Fuzzy Comparison Research Articles

Fuzzy comparison of drought vulnerability based on the analytical hierarchy process

The vulnerability represents the level to which any ecosystem experiences impairment due to natural distress. One such distress is drought, a prolonged phase of deficient rainfall that causes the depletion of water resources. The possibility of the influences of drought principally depends on the vulnerability of the affected area. The predominantly arid climate of Pakistan and the dependence of its economy on agriculture make it vulnerable to climate change. Rahim Yar Khan and Tharparkar have similar environmental conditions, but Tharparkar experiences more droughts. Vulnerability factors observed by the two districts among the regions are different even with similar climate conditions. The system vulnerability to drought was observed for two districts by using the analytical hierarchy process (AHP) and drought vulnerability index (DVI). The drought vulnerability index (DVI) was used to assess the meteorological, agricultural, hydrological, and socio-economic indicators to build the hierarchy for these inconsistence factors and evaluate the most vulnerable and affecting cause among the meteorological, agricultural, hydrological, and socio-economic indicators. The selected measures specify the hypotheses and the relativity of the indicators to the overall vulnerability of the system. The evaluated weights for each variable are derived from the analytical hierarchy process by comparing the variables of the selected indicators. Due to different meteorological, agricultural, and socio-economic conditions, the weights for the DVI were not the same in both study districts, i.e., Rahim Yar Khan and Tharparkar. The classification of vulnerability depending upon the drought vulnerability index with AHP suggests that the DV indexation is favorable in assessing the regional drought vulnerability. The drought vulnerability assessment of Tharparkar indicates that Tharparkar is highly vulnerable to drought, i.e., DVI = 0.066, as it is highly dependent on irrigation resources for its agriculture and livestock. The unavailability of hydrological resources has increased the drought vulnerability of the Tharparkar, which corresponds to a high level of agricultural damage due to droughts. However, the district of Rahim Yar Khan with developed irrigation resources has a lower drought vulnerability index (DVI = 0.011). It is necessary for Tharparkar to establish countermeasures to mitigate the drought vulnerability through the development of water resources. Future studies are needed to be focused on more indicators for assessing particular drought vulnerability issues in order to reduce the drought vulnerability of Tharparkar.

On fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic

In this paper we study some fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic. The definition of the order comes from the extension principle for interval order: a>b iff a−b>0 and from measurement sciences. In measurement sciences the order is given by a comparator whose operation is based on empirical determination of the difference of two input signals. Fuzzy comparison based on fuzzy sets subtraction is considered as an extension of substraction operation, namely a fuzzy set B is greater than a fuzzy set A if B−A is greater than zero in fuzzy arithmetic. In the paper we show that this fuzzy order is irreflexive, transitive, asymmetric and compact, subhomothetic, Archimedean and semi-Ferrers. Our idea refers to the work of M. K. Urbański (Modeling the measurement in algebraic fuzzy structures, Warsaw 2003, in polish) and to the fundamental problems in the measurement theory.

An [formula omitted]-cut intervals based Fuzzy Best–Worst Method for Multi-Criteria Decision-Making

To address ambiguity arising from linguistic decision judgments, Guo and Zhao introduced a model of the well-known Multi-Criteria Decision-Making (MCDM) method, Best-Worst Method (BWM), using fuzzy sets, known as Fuzzy Best–Worst Method (FBWM). Despite its versatility, FBWM has limitations, such as criteria-weights being independent of fuzzy comparison values’ shape and reliance on approximate fuzzy arithmetic operations. In response to these limitations, we introduce a novel model of Fuzzy Best–Worst Method based on α-cut intervals. In this model, the calculation of optimal weights involves formulating an optimization problem that utilizes exact fuzzy arithmetic operations defined in terms of α-cut intervals. This approach aims to optimize the entire shape of fuzzy comparison values simultaneously. However, it turns out that, although we have proven the existence of optimal solution for this problem, solving it proves to be challenging. To resolve this issue, we approximate optimal weight set(s) using triangular fuzzy weight sets and assess the Error of Approximation (EA). The approximate weight set with the desired EA is then defuzzified to obtain a crisp weight set. In situations where there are multiple approximate weight sets with the same EA, interval-weights are calculated. Following that, we establish the necessary conditions for a Fuzzy Pairwise Comparison System (FPCS) to be consistent. Using these conditions, we calculate a lower bound of the Consistency Index (CI), providing a measure of the accuracy of weights. Finally, we discuss numerical examples and a real-world scenario, ranking of risk factors in supply chain 4.0, to validate the effectiveness of the proposed model.

