The Probabilistic Interval-Valued Hesitant Pythagorean Fuzzy Set and Its Application in Selecting Processes of Project Private Partner

Si, Luo; Liu, Jun

doi:10.1109/access.2019.2954995

Cited by 9 publications

(5 citation statements)

References 44 publications

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“…• The FFSs can be combined with other information, for instance, the probabilistic interval-valued hesitant fuzzy [89]; and can evaluation and selection of smart city waste management systems under FFS information with other decision-making method, such as MULTIMOORA [90], [91], COPRAS [92] and others. However, the proposed study is unable to deal with the new generation of smart applications with more complex sets of heterogeneous information, data, systems, sensors, devices, etc.…”

Section: Discussionmentioning

confidence: 99%

“…In FST, each element is assigned a membership grade (MG) lying between 0 and 1. Since in an FS, the non-membership grade (NG) of an element cannot be preferred independently, therefore, Atanassov [89] pioneered the notion of ''intuitionistic fuzzy set (IFS)''. In the theory of IFS, each element has a MG and a NG lying between 0 and 1, with their sum is restricted to unity.…”

Section: A Challenges and Motivationsmentioning

confidence: 99%

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Assessing the Adaptation of Internet of Things (IoT) Barriers for Smart Cities’ Waste Management Using Fermatean Fuzzy Combined Compromise Solution Approach

Mishra¹,

Rani

Saha

et al. 2022

IEEE Access

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This study proposes a systematic methodology of the adoption of Internet of Things (IoT) barriers (IoTBs) that exist in the waste management structures of smart cities (SCs) in growing economies likely India. A hybrid multi-attribute decision-making (MADM) is applied and has recognized 15 IoTBs from literature and experts opinions obstructing the IoT adoption in SCs of India. The different IoTBs are studied using the similarity measure-based new weighting approach, and the combined compromise solution (CoCoSo) method. Considering that Fermatean fuzzy sets (FFSs) can represent this uncertainty, this paper proposes a decision-making framework for waste management system solutions based on the FFSs and builds a complete evaluation index system. Herein, we first combine the Archimedean Copula operations and Archimedean operations and term them as 'generalized Archimedean Copula operations' for FFSs. Based on these new operations, we develop the Fermatean fuzzy generalized Archimedean copula weighted averaging (FFGACWA) and Fermatean fuzzy generalized Archimedean copula weighted geometric (FFGACWG) operators. Then, we construct a decision algorithm based on FFWGAAC and FFWGGAC operators. Second, we propose new weighting procedure based on similarity measure to discuss the significance degree of IoTBs. Further, we apply this method to the evaluation and selection of a methodology of IoTBs in smart cities' waste management (SCWM) assignments, and prove the effectiveness of this method. The algorithm can represent the Fermatean fuzzy information in a complex environment. It cannot only consider the uncertainty of the decision-makers (DMEs) when giving the evaluation value but also synthesize the relationship between any numbers of evaluation criteria. Finally, the superiority of the methodology is discussed by sensitivity analysis and comparative study. The results show that the method can effectively handle the decision-making problems in complex environments. This paper will assist the representatives, stakeholders and government to know the importance of IoTBs affecting waste management processes, and it will certainly help them to take judgments for exterminating the IoTBs for an effective IoT employment in SCWM assignments.

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Section: Discussionmentioning

confidence: 99%

Section: A Challenges and Motivationsmentioning

confidence: 99%

Assessing the Adaptation of Internet of Things (IoT) Barriers for Smart Cities’ Waste Management Using Fermatean Fuzzy Combined Compromise Solution Approach

Mishra¹,

Rani

Saha

et al. 2022

IEEE Access

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“…Khan et al [54] investigated an interval-valued Pythagorean fuzzy Choquet integral geometric (IVPFCIG) operator based on fuzzy measures for solving MCGDM problems. Luo and Liu [55] used the Hamacher operation and Choquet interval to develop the probabilistic interval-valued hesitant Pythagorean fuzzy Hamacher Choquet integral geometric (PIVH-PFHCIG) operator. Shao et al [56] proposed the probabilistic neutrosophic hesitant fuzzy Choquet averaging and geometric operators to select the third-party logistics providers.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Interval-Valued Fermatean Hesitant Fuzzy Set and Its Application to Multi-Attribute Decision Making

