Spherical fuzzy sets (SFSs) are a new extension of Cuong's picture fuzzy sets (PFSs). In SFSs, membership degrees satisfy the condition 0≤P2(x)+I2(x)+N2(x)≤1 instead of 0≤P(x)+I(x)+N(x)≤1 as is in PFSs. In the present work, we extend different strict archimedean triangular norm and conorm to aggregate spherical fuzzy information. Firstly, we define the SFS and discuss some operational rules. Generalized spherical aggregation operators for spherical fuzzy numbers utilizing these strict Archimedean t‐norm and t‐conorm are proposed. Finally, based on these operators, a decision‐making method has been established for ranking the alternatives by utilizing a spherical fuzzy environment. The suggested technique has been demonstrated with a descriptive example for viewing their effectiveness as well as reliability. A test checking the reliability and validity has also been conducted for viewing the supremacy of the suggested technique.

Spherical aggregation operators and their application in multiattribute group decision‐making

As the extension of fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, and picture fuzzy set, the spherical fuzzy set is characterized by three functions expressing the positive-membership degree, the neutral-membership degree and the negative-membership degree which the sum squares of them is equal or less than 1. In this work, we shall present some novel Dice similarity measures of spherical fuzzy sets and the generalized Dice similarity measures of spherical fuzzy sets and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision making models with spherical fuzzy information. Then, we apply the generalized Dice similarity measures between spherical fuzzy sets to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.

https://informatica.vu.lt/journal/INFORMATICA/article/875/file/pdf

The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications

Reasonable and effective assessment of express service quality can help express company discover its own shortcomings and overcome them, which is crucial significant to enhance its service quality. When considering the decision assessment of express company, the key issue that emerge powerful ambiguity. Pythagorean fuzzy set as an efficient math tool can capture the indeterminacy successfully. The major focus of this manuscript is to explore various interactive Hamacher power aggregation operators for Pythagorean fuzzy numbers. Firstly, we defined novel interactive Hamacher operation, on this basis we presented some Pythagorean fuzzy interactive Hamacher power aggregation operators such as Pythagorean fuzzy interactive Hamacher power average, weighted average (PFIHPWA), ordered weighted average, Pythagorean fuzzy interactive Hamacher power geometric, weighted geometric (PFIHPWG) and ordered geometric operators,respectively. Meanwhile, we verified their general properties and specific cases as well. The salient feature of proposed operators is that they can not only reduce the impact of negative data and consider the interactions between membership and nonmembership degrees, but also provide more general results through a parameter. Secondly, we defined a Pythagorean fuzzy entropy measure, and then establish a method to determine the attribute weights. Further, based on the conceived PFIHPWA and PFIHPWG operators we explored a novel approach to manage multiple attribute decision making problems. At last, the proposed techniques are carried out in a real application concerning on the assessment of express service quality to display the applicability and effectiveness, as well as the influence of changed parameters on the results. In addition, its advantages are displayed by a systematic comparison with relevant approaches.

https://link.springer.com/content/pdf/10.1007/s00500-020-05193-z.pdf

Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight

Abstract Heronian mean (HM) operator has the advantages of considering the interrelationships between parameters, and linguistic intuitionistic fuzzy number (LIFN), in which the membership and non-membership are expressed by linguistic terms, can more easily describe the uncertain and the vague information existing in the real world. In this paper, we propose the partitioned Heronian mean (PHM) operator which assumes that all attributes are partitioned into several parts and members in the same part are interrelated while in different parts there are no interrelationships among members, and develop some new operational rules of LIFNs to consider the interactions between membership function and non-membership function, especially when the degree of non-membership is zero. Then we extend PHM operator to LIFNs based on new operational rules, and propose the linguistic intuitionistic fuzzy partitioned Heronian mean (LIFPHM) operator, the linguistic intuitionistic fuzzy weighted partitioned Heronian mean (LIFWPHM) operator, the linguistic intuitionistic fuzzy partitioned geometric Heronian mean (LIFPGHM) operator and linguistic intuitionistic fuzzy weighted partitioned geometric Heronian mean (LIFWPGHM) operator. Further, we develop two methods to solve multi-attribute group decision making (MAGDM) problems with the linguistic intuitionistic fuzzy information. Finally, we give some examples to verify the effectiveness of two proposed methods by comparing with the existing

Partitioned Heronian Means Based on Linguistic Intuitionistic Fuzzynumbers for Dealing with Multi-Attribute Group Decision Making

Inventive problem-solving map of innovative carbon emission strategies for solar energy-based transportation investment projects

