Some intuitionistic fuzzy power Bonferroni mean operators in the framework of Dempster–Shafer theory and their application to multicriteria decision making

A data-driven group emergency decision-making method based on interval-valued intuitionistic hesitant fuzzy sets and its application in COVID-19 pandemic

The outbreak of Corona Virus Disease 2019 (COVID-19) makes people more concerned about the validity and timeliness of emergency decision making. When an emergency occurs, it is difficult for decision makers (DMs) to give accurate assessment information in the early stage due to the urgency of time, the incompleteness of information, and the limitations of DMs’ cognition and knowledge. Hence, we use interval-valued intuitionistic hesitant fuzzy sets rather than exact numbers to better characterize the fuzziness and uncertainty of emergencies. In addition, the Internet has become a major platform for the public to express their opinions or concerns, so we can collect the user-generated content on social media to help DMs determine appropriate emergency decision-making criteria which are the premise and basis of scientific decisions. However, there is likely to be some correlation between the obtained criteria. To this end, we first extend the Bonferroni mean (BM) operator to the interval-valued intuitionistic hesitant fuzzy environment, and propose three interval-valued intuitionistic hesitant fuzzy BM operators to capture the interrelation of fuzzy input variables, including an interval-valued intuitionistic hesitant fuzzy BM operator, a simplified interval-valued intuitionistic hesitant fuzzy BM operator, and a simplified interval-valued intuitionistic hesitant fuzzy weighted BM (SIVIHFWBM) operator. Then, a new group emergency decision-making method based on the SIVIHFWBM operator and social media data is proposed, and the specific steps of ranking all emergency plans are put forward. Moreover, our method is applied to evaluate emergency plans for the prevention and control of COVID-19. Finally, the effectiveness and feasibility of the method are verified by the sensitivity analysis, validity test, and comparative analysis.

Logarithmic Negation of Basic Probability Assignment and Its Application in Target Recognition

The negation of probability distribution is a new perspective from which to obtain information. Dempster–Shafer (D–S) evidence theory, as an extension of possibility theory, is widely used in decision-making-level fusion. However, how to reasonably construct the negation of basic probability assignment (BPA) in D–S evidence theory is an open issue. This paper proposes a new negation of BPA, logarithmic negation. It solves the shortcoming of Yin’s negation that maximal entropy cannot be obtained when there are only two focal elements in the BPA. At the same time, the logarithmic negation of BPA inherits the good properties of the negation of probability, such as order reversal, involution, convergence, degeneration, and maximal entropy. Logarithmic negation degenerates into Gao’s negation when the values of the elements all approach 0. In addition, the data fusion method based on logarithmic negation has a higher belief value of the correct target in target recognition application.

Power Bonferroni mean operators under complex pythagorean fuzzy settings and their applications in decision-making problems

Bonferroni means (BM) operator is the extended form of the arithmetic mean operator, used for simplifying non-dominant and non-feasible problems diagnosed in genuine life scenarios. A lot of aggregation operators are the specific parts of the BM operators under the consideration of different values of parameters which are the main parts of the BM operators. In the presence of the BM operator and a very well-known conception in the scenario of fuzzy set, called complex Pythagorean fuzzy (CPF) setting, the objective of this scenario is to diagnose the CPF power BM (CPFPBM) operator and utilize their beneficial results with important properties. Moreover, a multi-attribute decision-making (MADM) technique is evaluated in the presence of invented operators for CPF settings. In the last of this study, we diagnosed the superiority and efficiency of the invented works with the help of sensitive analysis and graphical illustrations to enhance the gap of the research works.

A Novel Interval-Valued q-Rung Dual Hesitant Linguistic Multi-Attribute Decision-Making Method Based on Linguistic Scale Functions and Power Hamy Mean

The interval-valued q-rung dual hesitant linguistic (IVq-RDHL) sets are widely used to express the evaluation information of decision makers (DMs) in the process of multi-attribute decision-making (MADM). However, the existing MADM method based on IVq-RDHL sets has obvious shortcomings, i.e., the operational rules of IVq-RDHL values have some weaknesses and the existing IVq-RDHL aggregation operators are incapable of dealing with some special decision-making situations. In this paper, by analyzing these drawbacks, we then propose the operations for IVq-RDHL values based on a linguistic scale function. After it, we present novel aggregation operators for IVq-RDHL values based on the power Hamy mean and introduce the IVq-RDHL power Hamy mean operator and IVq-RDHL power weighted Hamy mean operator. Properties of these new aggregation operators are also studied. Based on these foundations, we further put forward a MADM method, which is more reasonable and rational than the existing one. Our proposed method not only provides a series of more reasonable operational laws but also offers a more powerful manner to fuse attribute values. Finally, we apply the new MADM method to solve the practical problem of patient admission evaluation. The performance and advantages of our method are illustrated in the comparative analysis with other methods.