Efficient fuzzy multi-criteria decision-making for optimal college location selection: A comparative study of min–max fuzzy TOPSIS approach

Ranking fuzzy values is often essential in fuzzy multi-criteria decision-making (FMCDM) systems since it is established on the comparison of hazy data pairs, even though the comparison needs temporal complexity. Then to provide a fuzzy MCDM approach under min–max operations for avoiding the fuzzy comparison. By using fuzzy TOPSIS’s min and max operations, the suggested method produces two positive and negative ideal solutions of each alternative. Here, before discussing the effectiveness of the matrices between the alternatives, first to analyze the weighted strength and weakness indices from both positive and negative indices. The results of the method have been described using a straightforward case study of a proper location for creating a college. The best location can be identified using this method based on various criteria. The outcomes are also compared with the suggested method for its effectiveness. Additionally, this problem analyzes the fuzzy TOPSIS approach in an interval-valued number for greater efficiency.

A Novel Fuzzy Best-Worst Multicriteria Decision-Making Method Based on the Dual Interval Algorithm for Environmental Decision Support Systems

Considering the double uncertainty caused by the ambiguity of statistical data and the ambiguity produced by the subjective assessment of decision makers, the crisp values of criteria may be insufficient to model the multi-criteria decision-making (MCDM) problem in the real world. This paper proposes a fuzzy best-worst method (FBWM) based on a dual-interval solution algorithm to extend the best-worst method (the most recent MCDM method) to fuzzy environments. The reference comparisons for the best criteria and for the worst criteria are represented by fuzzy numbers. Then, according to the BWM method, a nonlinear constrained optimization problem with fuzzy parameters is formulated. We decompose the membership function in fuzzy numbers into several interval numbers of special form and solve the aforementioned fuzzy BWM problem by compound interval algorithm to obtain fuzzy weights of different criteria. Meanwhile, an integral type-reduced method is proposed for determining the fuzzy consistency ratio in order to assess the reliability of the FBWM results. The viability of the new algorithm to expand the BWM method into fuzzy environments has been validated through three numerical examples. In contrast to the existing FBWM method, the proposed method avoids the arithmetic operation between fuzzy numbers during the solution process, directly transfers the uncertain information in the membership function corresponding to the fuzzy comparison vector to the result, and generates fuzzy weight value, which indicates that the proposed algorithm is able to obtain accurate BWM results in fuzzy environments. The results of the study provide new solution ideas for multi-criteria optimization problems under uncertainty.

Fuzzy optimisation based cricket talent identification

In this study, we proposed a cricket talent identification model based on fuzzy optimization that employs the fuzzy analytical hierarchy process (FAHP) and particle swarm optimization (PSO). To evaluate the performance of the model, we used a primary dataset (n = 56) collected from four different schools in J&K UT, India. Our model demonstrated high accuracy, precision, and recall with an accuracy of 92.8%, precision of 96%, and recall of 88%. The model also achieved a low miss rate of 11% and an F1-score of 92.3%. To the best of our knowledge, this is the first attempt to identify cricket talent using this methodology, which overcomes many limitations of conventional AHP-based models. By deriving an exact priority vector from the fuzzy comparison matrix for the criteria, our model eliminates the need for further procedures of defuzzification, making it more efficient and accurate. A comparative analysis of results gained from using Gaussian fuzzy numbers is also provided. Our study demonstrates the feasibility and potential of using fuzzy optimization techniques for cricket talent identification.

