Suppose that c and d are two real numbers. Then, Frank t-norm and Frank t-conorm are described as follows:…”

Section: Necessary Operations Of Frank Aggregation Modelsmentioning

confidence: 99%

“…A list of AOs based on a weighted average and weighted geometric operators was given by Wei [56], and Jana et al [55]invented some appropriate AOs of PF Dombi weighted average (PFDWA) and PF Dombi weighted geometric (PFDWG) operators. Seikh and Mandal [57] proposed some AOs based on Frank aggregation tools in the form of PF Frank weighted average (PFFWA) and PF Frank weighted geometric (PFFWG), AOs of PF Einstein weighted average (PFEWA) and PF Einstein weighted geometric (PFEWG) given by the Khan et al [60]. Wei [35] introduced some AOs of PF Hamacher weighted average (PFHWA) and PF Hamacher weighted geometric (PFHWG) operators, Senapati [61] proposed PF Aczel Alsina weighted average (PFAAWA), Naeem et al [62]also illustrate some new approaches of PF Aczel Alsina weighted geometric (PFAAWG) and Hussain et al [20]gave AOs of Complex PFSs under Hamy mean aggregation models.…”

Section: Comparative Studymentioning

confidence: 99%

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Evaluation of Electric Motor Cars Based Frank Power Aggregation Operators Under Picture Fuzzy Information and a Multi-Attribute Group Decision-Making Process

et al. 2023

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In this article, we expose the notion of power operator to reduce the impact of negative information on the decision-making (DM) process. The power aggregation tools are also robust mathematical aggregation operators (AOs) which allow input arguments to support each other in the DM process. The Frank aggregation expressions are reliable and updated versions of triangular norms which are used to handle complex and complicated information in a decision-making process. The picture fuzzy (PF) set (PFS) is an extended version of the fuzzy sets (FSs) and intuitionistic FSs (IFSs). A PFS has four terms of an object simultaneously such as positive grade (PG), Abstained grade (AG), negative grade (NG) and refusal grade (RG). By using basic operations of Frank aggregation expressions, we propose a list of new appropriate methodologies under consideration of PF information, including ''picture fuzzy frank power average'' (PFFPA), and ''picture fuzzy frank power geometric'' (PFFPG) operators. We also present some new approaches to PFSs based on Frank aggregation tools such as ''picture fuzzy frank power weighted average'' (PFFPWA) and ''picture fuzzy frank power weighted geometric'' (PFFPWG) operators. Some appropriate properties and special cases of our currently proposed approaches are also studied. Moreover, to ratify the intensity and reliability of our derived strategies, we illustrated an algorithm of the multiattribute group decision-making (MAGDM) technique under a PF environment. Furthermore, we illustrated a practical case study to evaluate a suitable optimal option by considering our proposed approaches and analyzed the performance of our currently derived approaches by comparing the results of existing methodologies.INDEX TERMS Frank aggregation tools, picture fuzzy numbers, power aggregation operates, multi-attribute group decision-making process.

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“…Definition 6 [57]: Suppose that c and d are two real numbers. Then, Frank t-norm and Frank t-conorm are described as follows:…”

Section: Necessary Operations Of Frank Aggregation Modelsmentioning

confidence: 99%

Section: Comparative Studymentioning

confidence: 99%

Evaluation of Electric Motor Cars Based Frank Power Aggregation Operators Under Picture Fuzzy Information and a Multi-Attribute Group Decision-Making Process

et al. 2023

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“…Some operations on various fuzzy sets have been introduced based on the Frank T-norm and S-norm, such as intuitionistic Frank operations (Xia et al 2012 ; Zhang et al 2015 ), single-valued neutrosophic Frank operations (Garg 2016 ), hesitant Frank operations (Qin et al 2016), dual-hesitant fuzzy Frank operations (Wang et al 2016 ), interval intuitionistic linguistic Frank aggregation operators (Du and Hou 2018 ), Frank prioritized Bonferroni mean operations (Ji et al 2018 ), linguistic intuitionistic fuzzy Frank weighted Heronian mean operator (Peng et al 2018 ), interval-valued probabilistic hesitant fuzzy aggregation operators (Yahya et al 2021 ), triangular interval type-2 fuzzy Frank operations (Qin and Liu 2014 ), interval-valued Pythagorean Frank power operations (Yang et al 2018), picture fuzzy Frank weighted averaging operator (Seikh and Mandal 2021a ). Some researchers also studied various mathematical properties of the Frank t-norms (Liu et al 2018 ; Xing et al 2019 ; Zhou et al 2019 ; Seikh and Mandal 2021b ).…”

