A Novel Picture Fuzzy Linguistic Aggregation Operator and Its Application to Group Decision-making

An extended picture fuzzy multicriteria group decision analysis with different weights: A case study of COVID-19 vaccine allocation

The high contagion rates of COVID-19 and the limited amounts of vaccines forced public health authorities to develop vaccinations strategies for minimizing mortality, avoiding the collapse of health care infrastructure, and reducing their negative impacts to societies and economies. We propose a Multi Criteria Group Decision Making for prioritizing a set of COVID-19 vaccination alternatives, under a picture fuzzy environment, where the weights for Decisions Experts (DE) and criteria are unknown. A panel of six DEs assess six criteria for prioritizing four groups for vaccination. The weights for DE and criteria are handled in the form of fuzzy sets. Three types of weights are calculated: subjective, objective, and mixture weights. According to our results, three out of the six criteria hold 60% of the strategic importance: 1) allocation and distribution, 2) COVID-19 strains and 3) capabilities and infrastructures. However, persons with comorbidities became the group with the highest priority, followed by essential workers, women, and adults older than 40 years. Governments, decision makers, and policy makers can find rigorous scientific evidence for articulating effective vaccinations campaigns from this work, and contribute to minimize undesired outputs, such as high mortality rates or collapse of hospitals.

Proposed distance and entropy measures of picture fuzzy sets in decision support systems

The picture fuzzy set is an extension of the fuzzy and intuitionistic fuzzy set for solving real-world problems. Entropy and distance measures play significant roles in measures for solving problems involving fuzzy environments. This paper has presented some new distance and entropy measures using picture fuzzy sets to solve problems of medical diagnosis and multi-criteria decision making problems. In addition, the entropy measure is induced from the distances of picture fuzzy sets in order to determine entropy measure of picture fuzzy sets. The proposed methods combined entropy and distance measures to construct the Technique for Order of Preference by Similarity to Ideal Solution model to solve multi-criteria decision making problem. To validate the proposed methods, some numerical examples are given to demonstrate new measurements. The efficiency of the measure is proven by comparison to other measures when solving medical diagnosis in multi-criteria decision making for illustrations in numerical COVID-19 medicine selection.

Generalized q-rung picture linguistic aggregation operators and their application in decision making

The q-rung picture linguistic set (q-RPLS) is an effective tool for managing complex and unpredictable information by changing the parameter ‘q’ regarding hesitancy degree. In this article, we devise some generalized operational laws of q-RPLS in terms of the Archimedean t-norm and t-conorm. Based on the proposed generalized operations, we define two types of generalized aggregation operators, namely the q-rung picture linguistic averaging operator and the q-rung picture linguistic geometric operator, and study their relevant characteristics in-depth. With a view toward applications, we discuss certain specific cases of the proposed generalized aggregation operators with a range of parameter values. Furthermore, we explore q-rung picture linguistic distance measure and its required axioms. Then we put forward a technique for q-RPLSs based on the proposed aggregation operators and distance measure to solve multi-attribute decision-making (MADM) challenges with unknown weight information. At last, a practical example is presented to demonstrate the suggested approaches’ viability and to perform the sensitivity and comparison analysis.

Picture fuzzy Z-linguistic set and its application in multiple attribute group decision-making

Picture fuzzy linguistic set is a vital solution to express complex and uncertain information, which has been applied in multi-attribute group decision-making (MAGDM). However, the credibility of decision-making information is unconsidered, which may give rise to the inaccuracy of final result. To solve this problem, the picture fuzzy Z-linguistic set (PFZLS) composed of linguistic term, picture fuzzy number, and credibility is proposed, which could express more complete decision-making information. Subsequently, operation rules, comparison methods, and distance measures of PFZLS are introduced. In addition, the weighted geometric average operator and the classical VIKOR method are extended and combined to solve the MAGDM problem under the picture fuzzy Z-linguistic environment. Finally, an illustrative example about the emergency decision-making (EDM) problem of forest fire accident is proposed, and a series of comparative analyses are presented to verify the rationality and superiority of the PFZLS.