A Novel q-Rung Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Entropy Weights

In this paper, a new multiple attribute decision-making (MADM) method under q-rung dual hesitant fuzzy environment from the perspective of aggregation operators is proposed. First, some aggregation operators are proposed for fusing q-rung dual hesitant fuzzy sets (q-RDHFSs). Afterwards, we present properties and some desirable special cases of the new operators. Second, a new entropy measure for q-RDHFSs is developed, which defines a method to calculate the weight information of aggregated q-rung dual hesitant fuzzy elements. Third, a novel MADM method is introduced to deal with decision-making problems under q-RDHFSs environment, wherein weight information is completely unknown. Finally, we present numerical example to show the effectiveness and performance of the new method. Additionally, comparative analysis is conducted to prove the superiorities of our new MADM method. This study mainly contributes to a novel method, which can help decision makes select optimal alternatives when dealing with practical MADM problems.

A Decision-Making Approach Based on New Aggregation Operators under Fermatean Fuzzy Linguistic Information Environment

Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function (LSF) is the better way to consider the semantics of the linguistic terms during the evaluation process. It is worth noting that the existing operational laws and aggregation operators (AOs) for Fermatean fuzzy linguistic numbers (FFLNs) are not valid in many situations, which can generate errors in real-life applications. The present study aims to define new robust operational laws and AOs under Fermatean fuzzy linguistic environment. To do so, first, we define some new modified operational laws for FFLNs based on LSF and prove some important mathematical properties of them. Next, the work defines several new AOs, namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under Fermatean fuzzy linguistic environment. Several properties of these AOs are investigated in detail. Further, based on the proposed AOs, a new decision-making approach with Fermatean fuzzy linguistic information is developed to solve group decision-making problems with multiple attributes. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs. Compared to the existing methods, the salient features of the developed approach are (1) it can solve decision-making problems with qualitative information data using FFLNs; (2) It can consider the attitudinal character of the decision-makers during the solution process; (3) It has a solid ability to distinguish the optimal alternative.

Probability multi-valued neutrosophic ELECTRE method for multi-criteria group decision-making

Probability multi-valued neutrosophic sets (PMVNSs) can better describe the incomplete and indeterminate evaluation information, and the ELECTRE method can rank the alternatives in the light of the outranking relations among criteria. To combine their advantages, this paper introduces an extended ELECTRE method to address multi-criteria group decision-making (MCGDM) problems with the information of PMVNSs. Firstly, we introduce the definitions of PMVNSs and the classical ELECTRE method, discuss the ELECTRE-based outranking relations for PMVNSs and analyze some properties of them. Furthermore, the probability multi-valued neutrosophic ELECTRE method is developed to address MCGDM problems based on the proposed distance measure and outranking relations for PMVNSs. Finally, a typical example for logistics outsourcing provider selection is devoted to demonstrate the feasibility of the proposed approach. Moreover, the same example-based comparisons with other existing methods are carried out, the results show our proposed approach outperforms the existing methods in solving the MCGDM problems with PMVNSs.

Novel Multi-Criteria Intuitionistic Fuzzy SWARA–COPRAS Approach for Sustainability Evaluation of the Bioenergy Production Process

Bioenergy is a kind of renewable energy that can potentially contribute to a broad spectrum of economic, environmental, and societal objectives and aid sustainable development. The assessment, management, and monitoring of the diverse bioenergy production technology alternatives are complex in nature and deliver different benefits due to the lack of precise and comprehensive data. Selection of an optimal bioenergy production technology (BPT) alternative is considered a complex multi-criteria decision-making (MCDM) problem that involves many incompatible tangible and intangible as well as qualitative and quantitative criteria. The procedure of defining and evaluating the weights of the criteria is an important concern for decision experts because the assessment and the final selection of the BPT alternative are carried out on the basis of the defined set of criteria. Intuitionistic fuzzy sets (IFSs) have received considerable attention due to their ability to handle the imprecision and vagueness that can arise in real-life situations. Thus, this study presents an integrated approach, based on stepwise weight assessment ratio analysis (SWARA) and complex proportional assessment (COPRAS) approaches, for the selection of BPT alternatives. In the integrated framework, criteria weights are determined by the SWARA procedure, and the ranking of BPT alternatives is decided by the COPRAS method using IFSs. The criteria weights evaluated by this approach involve the imprecision of experts’ opinions, which makes them more comprehensible. To express the efficiency and applicability of the integrated framework, a BPT selection problem is presented using IFSs. In addition, this study involved sensitivity analysis with respect to various sets of criteria weights to reveal the strength of the developed approach. The sensitivity analysis outcomes indicate that the agricultural and municipal waste of biogas (S3) consistently secures the highest rank, despite how the criteria weights vary. Finally, a comparative study is discussed to analyze the validity of the obtained result. The findings of this study confirm that the proposed framework is more useful than and consistent with previously developed methods using the IFSs environment.