Section: Introductionmentioning

confidence: 99%

Complex q-rung orthopair fuzzy Frank aggregation operators and their application to multi-attribute decision making

et al. 2022

Soft Comput

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The complex q-rung orthopair fuzzy sets (Cq-ROFSs) can serve as a generalization of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets FS (CFSs). Cq-ROFSs provide more freedom for people handling uncertainty and vagueness by the truth and falsity grades on the condition that the sum of the q-powers of the real part and imaginary part is within the unit interval. Further, Frank operational laws are an extended form of Archimedes' T mode and Archimedes' S mode and Frank aggregation operators have a certain parameter which makes them more flexible and more generalized than many other aggregation operators in the process of information fusion. The objectives of this paper are to extend the Frank operations to the complex q-rung orthopair fuzzy environment and to introduce their score function and accuracy function. Meanwhile, some complex q-rung fuzzy Frank aggregation operators are developed, such as the complex q-rung orthopair fuzzy Frank weighted averaging (Cq-ROFFWA) operator, the complex q-rung orthopair fuzzy Frank weighted geometric (Cq-ROFFWG) operator, and the complex q-rung orthopair fuzzy Frank ordered weighted averaging (Cq-ROFFOWA) operator, and their special cases are discussed. In addition, an innovative MADM method is introduced according to the propounded operators to deal with multi-attribute decision-making problems under the complex q-rung orthopair fuzzy environment. Consequently, the practicability and effectiveness of the created methods are proposed by parameter exploration and comparative analysis.

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“…For the first question, FTT [18] is noteworthy for its flexible information aggregation capability. Many scholars have studied the properties and applications of FTT [19,20,21]. So far, we have not seen much relevant researches on AOs of q-RDHFS based on FTT.…”

Section: Introductionmentioning

confidence: 99%

A Novel Decision-Making Method for Selecting Charging Pile Manufacturer with q-Rung Dual Hesitant Information

Tan

Shang

Wang

et al. 2022

Preprint

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In recent years, the development of electric vehicles has received extensive attention. However, how to choose a suitable charging pile manufacturer for electric vehicles is a matter of concern. The selection of charging pile manufacturers involves many factors, and it is hard for decision makers (DMs) to provide accurate assessments due to the uncertainty of subjective or objective factors. As a combination of q-rung orthopair fuzzy set (q-ROFS) and dual hesitant fuzzy set (DHFS), q-rung dual hesitant fuzzy set (q-RDHFS) provides more possibilities for information expression and gives DMs greater decision-making freedom. Because of the advantages of q-RDHFS in expressing uncertain information, we propose a novel decision method to capture DMs’ hesitant information with q-rung dual hesitant fuzzy elements (q-RDHFEs) to obtain the optimal scheme. Firstly, Frank t-norm and t-conorm (FTT) is well known for its flexibility in coping with compatibility compared to traditional algebraic operation. Considering the advantages of FTT, we extend FTT to q-RDHFS and provide the definition of Frank operational rules of q-RDHFS. Subsequently, according to generalized power average (GPA) and generalized power geometric (GPG) operators, some corresponding operators based on the novel operational laws are proposed. Then, with the proposed operators, a novel multi-attribute decision-making (MADM) method under q-RDHFS environment is introduced and applied to the selection of charging pile manufacturers. Finally, compared with the existing methods, the method proposed in this paper can better handle extreme evaluation information and is more flexible in operation.

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Some Picture Fuzzy Aggregation Operators based on Frank t-norm and t-conorm: Application to MADM Process

Cited by 43 publications

References 48 publications

Evaluation of Electric Motor Cars Based Frank Power Aggregation Operators Under Picture Fuzzy Information and a Multi-Attribute Group Decision-Making Process

Evaluation of Electric Motor Cars Based Frank Power Aggregation Operators Under Picture Fuzzy Information and a Multi-Attribute Group Decision-Making Process

Complex q-rung orthopair fuzzy Frank aggregation operators and their application to multi-attribute decision making

A Novel Decision-Making Method for Selecting Charging Pile Manufacturer with q-Rung Dual Hesitant Information

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