Fuzzy analytic hierarchy process for pentagonal fuzzy numbers and its application in sustainable supplier selection

Different fuzzy analytic hierarchy process (FAHP) methods are typically developed for conventional fuzzy numbers (FNs), mainly triangular and trapezoidal FNs. The ascending and descending parts of triangular and trapezoidal membership functions (MFs) are straight lines. Therefore, if the value of a member increases by the same values, its membership degrees in ascending (descending) part increase (decrease) equally. These MFs do not necessarily reflect the experts' preferences. Consider two different cases; in the first one, the product quality of supplier A compared to supplier B increases from 2 to 3 times, and in the second case, this quality increases from 8 to 9 times. Triangular and trapezoidal membership degrees in both cases increase equally. However, the quality advantage of supplier A increases by 50% in the first case, while it increases by 12.5% in the second case. Therefore, the experts’ preferences may increase differently for these cases that cannot be reflected accurately by triangular and trapezoidal MFs. To overcome this flaw, we develop four FAHP methods for pentagonal FNs (PFNs). We also use an indirect method to defuzzify the fuzzy local weights. Indirect defuzzification is a simple method equivalent to the center of gravity (COG) method and needs low computations. Numerical examples are used to illustrate the proposed methods. A real example of ranking suppliers in a sustainable framework based on pentagonal fuzzy preferences is also presented. To extract crisp local weights from pentagonal fuzzy comparison matrices, we use the pentagonal FAHP methods presented in this study.

Evaluating the impact of organizations’ corporate social responsibility from the banking industry perspective: A fuzzy analytic hierarchy process approach

The purpose of this study is to evaluate the impact of corporate social responsibility (CSR) from economic, employee, social and environmental dimensions in a hypothetical company setup. This study employs the fuzzy analytic hierarchy process (FAHP) in which the elements of the pairwise comparison matrix are expressed by triangular fuzzy elements. Furthermore, the classical non-fuzzy methods, such as the eigenvector and geometric mean, were also employed to calculate the weights of the fuzzy comparison matrices. First, some existing literature on CSR and its impact on the internal and external environments were explored. Second, the FAHP goal and the criteria were established, and this was followed by the pairwise comparison using the linguistic scale. Next is the computation of the geometric magnitude and weight of each criterion. Thereafter, the defuzzified and normalized weights were obtained. In the order of priority of CSR activities and their impact on the four identified criteria, alternative 1 (company 1) is ranked first, followed by alternative 2 (company 2), and alternative 3 (company 3) is ranked last. The implementation of CSR activities for companies 1 and 2 reflect positively in their internal and external environments, although to varying degrees. This study provides a practical guided approach for the use of the FAHP for solving a multi-criteria decision, such as ranking the impact of CSR activities in relation to certain criteria. The outcome of this study can guide organizations in making informed decisions regarding the implementation of CSR activities.

Mining Method Optimization of Difficult-to-Mine Complicated Orebody Using Pythagorean Fuzzy Sets and TOPSIS Method

In Suichang gold mine, the altered rock type gold deposits were cut by faults and joint fissures, leading to complex resource endowment characteristics, large changes in occurrence, a serious complex of ore vein branches and great difficulty in mining. In order to select a suitable mining method for such a difficult and complicated orebody, a multi-factor and multi-index comprehensive evaluation system involving benefits, costs, safety and other aspects was constructed by using the Pythagorean fuzzy sets and TOPSIS method. Taking Suichang gold mine as an example, the weighted aggregation evaluation matrix was constructed, the closeness index of the four mining schemes were 0.8436, 0.3370, 0.4296 and 0.4334, and the mechanized upward horizontal layering method was determined as the optimal scheme. This method overcame the fuzzy comparison of economic and technical indicators directly, but converted them into corresponding fuzzy numbers to obtain accurate closeness index for optimization. The application of this method not only ensured a safe, efficient and environment-friendly mining effect, but also provided a reference for the optimization of the mining scheme of the severely branched composite orebody.

Assessment of associated credit risk in the supply chain based on trade credit risk contagion.