Hybrid spectrum management using integrated fuzzy and femtocells in cognitive domain

In Today’s pandemic situation, ‘Spectrum accessing and smart usage’ is the sacred Mantra uttered by every individual citizen in the world. Work from home for techies, online classes for students, games for kids, webinar for teaching fraternity etc., are going almost on indoor coverage without any limit in pace because of the smart spectrum coverage by the network service providers. This paper provides an add-on facility to the existing wireless infrastructure to provide a better user experience in this highly regrettable routine. In this paper, a cognitive domain unused spectrum holes are efficiently handled by (i) adaptive spectrum management technique; (ii) Fuzzy Inference System based spectrum administration and (iii) Hybrid Cognitive Femtocell approaches based on the user demand and their applications. The proposed integrated cognitive femtocell and Fuzzy-based approach reduces the indoor coverage problems and enhances the throughput of the macrocell users by allowing adaptive spectrum management based on the demand, thereby eliminating spectrum underlay and overlay problems during critical conditions. In cognitive femtocell networks, the access points are prepared and installed with Cognitive Radio which can determine spectrum dynamically by macrocells and nearby Femto Access Points. It adjusts its radiating parameters to evade the macrocells’ interferences and the neighbouring femtocells, thereby maximising the spectrum band’s overall utility.

Hamacher heronian mean operators for multi-critria decision-making under multi-valued picture fuzzy uncertain lingsuitic environment

Picture fuzzy set (PFS) and linguistic term set (LTS) are two significant notions in multi-criteria decision-making (MCDM). In practice, decision-makers sometimes need utilize the multiple probable membership degrees for an uncertain linguistic term to express evaluation information. Motivated by these, to better convey the vagueness and uncertainty of cognitive information, multi-valued picture fuzzy uncertain linguistic set combining picture hesitant fuzzy set with uncertain linguistic term set is proposed. We firstly define the concepts of multi-valued picture fuzzy uncertain linguistic set and multi-valued picture fuzzy uncertain linguistic number. Hamacher operations are more general and flexible in information fusion, thus, Hamacher operations and comparison method are developed at the same time. Improved generalized Heronian Mean operator can simultaneously reflect correlations between values and prevent the redundant calculation. Then, two operators of improved generalized weighted Heronian mean and improved generalized geometric weighted Heronian mean in view of Hamacher operations are proposed. Meanwhile, some distinguished properties and instances of two operators are explored as well. Moreover, a novel MCDM approach applying the developed operators is constructed. Ultimately, an illustrative example on vendor selection is performed, and sensitivity analysis and comparison analysis are provided to verify the powerfulness of the proposed method.

Decision support framework for the risk ranking of agroforestry biomass power generation projects with picture fuzzy information

With the rapid growth of the global population and economy, energy consumption and demad are increasing sharply. As an essential renewable energy, biomass energy can promote the reform of energy production and consumption. Considering the characteristics of long investment cycle and large investment scale of agroforestry biomass power generation (AFBPG) projects, this study establishes a decision support framework for risk ranking of AFBPG project under picture fuzzy environment. The proposed framework considers not only the fuzziness and uncertainty of decision-making problems but also the decision-makers’ (DMs) psychological behavior. First, given the integrity of information representation, DMs provide risk assessment information expressed with picture fuzzy numbers, and then gives the distance of the picture fuzzy set (PFS) to maximize the PFS information. Second, the entropy weight method is used to compute the objective weight. Third, the VIKOR (Vlse Kriterijumska Optimizacija I Kompromisno Resenje) – TODIM (an acronym in Portuguese for an interactive multi-criteria decision making) method is suggested for ranking risk factors, which reflects the behavioral psychology of DMs. Moreover, the proposed evaluation model is successfully applied in a practical case. The results show that the model is valid for ranking risk factors under picture fuzzy environment. Last but not least, comparison and sensitivity analysis are implemented to verify the effectiveness and applicability of the proposed method and some suggestions for practical application are put forward.

