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

Green Supplier Selection in an Uncertain Environment in Agriculture Using a Hybrid MCDM Model: Z-Numbers–Fuzzy LMAW–Fuzzy CRADIS Model

The goal of this research was to find a selection of green suppliers (GSS) that will, in the best way, help agricultural producers to apply green agricultural production using uncertainty in decision making. In order to avoid the possibility of uncertainty in the expert decision making, Z-numbers were used together with the fuzzy LMAW (Logarithm Methodology of Additive Weights) method and fuzzy CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution) method. By applying Z-numbers and the fuzzy LMAW method, the weighting coefficients of the criteria were determined, where the experts, in addition to the criteria ratings, also defined the degrees of certainty in the criteria ratings they gave. The obtained results indicated that the criteria related to price and qualities are the most important during the selection process. To select the best alternative, the CRADIS method modified with Z-numbers and fuzzy numbers was applied. The results obtained by applying this method showed that suppliers A2 and A3 have the best characteristics and are the first choice for the procurement of raw and production materials. As part of the paper, the validation of the results and the sensitivity analysis of the model were carried out by conducting the procedure of comparing the obtained results with the results obtained by other MCDM methods and changing the weighting coefficients of the criteria. These analyses indicated that the model presented provides stable results. The conducted research showed how Z-numbers can be used to reduce uncertainty in decision making and how Z-numbers can be used with other fuzzy methods to perform GSS

Fuzzy Interval-Valued Multi Criteria Based Decision Making for Ranking Features in Multi-Modal 3D Face Recognition

Soodamani Ramalingam, 'Fuzzy interval-valued multi criteria based decision making for ranking features in multi-modal 3D face recognition', Fuzzy Sets and Systems, In Press version available online 13 June 2017. This is an Open Access paper, made available under the Creative Commons license CC BY 4.0 https://creativecommons.org/licenses/by/4.0/This paper describes an application of multi-criteria decision making (MCDM) for multi-modal fusion of features in a 3D face recognition system. A decision making process is outlined that is based on the performance of multi-modal features in a face recognition task involving a set of 3D face databases. In particular, the fuzzy interval valued MCDM technique called TOPSIS is applied for ranking and deciding on the best choice of multi-modal features at the decision stage. It provides a formal mechanism of benchmarking their performances against a set of criteria. The technique demonstrates its ability in scaling up the multi-modal features.Peer reviewedProo

A methodology for the selection of new technologies in the aviation industry

The purpose of this report is to present a technology selection methodology to quantify both tangible and intangible benefits of certain technology alternatives within a fuzzy environment. Specifically, it describes an application of the theory of fuzzy sets to hierarchical structural analysis and economic evaluations for utilisation in the industry. The report proposes a complete methodology to accurately select new technologies. A computer based prototype model has been developed to handle the more complex fuzzy calculations. Decision-makers are only required to express their opinions on comparative importance of various factors in linguistic terms rather than exact numerical values. These linguistic variable scales, such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’, are then converted into fuzzy numbers, since it becomes more meaningful to quantify a subjective measurement into a range rather than in an exact value. By aggregating the hierarchy, the preferential weight of each alternative technology is found, which is called fuzzy appropriate index. The fuzzy appropriate indices of different technologies are then ranked and preferential ranking orders of technologies are found. From the economic evaluation perspective, a fuzzy cash flow analysis is employed. This deals quantitatively with imprecision or uncertainties, as the cash flows are modelled as triangular fuzzy numbers which represent ‘the most likely possible value’, ‘the most pessimistic value’ and ‘the most optimistic value’. By using this methodology, the ambiguities involved in the assessment data can be effectively represented and processed to assure a more convincing and effective decision- making process when selecting new technologies in which to invest. The prototype model was validated with a case study within the aviation industry that ensured it was properly configured to meet the

Sustainability ranking of desalination plants using Mamdani Fuzzy Logic Inference Systems

As water desalination continues to expand globally, desalination plants are continually under pressure to meet the requirements of sustainable development. However, the majority of desalination sustainability research has focused on new desalination projects, with limited research on sustainability performance of existing desalination plants. This is particularly important while considering countries with limited resources for freshwater such as the United Arab Emirates (UAE) as it is heavily reliant on existing desalination infrastructure. In this regard, the current research deals with the sustainability analysis of desalination processes using a generic sustainability ranking framework based on Mamdani Fuzzy Logic Inference Systems. The fuzzy-based models were validated using data from two typical desalination plants in the UAE. The promising results obtained from the fuzzy ranking framework suggest this more in-depth sustainability analysis should be beneficial due to its flexibility and adaptability in meeting the requirements of desalination sustainability

Evaluation of e-learning web sites using fuzzy axiomatic design based approach

High quality web site has been generally recognized as a critical enabler to conduct online business. Numerous studies exist in the literature to measure the business performance in relation to web site quality. In this paper, an axiomatic design based approach for fuzzy group decision making is adopted to evaluate the quality of e-learning web sites. Another multi-criteria decision making technique, namely fuzzy TOPSIS, is applied in order to validate the outcome. The methodology proposed in this paper has the advantage of incorporating requirements and enabling reductions in the problem size, as compared to fuzzy TOPSIS. A case study focusing on Turkish e-learning websites is presented, and based on the empirical findings, managerial implications and recommendations for future research are offered