Assessment of associated credit risk in the supply chain is a challenge in current credit risk management practices. This paper proposes a new approach for assessing associated credit risk in the supply chain based on graph theory and fuzzy preference theory. First, we classified the credit risk of firms in the supply chain into two types, namely firms' "own credit risk" and "credit risk contagion"; second, we designed a system of indicators for assessing the credit risks of firms in the supply chain and used fuzzy preference relations to obtain the fuzzy comparison judgment matrix of credit risk assessment indicators, on which basis we constructed the basic model for assessing the own credit risk of firms in the supply chain; third, we established a derivative model for assessing credit risk contagion. On this basis, we carried out a comprehensive assessment of the credit risk of firms in the supply chain by combining the two assessment results, revealing the contagion effect of associated credit risk in the supply chain based on trade credit risk contagion (TCRC). The case study shows that the credit risk assessment method proposed in this paper enables banks to accurately identify the credit risk status of firms in the supply chain, which helps curb the accumulation and outbreak of systemic financial risks.

A study on the comparison of technical indicators used in stock price prediction with the BAHP method

Savers want to direct their savings to investment areas where they can get maximum efficiency. This is the most basic feature that a rational investor should have. Stock investors also want to manage their investments with this thought. In this respect, investors conduct detailed research on the sector and stock they plan to invest in. Predictions regarding the possible price formation of the stock in the future is one of these studies. In the finance literature, there are many indicators, ratios, analyzes, indicators and oscillators developed for the future price prediction of the stock. In this study, technical indicators used by licensed professional stock investors were obtained by taking expert opinion. These indicators were conveyed to the experts again to get their opinions with the help of the fuzzy comparison matrix and the experts were asked to compare the variables. The data obtained were analyzed with the Fuzzy Analytical Hierarchy Process (FAHP) method and the technical indicators and ratios used by the experts were listed according to a certain hierarchy. As a result of the analysis, it has been determined that the most important ratio in the stock price estimation process is the MV/BV ratio. While EBIT is the second most important ratio in stock price prediction, P/E is the third most important indicator.Savers want to direct their savings to investment areas where they can get maximum efficiency. This is the most basic feature that a rational investor should have. Stock investors also want to manage their investments with this thought. In this respect, investors conduct detailed research on the sector and stock they plan to invest in. Predictions regarding the possible price formation of the stock in the future is one of these studies. In the finance literature, there are many indicators, ratios, analyzes, indicators and oscillators developed for the future price prediction of the stock. In this study, technical indicators used by licensed professional stock investors were obtained by taking expert opinion. These indicators were conveyed to the experts again to get their opinions with the help of the fuzzy comparison matrix and the experts were asked to compare the variables. The data obtained were analyzed with the Fuzzy Analytical Hierarchy Process (FAHP) method and the technical indicators and ratios used by the experts were listed according to a certain hierarchy. As a result of the analysis, it has been determined that the most important ratio in the stock price estimation process is the MV/BV ratio. While EBIT is the second most important ratio in stock price prediction, P/E is the third most important indicator.

Optimizing the Transportation Route in the Distribution Network Using Fuzzy AHP Multi-Criteria Decision Making

In the field of transportation in the distribution network, route optimization is of great importance because it can reduce costs, increase efficiency, and improve service quality. In this paper, a new method to optimize the transportation route in the distribution network using fuzzy AHP multi-criteria decision making is introduced. First, using the fuzzy AHP method, various criteria such as distance and time, cost and service quality are evaluated. Then, by using the matrix of integrated fuzzy comparisons of the criteria, the preference of each criterion over the other is determined. In the next step, in order to improve the accuracy and efficiency, the sub-criteria related to each criterion are evaluated. Using the matrix of integrated fuzzy comparisons of sub-criteria and the normalization method, the degree of preference of each sub-criteria is determined and we rank them. According to the results obtained from the preference of criteria and sub-criteria, different transportation routes can be improved and optimized based on preferences and normalization of preferences. The results show that the use of fuzzy AHP multi-criteria decision-making in the optimization of the transportation route in the distribution network leads to improved efficiency and reduced costs, and ultimately increases the quality of services.