The Linguistic Picture Fuzzy Set and Its Application in Multi-Criteria Decision-Making: An Illustration to the TOPSIS and TODIM Methods Based on Entropy Weight

The paper considers the multi-criteria decision-making problem based on linguistic picture fuzzy information. Firstly, we propose the concept of linguistic picture fuzzy set(LPFS), where the positive-membership, the neutral-membership and the negative-membership are represented by linguistic variables, and its operation rules are also discussed. The linguistic picture fuzzy weighted averaging (LPFWA) operator and linguistic picture fuzzy weighted geometric (LPFWG) operator are developed based on the proposed operation rules. Secondly, we propose the generalized weighted distance measure, the generalized weighted Hausdorff distance measure, and the generalized hybrid weighted distance measure between LPFSs and discuss their properties. Thirdly, we extend the technique for order of preference by similarity to the ideal solution (TOPSIS) method and the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method to the proposed distance measure, and the linguistic picture fuzzy entropy method is proposed to calculate the weights of the criteria. Finally, an illustrative example is given to verify the feasibility and effectiveness of the proposed methods, the comparative analysis with other existing methods and sensitivity analysis of the proposed methods are also discussed.

Some Novel Picture 2-Tuple Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple Attribute Decision Making

When solving multiple attribute decision making (MADM) problems, the 2-tuple linguistic variable is an effective tool that can not only express complex cognitive information but also prevent loss of information in calculation. The picture fuzzy set (PFS) has three degrees and has more freedom to express cognitive information. In addition, Archimedean t-conorm and t-norm (ATT) can generalize most existing t-conorms and t-norms and Maclaurin symmetric mean (MSM) operators can catch the relationships among the multi-input parameters. Therefore, we investigate several novel aggregation operators, such as the picture 2-tuple linguistic MSM (2TLMSM) operator based on the ATT (ATT-P2TLMSM) and the picture 2-tuple linguistic generalized MSM (2TLGMSM) operator based on ATT (ATT-P2TLGMSM). Considering that the input parameters have different importance, we proposed picture 2-tuple linguistic weighted MSM (2TLWMSM) operators based on ATT (ATT-P2TLWMSM) and picture 2-tuple linguistic weighted generalized MSM (2TLWGMSM) operators based on ATT (ATT-P2TLWGMSM). Finally, a MADM method is introduced, and an expositive example is presented to explain the availability and applicability of the developed operators and methods.

Dual Hesitant q-Rung Orthopair Fuzzy Hamacher Aggregation Operators and their Applications in Scheme Selection of Construction Project

The q-rung orthopair fuzzy set (q-ROFS), which is the extension of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), satisfies the sum of q-th power of membership degree and nonmembership degree is limited 1. Evidently, the q-ROFS can depict more fuzzy assessment information and consider decision-maker’s (DM’s) hesitance. Thus, the concept of a dual hesitant q-rung orthopair fuzzy set (DHq-ROFS) is developed in this paper. Then, based on Hamacher operation laws, weighting average (WA) operator and weighting geometric (WG) operator, some dual hesitant q-rung orthopair fuzzy Hamacher aggregation operators are developed, such as the dual hesitant q-rung orthopair fuzzy Hamacher weighting average (DHq-ROFHWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher weighting geometric (DHq-ROFHWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighted average (DHq-ROFHOWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighting geometric (DHq-ROFHOWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher hybrid average (DHq-ROFHHA) operator, and the dual hesitant q-rung orthopair fuzzy Hamacher hybrid geometric (DHq-ROFHHG) operator. The precious merits and some particular cases of above mentioned aggregation operators are briefly introduced. In the end, an actual application for scheme selection of construction project is provided to testify the proposed operators and deliver a comparative analysis.

