Using Pythagorean Fuzzy Sets (PFS) in Multiple Criteria Group Decision Making (MCGDM) Methods for Engineering Materials Selection Applications

The process of materials’ selection is very critical during the initial stages of designing manufactured products. Inefficient decision-making outcomes in the material selection process could result in poor quality of products and unnecessary costs. In the last century, numerous materials have been developed for manufacturing mechanical components in different industries. Many of these new materials are similar in their properties and performances, thus creating great challenges for designers and engineers to make accurate selections. Our main objective in this work is to assist decision makers (DMs) within the manufacturing field to evaluate materials alternatives and to select the best alternative for specific manufacturing purposes. In this research, new hybrid fuzzy Multiple Criteria Group Decision Making (MCGDM) methods are proposed for the material selection problem. The proposed methods tackle some challenges that are associated with the material selection decision making process, such as aggregating decision makers’ (DMs) decisions appropriately and modeling uncertainty. In the proposed hybrid models, a novel aggregation approach is developed to convert DMs crisp decisions to Pythagorean fuzzy sets (PFS). This approach gives more flexibility to DMs to express their opinions than the traditional fuzzy and intuitionistic sets (IFS). Then, the proposed aggregation approach is integrated with a ranking method to solve the Pythagorean Fuzzy Multi Criteria Decision Making (PFMCGDM) problem and rank the material alternatives. The ranking methods used in the hybrid models are the Pythagorean Fuzzy TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution) and Pythagorean Fuzzy COPRAS (COmplex PRoportional Assessment). TOPSIS and COPRAS are selected based on their effectiveness and practicality in dealing with the nature of material selection problems. In the aggregation approach, the Sugeno Fuzzy measure and the Shapley value are used to fairly distribute the DMs weight in the Pythagorean Fuzzy numbers. Additionally, new functions to calculate uncertainty from DMs recommendations are developed using the Takagai-Sugeno approach. The literature reveals some work on these methods, but to our knowledge, there are no published works that integrate the proposed aggregation approach with the selected MCDM ranking methods under the Pythagorean Fuzzy environment for the use in materials selection problems. Furthermore, the proposed methods might be applied, due to its novelty, to any MCDM problem in other areas. A practical validation of the proposed hybrid PFMCGDM methods is investigated through conducting a case study of material selection for high pressure turbine blades in jet engines. The main objectives of the case study were: 1) to investigate the new developed aggregation approach in converting real DMs crisp decisions into Pythagorean fuzzy numbers; 2) to test the applicability of both the hybrid PFMCGDM TOPSIS and the hybrid PFMCGDM COPRAS methods in the field of material selection. In this case study, a group of five DMs, faculty members and graduate students, from the Materials Science and Engineering Department at the University of Wisconsin-Milwaukee, were selected to participate as DMs. Their evaluations fulfilled the first objective of the case study. A computer application for material selection was developed to assist designers and engineers in real life problems. A comparative analysis was performed to compare the results of both hybrid MCGDM methods. A sensitivity analysis was conducted to show the robustness and reliability of the outcomes obtained from both methods. It is concluded that using the proposed hybrid PFMCGDM TOPSIS method is more effective and practical in the material selection process than the proposed hybrid PFMCGDM COPRAS method. Additionally, recommendations for further research are suggested

A hybrid neutrosophic group ANP-TOPSIS framework for supplier selection problems

One of the most significant competitive strategies for organizations is sustainable supply chain management (SSCM). The vital part in the administration of a sustainable supply chain is the sustainable supplier selection, which is a multi-criteria decision-making issue, including many conflicting criteria.</div

A new measure of consensus with reciprocal preference relations: The correlation consensus degree

Producción CientíficaThe achievement of a ‘consensual’ solution in a group decision making problem depends on experts’ ideas, principles, knowledge, experience, etc. The measurement of consensus has been widely studied from the point of view of different research areas, and consequently different consensus measures have been formulated, although a common characteristic of most of them is that they are driven by the implementation of either distance or similarity functions. In the present work though, and within the framework of experts’ opinions modelled via reciprocal preference relations, a different approach to the measurement of consensus based on the Pearson correlation coefficient is studied. The new correlation consensus degree measures the concordance between the intensities of preference for pairs of alternatives as expressed by the experts. Although a detailed study of the formal properties of the new correlation consensus degree shows that it verifies important properties that are common either to distance or to similarity functions between intensities of preferences, it is also proved that it is different to traditional consensus measures. In order to emphasise novelty, two applications of the proposed methodology are also included. The first one is used to illustrate the computation process and discussion of the results, while the second one covers a real life application that makes use of data from Clinical Decision-Making.Ministerio de Economía, Industria y Competitividad (Project ECO2012-32178