Security Hardened and Privacy Preserved Android Malware Detection Using Fuzzy Hash of Reverse Engineered Source Code

The risk of malware has increased drastically in recent years due to advances in the IT industry but it also increased the need for malware analysis and prevention. Hackers inject malicious code using awful applications. In this research, a framework is proposed to identify malicious Android applications based on repacked malicious code. The sensitive features of android applications are extracted using source code. These extracted features are compared with existing malware signatures to identify repacked malicious android applications. Experiments are performed using 3490 android-based malware samples belonging to 21 different malware families. A threshold value for malware categorization is defined using fuzzy logic. If the fuzzy comparison match is greater than 40%, the application is malicious. Meanwhile, if the match is greater than 10% and less than 40%, the application is suspicious otherwise benign. Furthermore, the proposed framework presents around 74% of the repacked malware compared to other similar approaches.

Dynamic multi-objective optimization and fuzzy AHP for copper removal process of zinc hydrometallurgy

In order to improve the production efficiency and reduce the production cost of copper removal process (CRP), it is necessary to control the addition rate of zinc powder in CRP. In this study, the control of zinc powder addition rate is modeled as a dynamic multi-objective optimization problem (DMOP). A Pareto set which contains multiple control schemes is obtained by using multi-objective state transition algorithm based on decomposition, and then a new fuzzy multi-criteria decision-making (MCDM) is proposed to select the best control scheme. In the MCDM, according to the real-world requirements of CRP, four criteria are adopted to evaluate these schemes, and the fuzzy analytic hierarchy process (AHP) is adopted to determine the criteria weights according to a fuzzy comparison matrix. Furthermore, the nonlinear mixed integer programming model is established to guarantee consistency of the fuzzy comparison matrix. Experimental results of an industrial plant in China have demonstrated the effectiveness and superiority of the proposed method in terms of the cost, reaction rate, stability of outlet copper ion concentration, etc.

An Intelligent Approach to Evaluating CAD Software Packages Through Hesitant Fuzzy AHP

The evaluation of computer-aided design (CAD) packages among the rising number of alternatives in the market has been a critical process for companies because it directly affects the performance of their design/engineering-related activities in a new product development (NPD) as well as in R&D departments. Moreover, it is seen as an important step towards the computer-integrated manufacturing (CIM) environment. On the other hand, the evaluation process of CAD software packages is a multiple-criteria decision-making (MCDM) problem in the presence of sets of alternatives and evaluation criteria, which should be solved using one of the MCDM methods in the current literature. Therefore, in this study, the analytic hierarchy process (AHP), successfully implemented in both academic research and practices, is used for CAD software selection problem. The method is also used with the group decision-making approach to reach a more reliable solution. Additionally, due to the fact that the crisp pairwise comparison in the traditional AHP method seems to be insufficient and imprecise to capture the right judgments of decision makers (DMs), the hesitant fuzzy linguistic term-sets are integrated with the AHP approach (the hesitant F-AHP) to model the vagueness and uncertainty on judgments of the DMs. This proposed approach is also supported with a user-friendly Excel template that provides an effective tool for companies to evaluate and rank CAD software packages without many tiresome fuzzy comparisons and complex calculations. Moreover, in the paper, a numerical example is presented to demonstrate the effectiveness and applicability of the proposed approach to potential readers and practitioners. In this example, five CAD software options are evaluated based on six criteria by three DMs; and the best alternative is determined.

The revised extent analysis method

AbstractThe degree of possibility is used by the extent analysis (EA) to extract the crisp local weights from a triangular fuzzy comparison matrix (FCM); while, it is just a relation for comparing two triangular fuzzy numbers. This causes EA to extract the inaccurate local weights from a FCM and sometimes to rank the alternatives incorrectly. In this study, we revise the EA to avoid this misapplication. For this purpose, we propose a procedure in which the global weights of alternatives are obtained as fuzzy values; then, the degree of possibility is used just for ranking the alternatives based on their fuzzy global weights. The advantages of the revised extent analysis (REA), proposed in this study, compared with other fuzzy analytic hierarchy process are its simplicity and low computations. This study gives three numerical examples to illustrate how REA avoids the flaws of EA.

