Fuzzy Multi-attribute Decision-making Method Research Articles

Assessment of polluted region using an integrated weighting approach and fuzzy VIKOR method

Air pollution exerts a profound impact on both public health and the natural environment. In India, festivals like Diwali also contaminate the air by releasing pollutants into the atmosphere. It is essential to identify the most polluted region by estimating these pollutants. Since air quality assessment involves multiple air pollutants, there may be inherent uncertainty associated with data. This study employs a fuzzy Multi Attribute Decision Making (MADM) framework fuzzy Analytical Hierarchy Process-Entropy-fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje (FAHP-Entropy-FVIKOR) to model the impact of air pollution as a decision-making problem to address the uncertainty and assess the air quality during the Diwali festival from 2019 to 2021 in Tamil Nadu, India. An integrated weighting approach is utilised to determine the weights of the air pollutants using a fuzzy Analytical Hierarchy Process and Entropy methods. Mainly, the fuzzy VIKOR approach is employed to rank the polluted regions. The validation of the proposed model is established through a comparative analysis using Spearman’s rank correlation with two other existing fuzzy MADM methods. Furthermore, a sensitivity analysis is conducted to evaluate the influence of priority weights and the interdependence of pollutants in determining regional rankings. The results conclude that a strong positive correlation is attained between the proposed and existing methods and the highest levels of air pollution during the festival period are observed in Gandhi Nagar (2019), Rayapuram (2020), T. Nagar, Sowcarpet and Triplicane (2021) in their respective years. These findings substantiate the consistency and effectiveness of the proposed approach.

The Practice and Application of Enterprise Leadership Strategic Management Based on Fuzzy Decision Model

Abstract This paper gives a pseudo metric between any two hesitation fuzzy elements based on the closeness of the hesitation fuzzy elements; based on the hesitation fuzzy pseudo metric, a hesitation fuzzy multi-attribute decision-making method based on the pseudo metric closeness is proposed. Understanding the level of strategic management ability and enterprise leaders’ ability level can be achieved by measuring the size of fuzzy weighted closeness. From the perspective of group consistency analysis, a hesitation fuzzy attribute weight optimization model based on group consistency index maximization is established, and a hesitation fuzzy multi-attribute decision-making method based on group consistency and grey correlation analysis is proposed in combination with grey correlation analysis. Enterprise leaders’ strategic management abilities are assessed during the application stage using the hesitation fuzzy multi-attribute decision-making method. Analyzing the relationship between the strategic stage and the match between different types of strategic styles of business leaders and business performance is done using cross-linkage. The analysis results show that the distance value between the comprehensive fuzzy assessment value of each level of the leader’s strategic management capability and the semantic variable of each assessment value is at least 0.052, which is consistent with the overall assessment results of the five experts on the leader’s strategic management capability. The match between the strategic style of the business leader and the strategic stage in which the enterprise is located has a significant interaction effect on the performance indicators of the enterprise P=0.007<0.01. The results verify the accuracy of the evaluation method of this paper and the existence of a correlation between the strategic leadership of the business leader and the performance of the enterprise.

Basic uncertainty information hesitant fuzzy multi-attribute decision-making method with credibility

This study addresses the inadequacy of the current quantitative calculation method for decision-maker credibility in hesitant fuzzy multi-attribute decision-making, where credibility is considered. To overcome this limitation, a novel quantitative calculation method for decision-maker credibility is proposed based on the principles of basic uncertainty information theory under a hesitant fuzzy environment. Furthermore, a credible-based hesitant fuzzy multi-attribute decision model is developed. Initially, the paper introduces the concept of a basic uncertainty hesitant fuzzy set by combining basic uncertainty information theory with hesitant fuzzy set theory, thereby enhancing the understanding of basic uncertainty information theory within the realm of non-interval fuzzy information. Building on this foundation, the method for determining the hesitant degree of each element in the basic uncertainty hesitant fuzzy set is provided, followed by the proposed quantitative calculation method for decision-maker’s credibility under the hesitant fuzzy environment, which addresses the lack of a quantitative approach for assessing expert credibility under such circumstances. Subsequently, an attribute weight assignment method is introduced, considering the decision-maker’s credibility, leading to the formulation of a basic uncertainty hesitant fuzzy multi-attribute decision model based on credibility. This model enhances existing hesitant fuzzy multi-attribute decision-making methods that take credibility into account. To validate the proposed approach, the study applies it to the selection of new energy vehicle battery suppliers. The results of the analysis using actual data and sensitivity analysis demonstrate that decision-maker credibility can be quantitatively determined using the proposed method. Additionally, the basic uncertainty hesitant fuzzy multi-attribute decision-making model based on credibility effectively aids in supplier selection. The feasibility and stability of this method are verified through the examination of risk appetite coefficient and hesitancy coefficient.