Some q-Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment

The recently proposed q-rung picture fuzzy set (q-RPFSs) can describe complex fuzzy and uncertain information effectively. The Hamy mean (HM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this study, we extend HM to q-rung picture fuzzy environment, propose novel q-rung picture fuzzy aggregation operators, and demonstrate their application to multi-attribute group decision-making (MAGDM). First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of q-rung picture fuzzy numbers (q-RPFNs). Second, we propose some new aggregation operators of q-RPFNs based on the newly-developed operations, i.e., the q-rung picture fuzzy Dombi Hamy mean (q-RPFDHM) operator, the q-rung picture fuzzy Dombi weighted Hamy mean (q-RPFDWHM) operator, the q-rung picture fuzzy Dombi dual Hamy mean (q-RPFDDHM) operator, and the q-rung picture fuzzy Dombi weighted dual Hamy mean (q-RPFDWDHM) operator. Properties of these operators are also discussed. Third, a new q-rung picture fuzzy MAGDM method is proposed with the help of the proposed operators. Finally, a best project selection example is provided to demonstrate the practicality and effectiveness of the new method. The superiorities of the proposed method are illustrated through comparative analysis.

An Extended Picture Fuzzy VIKOR Approach for Sustainable Supplier Management and Its Application in the Beef Industry

Nowadays, sustainable supply chain management (SSCM) has received considerable attention because of strict government requirements and increased pressure from the public. In the SSCM, selecting suitable suppliers plays a significant role in improving the overall sustainability performance of a company. Therefore, this article aims to develop a modified VIKOR (in Serbian: VlseKriterijumska Optimizacija I Kompromisno Resenje) technique for sustainable supplier evaluation and selection, that uses ordered weighted distance operators in the aggregation of picture fuzzy information. Concretely, we first propose the picture fuzzy-ordered weighted standardized distance (PFOWSD) operator and the picture fuzzy Euclidean-ordered weighted standardized distance (PFEOWSD) operator, and extended them by using the hybrid average operator. Then, we develop a sustainable supplier selection approach by combining the picture fuzzy distance operators and the VIKOR method. The new approach can manipulate attitudinal character of the classical VIKOR method, so that a decision maker can take decisions according to his or her preference. Further, by using the PFOWSD operator, one can parametrize the VIKOR method from the maximum to the minimum result. Thus, the information obtained using the new sustainable supplier selection approach is much more complete. Finally, a practical case example in the beef supply chain is given to explain the proposed picture fuzzy-ordered weighted distance (PFOWD)-VIKOR model, and the results are compared with current relevant representative approaches to verify its feasibility and superiority.

Dry Bulk Carrier Investment Selection through a Dual Group Decision Fusing Mechanism in the Green Supply Chain

Uncertain linguistic variables and scoring evaluations are two important evaluation mechanisms in the decision making field. Sustainability requirements for ship investment lead to the complexity of influence factors and the decision making process. The uncertain linguistic assessment features a large amount of ambiguity and subjectivity, while the scoring evaluation features high precision and distinct gradations. This paper constructs a criteria system in the green supply chain and proposes a dual group decision fusing mechanism for integrating the linguistic variable and scoring evaluation into a unified evaluation term. A hierarchical cloud of linguistic variable terms is constructed based on scoring via a reverse cloud generator, and then, the ship investment linguistic terms are transformed into prospect values. In addition, the consistency and investment selection performance are measured after aggregating the individual decision matrices for group decision making. The empirical research results on the selection of dry bulk carriers for investment show that dual group decision fusing mechanisms could effectively improve the consistency, decision making efficiency, and accuracy of dry bulk ship investment choices and reduce the cost of feedback adjustment for group decisions. In comparison with the trapezoidal fuzzy and fuzzy TOPSIS methods of group decision making, the proposed method performs better when there are a large number of alternatives.