Indicator system optimization model for evaluating resilience of regional agricultural soil–water resource composite system

Abstract Resilience is an important indicator for measuring regional sustainable development capacity. The construction of a suitable evaluation indicator system is the premise of evaluating regional sustainable development. In this study, taking the Jiansanjiang Administration of Heilongjiang Province in China as an example, a preliminary selection library of the evaluation indicator system for the resilience of a regional agricultural soil–water resource composite system covering seven subsystems and 59 indicators was established. Selection criteria such as the Dale indicator criteria, subjective and objective combination weighting and principal component analysis were introduced to construct an optimization model for the resilience evaluation indicator system for the ASWRS. First, 14 indicators that were incomplete or incapable were removed. Then, the Dale indicator selection criteria were used to ensure that 14 indicators were selected. The binary fuzzy comparison method and criteria importance through interference correlation method were used to calculate the combination weight. Finally, an indicator system optimization model was established. The indicator system was optimized from 59 to 35 indicators, and the completeness of the indicator system reached 85.75%. The proposed method had obvious advantages in terms of indicator identification and elimination, and it may truly achieve the goal of indicator optimization.

Extended Fuzzy Analytic Hierarchy Process (E-FAHP): A General Approach

Fuzzy analytic hierarchy process (FAHP) methodologies have witnessed a growing development from the late 1980s until now, and countless FAHP based applications have been published in many fields including economics, finance, environment or engineering. In this context, the FAHP methodologies have been generally restricted to fuzzy numbers with linear type of membership functions (triangular numbers—TN—and trapezoidal numbers—TrN). This paper proposes an extended FAHP model (E-FAHP) where pairwise fuzzy comparison matrices are represented by a special type of fuzzy numbers referred to as (m,n)-trapezoidal numbers (TrN (m,n)) with nonlinear membership functions. It is then demonstrated that there are a significant number of FAHP approaches that can be reduced to the proposed E-FAHP structure. A comparative analysis of E-FAHP and Mikhailov’s model is illustrated with a case study showing that E-FAHP includes linear and nonlinear fuzzy numbers.

A Lean Green Implementation Evaluation Method Based on Fuzzy Analytic Net Process and Fuzzy Complex Proportional Assessment

For the issue that the optimal selection of lean green implementation tools for performance effect, a method combining fuzzy analytic net process (FANP) with fuzzy complex proportional assessment (COPRAS) is proposed. Firstly, the main properties of the lean green performance and candidate tools are determined based on the production requirements and expert knowledge. Then, the fuzzy comparison matrix of each attribute is constructed according to the expert judgment represented by triangular fuzzy number, and the FANP method is used to obtain the importance weight of each attribute. After that, the fuzzy decision matrix between attributes with tools alternatives is constructed, and multiplying it with the attribute weight so as to obtain the weighted normalized decision matrix. Finally, the fuzzy COPRAS method is used to analyze the decision matrix to get the utility of each tools alternative. Based on the model and analysis, these results make us understand and be familiar with the most influential practice tools on performance benefits. These findings are expected to policy makers and industrial practitioners to focus on key elements of the success of the manufacturing business to facilitate both lean and green manufacturing implementation and assessment, and contribute to sustainable growth.

Fuzzy Group Full Consistency Method for Weight Determination

Abstract In this paper, the FUll COnsistency Method (FUCOM) is extended to work in a collective manner, to solve a fuzzy optimization problem and to obtain the fuzzy weights of criteria. The employment of a predefined order of criteria decreases the number of fuzzy comparisons needed in the evaluation phase. The defuzzified values of the optimal weight coefficients are calculated by Graded Mean Integration Representation formula. This feature also reduces time complexity without affecting the quality of the solution. Two practical examples are presented to verify the reliability and feasibility of the proposed fuzzy group FUCOM. The obtained results demonstrate that the new fuzzy group weight determination method can obtain appropriate criteria importance.