Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making

Ateş, Fatma; Akay, Diyar

doi:10.1002/int.22220

Cited by 50 publications

(36 citation statements)

References 34 publications

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“…To further demonstrate the superiorities of the proposed MADM method using the PFHWPIGHM operator and the PFHWGPIGHM operator, we compare the method proposed in this paper with the existing method proposed by Wei [45], based on the PFHWA operator and the PFHWG operator, and the method proposed by Ates and Akay [41], based on the PFNWBM operator. e rankings of different AOs are listed in Table 7.…”

Section: Comparison Analysismentioning

confidence: 99%

“…e method of Wei [45] does not consider the correlations of attributes and the influence of biased data, and only one parameter is considered. e method of Ates and Akay [41] considers the correlations of attributes but cannot reduce the influence of biased data, and it is based on Algebraic operations, which is only a special case of Hamacher operations, and only two parameters are considered. In contrast, our method not only considers the correlations of attributes but also reduces the influence of biased data.…”

Section: Comparison Analysismentioning

confidence: 99%

“…Zhang et al [40] introduced Heronian mean (HM) operators using Dombi operations to PFS. Ates and Akay [41] expanded some Bonferroni mean (BM) to picture fuzzy set to handle MADM, including PFBM, PFNWBM, and PFOWBM operators. Luo and Xing [42] proposed picture fuzzy interaction partitioned Heronian (PFIPH) operator for selecting hotel.…”

Section: Introductionmentioning

confidence: 99%

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Power Improved Generalized Heronian Mean Operators Utilizing Hamacher Operations with Picture Fuzzy Information

Yang

2021

Complexity

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In multiple attribute decision-making (MADM), to better denote complicated preference information of decision-makers (DMs), picture fuzzy set (PFS) as an expansion of intuitionistic fuzzy set (IFS) has become a powerful tool in the recent years. Meanwhile, to remove the impact of abnormal data and capture the correlations among attributes in MADM issue, we propose the power improved generalized Heronian mean (PIGHM) operators in this paper, which have the merits of both power average (PA) operator and improved generalized Heronian mean (IGHM) operator. Additionally, Hamacher operations as a generalization of Algebraic operations and Einstein operations demonstrate good smooth approximate. Motivated by these, the main purpose is to explore PIGHM operators utilizing Hamacher operations to cope with MADM issue with picture fuzzy information. First, we introduce the Hamacher operations, the normalized hamming distance, and similarity measure of picture fuzzy numbers (PHNs). Second, based on these, two new picture fuzzy aggregating operators (AOs), the picture fuzzy Hamacher weighted power improved generalized Heronian mean (PFHWPIGHM) operator and the picture fuzzy Hamacher weighted geometric power improved generalized Heronian mean (PFHWGPIGHM) operator, are put forward, and some properties and special instances of proposed AOs are also investigated. Third, a new MADM model in terms of the PIGHM AOs is developed. Eventually, a practical MADM example, together with sensitivity analysis and comparative analysis, is conducted to verify the credibility and superiority of the new MADM model.

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Section: Comparison Analysismentioning

confidence: 99%

Section: Comparison Analysismentioning

confidence: 99%

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Power Improved Generalized Heronian Mean Operators Utilizing Hamacher Operations with Picture Fuzzy Information

Yang

2021

Complexity

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“…This novel extension of fuzzy sets shows superiority in describing decision-maker preferences [34] and mitigating information loss [64]. PFSs are characterized by degrees of positive, neutral, negative, and refusal membership [3,50]. These advanced fuzzy sets are considerably more close to human nature [56].…”

Section: Introductionmentioning

confidence: 99%

Picture fuzzy WASPAS method for selecting last-mile delivery mode: a case study of Belgrade

Šimić

Lazarević

Dobrodolac

2021

Eur. Transp. Res. Rev.

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Background Last-mile delivery (LMD) is becoming more and more demanding due to an increasing number of users and traffic problems in cities. Besides, medical crises (like the COVID-19 outbreak) and air pollution represent additional motives for the transition from traditional to socially and environmentally sustainable LMD mode. An emerging problem for companies in the postal and logistics industry is how to determine the best LMD mode in a multi-criteria setting under uncertainty. Method For the first time, an extension of the Weighted Aggregated Sum Product ASsessment (WASPAS) method under the picture fuzzy environment is presented to solve the LMD mode selection problem. The introduced picture fuzzy set (PFS) based multi-criteria decision-making (MCDM) method can be highly beneficial to managers who are in charge of LMD since it can take into account the neutral/refusal information and efficiently deal with high levels of imprecise, vague, and uncertain information. The comparative analysis with the existing state-of-the-art PFS-based MCDM methods approved the high reliability of the proposed picture fuzzy WASPAS method. Its high robustness and consistency are also confirmed. The presented method can be used to improve LMD in urban areas worldwide. Besides, it can be applied to solve other emerging MCDM problems in an uncertain environment. Findings A real-life case study of Belgrade is presented to fully illustrate the potentials and applicability of the picture fuzzy WASPAS method. The results show that postomates are the best mode for LMD in Belgrade, followed by cargo bicycles, drones, traditional delivery, autonomous vehicles, and tube transport.

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“…Another such generalization of fuzzy numbers, in fact, IFNs are picture fuzzy numbers and neutrosophic numbers, which incorporates the indeterminacy-membership apart from the truth-membership and falsitymembership functions. As such many works are done on the application of these numbers in various decision making problems, namely, Si et al, 5 Riaz et al, 6 Arya and Kumar, 7 Ates and Akay, 8 and so forth. The generalization of neutrosophic numbers is possible through the pioneering work by Smarandache.…”

Section: Introductionmentioning

confidence: 99%

Ordering single‐valued neutrosophic numbers based on flexibility parameters and its reasonable properties

et al. 2021

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Undoubtedly, most of the information conveyed is full of impreciseness or vagueness. In such situation, fuzzy set theory is a proper tool to handle these types of impreciseness or vagueness. Fuzzy numbers are also of different types based on the presence of uncertainty. Neutrosphic numbers are one type of fuzzy number that consists of three types of membership functions, namely, truth, indeterminacy and falsity. In fact, neutrosophic numbers are generalization of intuitionistic fuzzy numbers. These numbers might be used in decision making problems, where it is essential to rank those numbers. So, ordering of these numbers becomes a new trends with more challenges. In this paper, an innovative ranking approach of single-valued neutrosophic number has been put forwarded. The method is based on value, ambiguity and θ function. Value and ambiguity are defined on three functions of the neutrosophic numbers. Further, the reliability of the proposed method is established by considering the reasonable properties of ranking method. One important aspect of ranking neutrosophic numbers is to consider the consistency in ordering the neutrosophic numbers and their corresponding images. It is worth to mention that the current approach consistently ranks

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Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making

Cited by 50 publications

References 34 publications

Power Improved Generalized Heronian Mean Operators Utilizing Hamacher Operations with Picture Fuzzy Information

Power Improved Generalized Heronian Mean Operators Utilizing Hamacher Operations with Picture Fuzzy Information

Picture fuzzy WASPAS method for selecting last-mile delivery mode: a case study of Belgrade

Ordering single‐valued neutrosophic numbers based on flexibility parameters and its reasonable properties

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