Generalized Orthopair Fuzzy Weighted Power Bonferroni Mean Operator and Its Application in Decision Making

The generalized orthopair fuzzy set is more favored by decision-makers and extensively utilized in areas like supply chain management, risk investment, and pattern recognition because it offers a broader decision information boundary than the intuitionistic fuzzy set and Pythagorean fuzzy set. This enables it to express fuzzy information more comprehensively and accurately in multi-attribute decision-making problems. To this end, this paper combines the ability of the power average (PA) operator to eliminate the impact of extreme values and the advantage of the Bonferroni mean (BMs,t) operator in reflecting the relationships between variables, then incorporates weight indicators for different attributes to define the generalized orthopair fuzzy weighted power Bonferroni mean operator. The effectiveness of this operator is demonstrated through aggregation laws for generalized orthopair fuzzy information. Subsequently, the desirable properties of this operator are discussed. Based on these findings, a novel generalized orthopair fuzzy multi-attribute decision-making method, with a correlation between attributes, is proposed. Lastly, an investment decision-making example illustrates the feasibility and superiority of this method.

The Probabilistic Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Cumulative Prospect Theory and Its Application

Addressing the complex issue of multi-attribute decision-making within a probabilistic dual hesitant fuzzy context, where attribute weights are unknown, a novel decision-making method based on cumulative prospect theory is proposed, named the probabilistic dual hesitant fuzzy multi-attribute decision-making method based on cumulative prospect theory. Firstly, a decision matrix is formulated, representing probabilistic dual hesitant fuzzy information. Secondly, according to the decision maker’s authentic preference and non-membership information sensitivity, a comprehensive score function suitable for probabilistic dual hesitant fuzzy elements is proposed. The attribute weights are then determined using the entropy method. Next, the value function and decision weight function from the cumulative prospect theory are employed to compute the cumulative prospect value attributed to each available scheme. In addition, a cumulative prospect matrix is constructed, enabling the establishment of scheme rankings based on the comprehensive cumulative prospect value. Finally, the analysis of specific cases and a comparative assessment of methods pertaining to the selection of emergency response schemes collectively demonstrate the rationality and efficacy of the decision-making method presented in this study.

Interval type-2 trapezoidal fuzzy multi-attribute decision-making method and its application to the corporate investment selection

Interval type-2 trapezoidal fuzzy (IT2TrF) number is a powerful tool to depict fuzzy information. Information measures methods have received more and more attention in recent years as they play an important role in decision-making theory. A new multi-attribute decision-making (MADM) method supported by IT2TrF information measures is investigated in this paper under the IT2TrF information environment. Firstly, three axiomatic definitions of IT2TrF information measures are introduced, which include information entropy, similarity measure and cross-entropy. Secondly, with the help of the exponential function, we formulate some information measure formulas, which are followed by the proofs that the exponential entropy, exponential similarity measure and exponential cross-entropy fit the three axiomatic definitions. Subsequently, a novel IT2TrF MADM method is designed, in which the IT2TrF exponential entropy and cross-entropy are utilized to generate the attribute weights, the IT2TrF exponential similarity measure is employed to obtain the closeness degree of the ideal solution and derive the most satisfying solution. Lastly, we provide a numerical example of corporate investment to demonstrate the applicability and feasibility of the proposed MADM method. The robustness and merits of the developed MADM method are highlighted by the comparative analysis.

A probabilistic dual hesitant fuzzy multi-attribute decision-making method based on entropy and cross-entropy

A probabilistic dual hesitant fuzzy multi-attribute decision-making method based on entropy and cross-entropy

Exponential information measures-driven Pythagorean fuzzy MADM method and its application to new energy battery supplier evaluation problem

Under the Pythagorean fuzzy environment, this paper presents a multi-attribute decision-making (MADM) model based on exponential entropy measure and exponential similarity measure to evaluate new energy battery supplier’s performance. In this method, the notion of Pythagorean fuzzy linguistic sets (PFLSs) is first introduced by combining the linguistic fuzzy sets (LFSs) and the Pythagorean fuzzy sets (PFSs). Then, the axiomatic definitions of Pythagorean fuzzy entropy and Pythagorean fuzzy similarity measure are developed to measure the degree of uncertainty and similarity between two Pythagorean fuzzy linguistic values (PFLVs). The PFLVs can be expressed by the linguistic membership degree (LMD) and linguistic non-membership degree (LNMD). In addition, we construct two new information measure formulas based on exponential function. Through a series of proofs, we verify that they satisfy the axiomatic conditions of entropy and similarity measure of Pythagorean fuzzy language respectively. On this basis, we research the relationship between the two information measures. Finally, we present a novel Pythagorean fuzzy linguistic MADM model. An example for evaluating performance of new energy battery supplier is given to explain the effectiveness of the newly-developed approach. The stability and validity of the newly-developed approach is performed by sensitivity analysis and comparative analysis.