Ruan,

Chen

2023

Axioms

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It is difficult to describe the hesitation and uncertainty of experts by single-valued information, and the differences in the importance of attributes are often ignored during the decision-making process. This paper introduces the probability and interval values into Fermatean hesitant fuzzy set (FHFS) and creatively proposes the probabilistic interval-valued Fermatean hesitant fuzzy set (PIVFHFS) to deal with information loss. This new fuzzy set allows decision makers to use interval-valued information with probability to express their quantitative evaluation, which broadens the range of information expression, effectively reflects the important degree of different membership degrees, and can describe uncertain information more completely and accurately. Under the probabilistic interval-valued Fermatean hesitant fuzzy environment, several new aggregation operators based on Hamacher operation are proposed, including the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher weighted averaging (PIVFHFHWA) operator and geometric (PIVFHFHWG) operator, and their basic properties and particular forms are studied. Then, considering the general correlation between different attributes, this paper defines the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher Choquet integral averaging (PIVFHFHCIA) operator and geometric (PIVFHFHCIG) operator and discusses related properties. Finally, a multi-attribute decision-making (MADM) method is presented and applied to the decision-making problem of reducing carbon emissions of manufacturers in the supply chain. The stability and feasibility of this method are demonstrated by sensitivity analysis and comparative analysis. The proposed new operators can not only consider the correlation between various factors but also express the preference information of decision makers more effectively by using probability, thus avoiding information loss in decision-making progress to some extent.

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“…See [28,29]. In 2019, Luo and Liu [30] put forward the probabilistic interval-value hesitation PFNs and applied it to the selecting processes of project private partner. In 2020, Gao and Liu et al [31] proposed the decision-making algorithm for sharing accmmodation by using PrHFSs and bipartite network projection, a bipartite graph connecting users and alternatives is established.…”

Section: Introductionmentioning

confidence: 99%

Interactive group decision making method based on probabilistic hesitant Pythagorean fuzzy information representation

2022

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Interactive group evaluation is a decision-making method to obtain group consensus by constantly modifying the initial weight of experts. Probabilistic hesitant Pythagorean fuzzy set (PrHPFS) is to be added the corresponding probability values for each membership degree and non-membership degree on the hesitant Pythagorean fuzzy set (HPFS). It is not only a generalization of HPFS and the Pythagorean fuzzy set (PFS), but also a more comprehensive and accurate reflection of the initial decision information given by experts. Especially, it can deal with the decision-making problem of multi-attribute fuzzy information in a wider area. In this paper, some basic definitions and related operations of the probabilistic hesitant Pythagorean fuzzy numbers (PrHPFNs) are first reviewed, and propose score function and accuracy function in PrHPFNs environment. Secondly, the concepts of Hamming distance measure, weighted distance measure and degree of similarity are put forward in PrHPFNs space, and the degree of similarity of two probabilistic hesitant Pythagorean fuzzy matrices (PrHPFMs) is suggested through the aggregation operator formula of PFNs. Finally, an interactive group decision-making method is designed based on the PrHPFM and the degree of similarity under the PrHPFNs environment, the effectiveness of the method is verified by an example, so as to overcome the hesitant psychological state of experts and achieve the consistent consensus evaluation of group preference.

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The Probabilistic Interval-Valued Hesitant Pythagorean Fuzzy Set and Its Application in Selecting Processes of Project Private Partner

Cited by 9 publications

References 44 publications

Assessing the Adaptation of Internet of Things (IoT) Barriers for Smart Cities’ Waste Management Using Fermatean Fuzzy Combined Compromise Solution Approach

Assessing the Adaptation of Internet of Things (IoT) Barriers for Smart Cities’ Waste Management Using Fermatean Fuzzy Combined Compromise Solution Approach

Probabilistic Interval-Valued Fermatean Hesitant Fuzzy Set and Its Application to Multi-Attribute Decision Making

Interactive group decision making method based on probabilistic hesitant Pythagorean fuzzy information representation

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