A new measure of consensus with reciprocal preference relations: The correlation consensus degree

Producción CientíficaThe achievement of a ‘consensual’ solution in a group decision making problem depends on experts’ ideas, principles, knowledge, experience, etc. The measurement of consensus has been widely studied from the point of view of different research areas, and consequently different consensus measures have been formulated, although a common characteristic of most of them is that they are driven by the implementation of either distance or similarity functions. In the present work though, and within the framework of experts’ opinions modelled via reciprocal preference relations, a different approach to the measurement of consensus based on the Pearson correlation coefficient is studied. The new correlation consensus degree measures the concordance between the intensities of preference for pairs of alternatives as expressed by the experts. Although a detailed study of the formal properties of the new correlation consensus degree shows that it verifies important properties that are common either to distance or to similarity functions between intensities of preferences, it is also proved that it is different to traditional consensus measures. In order to emphasise novelty, two applications of the proposed methodology are also included. The first one is used to illustrate the computation process and discussion of the results, while the second one covers a real life application that makes use of data from Clinical Decision-Making.Ministerio de Economía, Industria y Competitividad (Project ECO2012-32178

Creating a common priority vector in intuitionistic fuzzy AHP: a comparison of entropy-based and distance-based models

In the case of conflicting individuals or evaluator groups, finding the common preferences of the participants is a challenging task. This statement also refers to Intuitionistic Fuzzy Analytic Hierarchy Process models, in which uncertainty of the scoring of individuals is well-handled, however, the aggregation of the modified scores is generally conducted by the conventional way of multi-criteria decision-making. This paper offers two options for this aggregation: the relatively well-known entropy-based, and the lately emerged distance-based aggregations. The manuscript can be considered as a pioneer work by analyzing the nature of distance-based aggregation under a fuzzy environment. In the proposed model, three clearly separable conflicting groups are examined, and the objective is to find their common priority vector, which can be satisfactory to all participant clusters. We have tested the model results on a real-world case study, on a public transport development decision-making problem by conducting a large-scale survey involving three different stakeholder groups of transportation. The comparison of the different approaches has shown that both entropy-based and distance-based techniques can provide a feasible solution based on their high similarity in the final ordinal and cardinal outcomes

STUDY TOWARDS THE TIME-BASED MCDA RANKING ANALYSIS – A SUPPLIER SELECTION CASE STUDY

Decision-making processes increasingly use models based on various methods to ensure professional analysis and evaluation of the considered alternatives. However, the abundance of these methods makes it difficult to choose the proper method to solve a given problem. Also, it is worth noting whether different results can be obtained using different methods within a single decision problem. In this paper, we used three selected Multi-Criteria Decision Analysis (MCDA) methods called COMET, TOPSIS, and SPOTIS in order to examine how the obtained rankings vary. The selection of material suppliers was taken into consideration. The equal weights, entropy and standard deviation methods were used to determine the weights for criteria. Final preferences values were then compared with the WS similarity coefficient and weighted Spearman correlation coefficient to check the similarity of the received rankings. It was noticed that in the given problem, all of the methods provide highly correlated results, and the obtained positional rankings are not significantly different. However, practical conclusions indicate the need to look for improved solutions in the correct and accurate assessment of suppliers in a given period

An IVIF-ELECTRE outranking method for multiple criteria decision-making with interval-valued intuitionistic fuzzy sets

The method of ELimination Et Choix Traduisant la REalité (ELimination and Choice Expressing Reality, ELECTRE) is a well-known and widely used outranking method for handling decision-making problems. The purpose of this paper is to develop an interval-valued intuitionistic fuzzy ELECTRE (IVIF-ELECTRE) method and apply it to multiple criteria decision analysis (MCDA) involving the multiple criteria evaluation/selection of alternatives. Using interval-valued intuitionistic fuzzy (IVIF) sets with an inclusion comparison approach, concordance and discordance sets are identified for each pair of alternatives. Next, concordance and discordance indices are determined using an aggregate importance weight score function and a generalised distance measurement between weighted evaluative ratings, respectively. Based on the concordance and discordance dominance matrices, two IVIF-ELECTRE ranking procedures are developed for the partial and complete ranking of the alternatives. The feasibility and applicability of the proposed methods are illustrated with a multiple criteria decision-making problem of watershed site selection. A comparative analysis of other MCDA methods is conducted to demonstrate the advantages of the proposed IVIF-ELECTRE methods. Finally, an empirical study of job choices is implemented to validate the effectiveness of the current methods in the real world. First published online: 17 Sep 201