Evaluation of Geo-Environment Carrying Capacity Based on Intuitionistic Fuzzy TOPSIS Method: A Case Study of China

The resource environment is a fundamental prerequisite for the construction of ecological civilization and the realization of sustainable development goals. It is also a core guarantee for human production activities. Conducting an evaluation of regional geo-environmental carrying capacity has significant practical importance for achieving sustainable development in the region. However, the existing evaluation methods for geo-environmental carrying capacity fail to effectively integrate multi-source data, resulting in an incomplete reflection of the level of regional geological carrying capacity. To address this issue, this study introduces the intuitionistic fuzzy multi-attribute decision-making method into the geo-environmental carrying capacity evaluation, according to the unique topographic and geomorphological characteristics of the region. A complete analysis framework is established, which integrates the intuitionistic fuzzy and TOPSIS models to classify the geo-environmental carrying capacity evaluation into five grades: high, relatively high, medium, relatively poor, and poor. Using Meishan, China as an example, the region is divided into 33 geomorphological units based on its geographical features. The results show that: (a) the percentage of natural units with high carrying capacity is 17.27%, that of relatively high natural units is 14.07%, that of medium natural units is 31.70%, that of relatively poor natural units is 27.51%, and that of poor natural units is 9.45%; (b) the geo-environmental carrying capacity exhibits spatial differences and uneven distribution. Furthermore, the average annual rainfall and degree of karst development are the main factors affecting the geo-environmental carrying capacity. These research results and findings can provide technical support for urban planning, regional sustainable development, and ecological environmental protection.

RETRACTED: Theory and method for evaluating the importance of college course teaching for future education: From virtual reality to metaverse

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219329.

RETRACTED: Fuzzy theory and method for evaluating the importance of college course teaching for future education

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219329.

A Green Supply Chain Member Selection Method Considering Green Innovation Capability in a Hesitant Fuzzy Environment

The purpose of this paper is to propose an improved hesitation fuzzy multi-attribute decision-making method to realize green supply chain member selection under green innovation vision. The method uses hesitation fuzzy sets to express decision information of decision makers, takes green innovation capability as the evaluation perspective, and selects green innovation input, synergy of subjects in green supply chain, green innovation output capability, institutional innovation capability of enterprises in green supply chain, and green innovation sustainability as the indexes to evaluate the green innovation capability of enterprises. The multi-attribute decision method proposed in this paper takes into account the shortcomings of the original hesitant fuzzy multi-attribute decision method considering attribute weight optimization in the determination of attribute weights and scheme ranking, then proposes a three-point estimation method for scheme ranking and optimizes the attribute weights by quantifying the balance coefficients of the original decision method. Finally, an example is used to verify the rationality and effectiveness of the proposed method, and a comparison with the original method is made to highlight the advantages of this paper’s method. This paper provides a certain theoretical basis for the selection of members in green supply chains, which helps the selection of members in green supply chains and provides some insight for similar hesitant fuzzy multi-attribute decision-making problems in other fields. In future research, the method proposed in this paper can be considered to combine with probabilistic hesitant fuzzy sets and some other fuzzy sets for method extensions to solve multi-attribute decision-making problems.

A multi-attribute decision-making method for the location selection of emergency rescue centers based on improved cumulative prospect theory under the background of ecological sustainable development