Grey Fuzzy Multiple Attribute Group Decision-Making Methods Based on Interval Grey Triangular Fuzzy Numbers Partitioned Bonferroni Mean

Considering the characteristics such as fuzziness and greyness in real decision-making, the interval grey triangular fuzzy number is easy to express fuzzy and grey information simultaneously. And the partition Bonferroni mean (PBM) operator has the ability to calculate the interrelationship among the attributes. In this study, we combine the PBM operator into the interval grey triangular fuzzy numbers to increase the applicable scope of PBM operators. First of all, we introduced the definition, properties, expectation, and distance of the interval grey triangular fuzzy numbers, and then we proposed the interval grey triangular fuzzy numbers partitioned Bonferroni mean (IGTFPBM) and the interval grey triangular fuzzy numbers weighted partitioned Bonferroni mean (IGTFWPBM), the adjusting of parameters in the operator can bring symmetry effect to the evaluation results. After that, a novel method based on IGTFWPBM is developed for solving the grey fuzzy multiple attribute group decision-making (GFMAGDM) problems. Finally, we give an example to expound the practicability and superiority of this method.

Novel Multiple Attribute Group Decision-Making Methods Based on Linguistic Intuitionistic Fuzzy Information

As an effective technique to qualitatively depict assessment information, a linguistic intuitionistic fuzzy number (LIFN) is more appropriate to portray vagueness and indeterminacy in actual situations than intuitionistic fuzzy number (IFN). The prominent feature of a Muirhead mean (MM) operator is that it has the powerful ability to capture the correlations between any input-data and MM operator covers other common operators by assigning the different parameter vectors. In the article, we first analyze the limitations of the existing ranking approaches of LIFN and propose a novel ranking approach to surmount these limitations. Secondly, we propound several novel MM operators to fuse linguistic intuitionistic fuzzy (LIF) information, such as the LIF Muirhead mean (LIFMM) operator, the weighted LIF Muirhead mean (WLIFMM) operator and their dual operators, the LIFDMM operator and the WLIFDMM operator. Subsequently, we discuss several desirable properties along with exceptional cases of them. Moreover, two novel multiple attribute group decision-making approaches are developed based upon these operators. Ultimately, the effectuality and practicability of the propounded methods are validated through dealing with a global supplier selection issue, and the comparative analysis and the merits of the presented approaches are demonstrated by comparing them with existing approaches.

The Evaluation Method of Low-Carbon Scenic Spots by Combining IBWM with B-DST and VIKOR in Fuzzy Environment

With the concept of sustainability gaining popularity, low-carbon tourism has been widely considered. In this paper, a multicriteria group decision making (MCGDM) process based on an uncertain environment is proposed to study the evaluation problem of low-carbon scenic spots (LSSs). In order to minimize the influence of subjective and objective factors, the traditional Vlse Kriterjumska Optimizacija I Kompromisno Resenje (VIKOR) method is expanded, using the improved best and worst method (IBWM) and Bayes approximation method, based on Dempster-Shafer Theory (B-DST). First, in order to make the evaluation process more professional, a number of evaluation criteria are established as effective systems, followed by the use of triangular intuitionistic fuzzy numbers (TIFNs) to evaluate alternatives of LSSs. Next, according to the evaluation results, the weights of the criteria are determined by the IBWM method, and the weights of the expert panels (Eps) are determined by B-DST. Finally, a weighted averaging algorithm of TIFN is used to integrate the above results to expand the traditional VIKOR and obtain the optimal LSS. The applicability of this method is proven by example calculation. The main conclusions are as follows: tourist facilities and the eco-environment are the two most important factors influencing the choice of LSSs. Meanwhile, the roles of management and participant attitudes in LSS evaluations cannot be ignored.