Client acceptance method for audit firms based on interval-valued fuzzy numbers

To ensure that investors are getting financial statements that conform to Generally Accepted Accounting Principles, the security exchange committee requires publicly traded companies to hire external auditors. Because the information provided in company financial statements has significant economic and social consequences for various parties, external auditors are needed to minimize litigation. Therefore, it is important for audit firms’ risk management teams to evaluate which clients to accept. In this paper, we propose a client acceptance method (CAM) that uses a technique for order preference using similarity to the ideal solution (i.e. TOPSIS) approach to evaluate potential new clients using a decision-making method with interval-valued fuzzy numbers (IVFNs). Through a case study, this paper shows that this CAM results in a high Spearman rankorder correlation coefficient (0.9 to 1.0) with human judgment. This result indicates that CAM could help decision makers evaluate potential clients before acceptance, especially when there are several potential clients but limited resources to provide services. The CAM also could help audit firms more easily ensure that decision makers are complying with firm policies concerning client acceptance through the establishment of uncertainty factor weights. First published online: 28 Jan 201

A novel fuzzy hybrid neutrosophic decision-making approach for the resilient supplier selection problem

The objectives of this study are to mitigate the risk and disturbances to the supply chain, to offer required models for resolving the complex issues that arise, and to maintain the stability of the support system. Also, the uncertain conditions in a supply chain force decision-makers and experts to adopt a fuzzy-based evaluation platform to ensure secure and reliable consequences. The current study proposed a fuzzy neutrosophic decision-making approach for supplier evaluation and selection. The model is composed of a new weight aggregator that uses pairwise comparison, which has not been reported to date. The model uses a Dombi aggregator that is more qualified than other aggregators. The Dombi t-conorms and t-norms have the same properties as those of the general t-conorm and t-norm, which can enhance the flexibility of the information aggregation process via the adjustment of a parameter. A decision-making environment with uncertain condition and multiple factors is supposed. We applied this approach in a construction company to analyse the suppliers in a resilient supply chain management (RSCM) system using a MABAC (multi-attribute border approximation area comparison) tool. The accuracy of the proposed model was examined via sensitivity analysis tests. This study proposes a novel fuzzy-neutrosophic-based approach for resilient supplier selection. The main contributions of this research work are the design, implementation and analysis of a multi-attribute evaluation system with respect to fuzzy neutrosophic values. In this evaluation system, a new pairwise comparison is conducted with trapezoidal neutrosophic linguistic variables to determine the importance weights of supplier criteria. Typically, the provision of opinions regarding the qualitative performances of suppliers is a difficult and confusing responsibility for experts and supplier evaluators. Therefore, the propsed approach overcomes this problem by utilizing a pairwise comparison by neutrosophic values and proposes original Dombi aggregation operators for dealing with fuzzy neutrosophic sets

Introducing alternatives ranking with elected nominee (ARWEN) method: a case study of supplier selection

Supply chain management (SCM) has gradually evolved beyond the straightforward logic of benefits and economic viewpoints. Supplier selection and performance evaluation are the crucial strategic components of any SCM system with a substantial economic impact and risk reduction. Several conflicting factors make supplier selection a challenging multi-criteria decision-making problem. This paper introduces a method called alternative ranking with the elected nominee (ARWEN) to select suppliers in Iran’s dairy product chain store. The primary principle of ARWEN is to choose the best alternative based on the lowest change rate rather than the elected nominee. Four extensions of the ARWEN method are proposed depending upon the nature and level of information available to the decision-makers. A fifth extended version termed E-ARWEN is also recommended to consider the negative form of the elected nominee. Two novel statistical tools, the ranking performance index and the Zakeri-Konstantas distance product correlation coefficient, are also put forth to validate the ARWEN extensions’ outcomes. The results and verification of this new method are carried out through two supplier selection case examples. Comprehensive comparisons were carried out to explore the new methods’ behaviors, indicating ARWEN III and E-ARWEN have similar behavior to VIKOR, SAW, and EDAS in generating rankings