The location decision of the emergency rescue center, as a necessary link in the early stage to ensure the smooth development of emergency management, has become increasingly important. This paper analyzes the research theories and methods of location problem at home and abroad. By considering the decision-making psychological behavior of decision-makers, based on the idea of cumulative prospect theory, combined with the Pythagorean fuzzy multi-attribute evaluation method, this paper proposes a Pythagorean fuzzy multi-attribute decision-making evaluation method based on improved cumulative prospect theory. This method is to sort the results of each decision-making scheme by calculating the comprehensive cumulative prospect value. Based on the utility curve improved cumulative prospect theory, the research first depicts the psychological behavior characteristics of various decision-making groups under different risk preferences, and then designs a distance measurement method based on the geometric center of Pythagorean fuzzy right triangle. The main core of the distance measurement method is to convert Pythagorean fuzzy numbers into Pythagorean fuzzy right triangles. In the aspect of attribute weight assignment, a subjective and objective weighting method based on the combination of value function and deviation method of improved cumulative prospect theory is proposed. Finally, the Pythagorean fuzzy multi-attribute decision-making method based on the improved cumulative prospect theory is realized through the selection of reference objects, the calculation of value function value, weight function value and cumulative prospect value. This study takes the site selection of emergency rescue center in the construction period of Ya’an Linzhi Section of Sichuan Tibet Railway in China as an example, and proposes 10 emergency rescue centers as alternatives. Considering the different preferences of decision-makers, the improved decision-making method proposed in this paper is used to obtain the most optimal site selection scheme under different decision-making preferences.

A multi-attribute decision-making method for the location selection of emergency rescue centers based on improved cumulative prospect theory under the background of ecological sustainable development

This research proposes a Pythagorean fuzzy multi-attribute decision-making evaluation method based on the improved cumulative prospect theory. The method ranks the decision-making results by calculating the comprehensive cumulative prospect value. Firstly, the research improves the cumulative prospect theory based on the utility curve, and describes the psychological and behavioral characteristics of various decision-making groups with different risk preferences. Then, a distance measure method based on the geometric center of the Pythagorean fuzzy right triangle is designed. The main core of the distance measure method is that it converts the Pythagorean fuzzy number into a Pythagorean fuzzy right triangle. In terms of attribute weighting, this research proposes a subjective and objective weighting method based on the combination of value function and deviation method of improved cumulative prospect theory. Finally, the Pythagorean fuzzy multi-attribute decision-making method based on the improved cumulative prospect theory is realized through the selection of reference object, the calculation of value function value, weight function value and cumulative prospect value. The results analysis and the comparison with other methods verify the effectiveness and advancement of the proposed decision-making method, especially that the proposed method has good applicability for the decision-making cases where the attribute value is Pythagorean fuzzy number, the attribute weight is unknown, and the psychological behavior of decision makers cannot be reflected.

A novel intuitionistic fuzzy goal programming method for heterogeneous MADM with application to regional green manufacturing level evaluation under multi-source information

The existed regional green manufacturing level assessment methods pay little attention to the multi-source information such as the expert’s psychological preference information, the preference information among regions, the heterogeneous information of regions on attributes and the interactions information between attributes at the same time, which is as a heterogeneous multi-attribute decision making (MADM) problems. A novel intuitionistic fuzzy goal programming is proposed for HMADM problems under multi-source information. The Choquet integral-based relative ratio is proposed on the basis of the Choquet integral measure. It is far away from the negative-ideal solution (NIS) and closeness to the positive-ideal solution (NIS) simultaneously with the interactions between attributes. Hereby the consistency and inconsistency indices with expert’s hesitation degrees are defined, the attribute weights are solved by using the developed intuitionistic fuzzy goal programming models with the optimistic, pessimistic and mixed methods. The Choquet integral-based relative ratios of alternatives can be calculated to generate their ranking orders. Finally, a regional green manufacturing level assessment example and compared with existed methods show that the superiority and validity of the proposed method, which improves the intuitionistic fuzzy goal programming methods, LINMAP methods and MADM methods with the interactions between attributes.

Probabilistic hesitant fuzzy multi-attribute decision-making method based on improved distance measurement

In order to solve the problem of multi-attribute decision-making with unknown weights under probabilistic hesitant fuzzy information, considering the shortcomings of the existing probabilistic hesitant fuzzy distance measure, such as weak distinguishing ability, a probabilistic hesitant fuzzy multi-attribute decision-making method based on improved distance measures is proposed. Firstly, the hesitancy degree of probabilistic hesitant fuzzy element and the improved difference measure of probabilistic hesitant fuzzy element are defined, and an improved probabilistic hesitant fuzzy distance measure based on hesitancy degree, incompleteness degree and improved difference measure is proposed. Secondly, based on the improved distance measure, a mathematical programming model with the goal of minimizing the relative approach degree is con-structed to determine the attribute weights of evaluation indexes in multi-attribute decision making problems. Using it as a base, a new probabilistic hesitant fuzzy multi-attribute decision-making method is proposed by combining the improved probabilistic hesitant fuzzy distance measure with the compromise ratio method. Finally, the proposed method is applied to the problem of green supplier selection, and the feasibility and effectiveness of the proposed method are verified by case analysis and comparison with other methods.