The influence of COVID-19 on individuals, businesses, and corporations is indisputable. Many markets, particularly financial markets, have been severely shaken and have suffered significant losses. Significant issues have arisen in supply chain networks, particularly in terms of financing. The COVID-19 consequences had a significant effect on supply chain financing (SCF), which is responsible for finance supply chain components and improved supply chain performance. The primary source of supply chain financing is financial providers. Among financial providers, the banking sector is referred to as the primary source of financing. Any hiccup in the banking operational systems can have a massive influence on the financing process. In this study, we attempted to comprehend the key consequences of the COVID-19 epidemic and how to mitigate COVID-19’s impact on Pakistan’s banking industry. For this, three extended hybrid approaches which consists of TOPSIS, VIKOR, and Grey are established to address the uncertainty in supply chain finance under q-rung orthopair probabilistic hesitant fuzzy environment with unknown weight information of decision-making experts as well as the criteria. The study is split into three parts. First, the novel q-rung orthopair probabilistic hesitant fuzzy (qROPHF) entropy measure is established using generalized distance measure under qROPHF information to determine the unknown weights information of the attributes. The second part consists of three decision-making techniques (TOPSIS, VIKOR, and GRA) in the form of algorithm to tackle the uncertain information under qROPHF settings. Last part consists of a real-life case study of supply chain finance in Pakistan to analyze the effects of emergency situation of COVID-19 on Pakistani banks. Therefore, to help the government, we chose the best alternative form list of consider five alternatives (investment, government support, propositions and brands, channels, and digital and markets segments) by using proposed algorithm that minimize the effect of COVID-19 on supply chain finance of Pakistani banks. The results indicate that the proposed techniques are applicable and effective to cope with ambiguous data in decision-making challenges.

/pdf/decision-making-techniques-based-on-q-rung-orthopair-21zp9axs.pdf

Decision-Making Techniques Based on q-Rung Orthopair Probabilistic Hesitant Fuzzy Information: Application in Supply Chain Financing

The single valued neutrosophic probabilistic hesitant fuzzy rough Einstein aggregation operator (SV-NPHFRE-AO) is an extension of the neutrosophic probabilistic hesitant fuzzy rough set theory. It is a powerful decision-making tool that combines the concepts of neutrosophic logic, probability theory, hesitant fuzzy sets, rough sets, and Einstein aggregation operators. SV-NPHFRE-AO can be applied in many fields, including livestock decision making. Making judgments about a wide range of issues, including feed formulation, breeding program design, disease diagnostics, and market analysis, is part of the process of managing livestock. By combining data from many sources, SV-NPHFRE-AO can assist decision-makers in livestock management in integrating and evaluating diverse criteria, which can result in more informed choices. It also provides a more accurate and comprehensive representation of decision-making problems by considering the multiple criteria involved and the relationships between them. The single valued neutrosophic set (SV-NS) aggregation operators (AOs) based on Einstein properties using hesitant fuzzy sets (HFSs) and probabilistic hesitant fuzzy sets (PHFSs) with rough sets (RSs) are proposed in this study and can handle a large volume of data, making them suitable for complex and large-scale livestock decision-making problems. We first defined SV-neutrosophic probabilistic hesitant fuzzy rough weighted averaging (SV-NPHFRWA), SV-neutrosophic probabilistic hesitant fuzzy rough weighted geometric (SV-NPHFRWG), SV-neutrosophic probabilistic hesitant fuzzy rough ordered weighted averaging (SV-NPHFROWA) and SV-neutrosophic probabilistic hesitant fuzzy rough hybrid weighted averaging (SV-NPHFRHWA) AOs. Then, based on Einstein properties, we extended these operators and developed the single-valued neutrosophic probabilistic hesitant fuzzy rough Einstein weighted averaging (SV-NPHFREWA) operator. Additionally, an illustrative scenario to show the applicability of the suggested decision-making approach is provided, along with a sensitivity analysis and comparison analysis, which demonstrate that its outcomes are realistic and reliable. We also provide another relation between criteria and alternatives of decision-making using neutrosophic information with quaternion context. By using such type of operators, livestock managers can make more informed decisions, leading to better animal health, higher productivity, and increased profitability.

An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator

Simulation software replicates the behavior of real electrical equipment using mathematical models. This is efficient not only in regard to time savings but also in terms of investment. It, at large scale for instance airplane pilots, chemical or nuclear plant operators, etc., provides valuable experiential learning without the risk of a catastrophic outcome. But the selection of a circuit simulator with effective simulation accuracy poses significant challenges for today's decision-makers because of uncertainty and ambiguity. Thus, better judgments with increased productivity and accuracy are crucial. For this, we developed a complex probabilistic hesitant fuzzy soft set (CPHFSS) to capture ambiguity and uncertain information with higher accuracy in application scenarios. In this manuscript, the novel concept of CPHFSS is explored and its fundamental laws are discussed. Additionally, we investigated several algebraic aspects of CPHFSS, including union, intersections, soft max-AND, and soft min-OR operators, and we provided numerical examples to illustrate these key qualities. The three decision-making strategies are also constructed using the investigated idea of CPHFSS. Furthermore, numerical examples related to bridges and circuit simulation are provided in order to assess the validity and efficacy of the proposed methodologies. The graphical expressions of the acquired results are also explored. Finally, we conclude the whole work.

Simulator selection based on complex probabilistic hesitant fuzzy soft structure using multi-parameters group decision-making

/pdf/retraction-note-to-decision-aid-modeling-based-on-sine-2soo2fba.pdf

Retraction Note to: Decision aid modeling based on sine trigonometric spherical fuzzy aggregation information

/pdf/retraction-note-a-new-emergency-response-of-spherical-29i8s9pk.pdf

Shahzaib Ashraf

Papers

Decision-Making Techniques Based on q-Rung Orthopair Probabilistic Hesitant Fuzzy Information: Application in Supply Chain Financing

An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator

Simulator selection based on complex probabilistic hesitant fuzzy soft structure using multi-parameters group decision-making

Retraction Note to: Decision aid modeling based on sine trigonometric spherical fuzzy aggregation information

Retraction Note: A new emergency response of spherical intelligent fuzzy decision process to diagnose of COVID19