Feasibility evaluation of virtual power plants participating in rural Energy Internet under zoning and stratification using prospect theory

In the context of the continuous promotion of Henan Lankao Energy Internet, there are problems where new energy cannot be effectively utilized, and the utilization efficiency is not high. A virtual power plant can solve this problem by optimizing the output of distributed generation to participate in the Energy Internet. Therefore, this paper evaluates the feasibility of virtual power plants participating in the Energy Internet under layered typical application scenarios. Firstly, from the perspective of horizontal zoning and vertical stratification, the typical application scenario of a virtual power plant participating in the rural Energy Internet is designed. Then, considering multiple uncertainties, a business model of the virtual power plant participating in the rural Energy Internet in different stages is designed. Furthermore, the probability hesitation fuzzy multi-attribute decision-making method is used to study the feasibility of virtual power plant participating in rural Energy Internet.

Health, safety, and environmental failure evaluation by hybridizing fuzzy multi-attribute decision-making methods for maritime scrubber systems

Many shipping companies have started using scrubbers in their fleet to eliminate sulfur emissions from ships, per IMO (International Maritime Organization) rules. Before and during the scrubbers' selection, the scrubbers' operational failures have also started to appear and cause serious concerns. In this study, classified scrubber types are explained and open type, closed type, and hybrid scrubber systems are evaluated. To contribute to this gap in the literature, scrubber failures were identified, five experts with different perspectives were consulted, and the most common and critical malfunctions were evaluated with the fuzzy best-worst method (F-BWM) and fuzzy technique for order preference by similarity to an ideal solution (F-TOPSIS). F-BWM was used to determine the importance weights of the risk parameters used in evaluating failures since it provides fewer comparisons among pairwise comparison-based decision-making methods and a more consistent judgment in the evaluation. F-TOPSIS, on the other hand, was used to determine the final priority scores of the scrubber failures, taking into account the risk parameter weights obtained in the first stage. It has been preferred due to its easy to useness and based on its closeness to the ideal solution and applicability to risk and failure analysis problems. Considering all different systems in general, important issues such as collection efficiency, sulfur emission problem, abrasion, leakages, pump failures, heat exchanger failures, air fan sealing failures, sensors and failures in monitoring the whole system have been investigated. Results show that too high axial velocity for separator and flooded separator, too high solids concentration in recirculation liquid (SF2), piping leakages (SF5), poor quality or inappropriate consumables and chemicals (SF11), and feed circulation pump problems (SF6) are found to be the most important problems among thirteen failures.

Interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering risk preference of decision-makers and its application

An improved interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering the risk preference of decision-makers is proposed to solve the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy numbers and the condition that the attribute weight information is completely unknown. Firstly, the decision-maker weight of each attribute is determined by combining similarity and proximity. In order to consider the influence of the decision-maker's risk preference on the decision result and avoid the asymptotic behavior of interval-valued intuitionistic fuzzy matrix, the risk aversion coefficient of the decision-maker is introduced and combined with the determined decision-maker's weight aggregation to form a group decision matrix. Then, the information of group decision matrix is mined, and the interval-valued intuitionistic fuzzy entropy is used to determine the attribute weight and relative weight. Based on the interval-valued intuitionistic fuzzy distance measure formula and the TODIM method, the overall superiority of each scheme relative to other schemes is obtained by calculating the superiority between schemes, and the optimal scheme is determined by comparing and sequencing. Finally, the rationality and effectiveness of the proposed method are verified by an example of mechanical assembly supplier selection decision.

Comprehensive Evaluation of Basic Public Health Service Quality Based on TOPSIS Improved Dynamic Triangle Fuzzy-- A Case Study of Zhengzhou

To comprehensively evaluate the development of basic public health services in Zhengzhou, and to provide data reference for relevant departments to adjust their future decisions. TOPSIS was adopted dynamic triangulation fuzzy multi-attribute decision-making method to comprehensively evaluate the quality of basic public health service in Zhengzhou. After comprehensive evaluation, the top three places of basic public health service quality were Zhongmou in 2016, Zhongmou in 2015 and Erqi in 2016, and the bottom three places were Zhongyuan in 2011, Gangqu in 2011 and Gangqu in 2012. This method comprehensively considers the growth and difference degree of evaluation indexes in different years and regions, and selects the best schemes according to the comprehensive evaluation value. Compared with other methods, this method objectively considers the difference degree of attribute value, growth and change as well as the different psychological preferences of decision makers, and finally obtains scientific and reasonable ranking results, which can effectively meet the actual decision-making needs.