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

Introducing a multi-criteria evaluation method using Pythagorean fuzzy sets: A case study focusing on resilient construction project selection

© 2020, Emerald Publishing Limited. Purpose: Project selection is a critical decision for any organization seeking to commission a large-scale construction project. Project selection is a complex multi-criteria decision-making problem with significant uncertainty and high risks. Fuzzy set theory has been used to address various aspects of project uncertainty, but with key practical limitations. This study aims to develop and apply a novel Pythagorean fuzzy sets (PFSs) approach that overcomes these key limitations. Design/methodology/approach: The study is particular to complex project selection in the context of increasing interest in resilience as a key project selection criterion. Project resilience is proposed and considered in the specific situation of a large-scale construction project selection case study. The case study develops and applies a PFS approach to manage project uncertainty. The case study is presented to demonstrate how PFS is applied to a practical problem of realistic complexity. Working through the case study highlights some of the key benefits of the PFS approach for practicing project managers and decision-makers in general. Findings: The PFSs approach proposed in this study is shown to be scalable, efficient, generalizable and practical. The results confirm that the inclusion of last aggregation and last defuzzification avoids the potentially critical information loss and relative lack of transparency. Most especially, the developed PFS is able to accommodate and manage domain expert expressions of uncertainty that are realistic and practical. Originality/value: The main novelty of this study is to address project resilience in the form of multi-criteria evaluation and decision-making under PFS uncertainty. The approach is defined mathematically and presented as a six-step approach to decision-making. The PFS approach is given to allow multiple domain experts to focus more clearly on accurate expressions of their agreement and disagreement. PFS is shown to be an important new direction in practical multi-criteria decision-making methods for the project management practitioner

Evaluating large, high-technology project portfolios using a novel interval-valued Pythagorean fuzzy set framework: An automated crane project case study

© 2019 Elsevier Ltd The contemporary organization relies increasingly on developing large, high technology projects in order to gain local and global competitive advantage. Uncertainty and the complexity of project evaluation requires improved and tailored decision making support systems. A new framework for high technology project portfolio evaluation is introduced. Novel development of an interval-valued Pythagorean fuzzy set (IVPFS) approach is shown to accommodate degrees of membership, non-membership and hesitancy in the evaluation process. Developed methods of linear assignment, IVPFS ranking, IVPFS knowledge index, and IVPFS comparison provide a new framework for group evaluation based on a weighting for each decision expert. The framework is developed as a last aggregation which avoids information loss and introduces a new aggregation process. A novel multi-objective model is then introduced to address project portfolio selection while optimizing the value of the portfolio in terms of resilience (the risk of disruption and delays) and skill utilization (assignment of human resources). The applicability of this framework is demonstrated through a case study in high technology portfolio evaluation. The case study shows that the presented framework can be applied as the core to a high technology evaluation decision support system

Analysis of environmental priorities for green project investments using an integrated q-rung orthopair fuzzy modeling

Green energy projects contribute to sustainable economic development of countries with the employment of environmentally friendly energy production strategies. However, environmental priorities should be examined for this situation. Therefore, priority analysis should be executed for the environmental issues while implementing green investment projects. Accordingly, this study aims at proposing a unique decision-making model based on orthopair fuzzy sets and the golden cut degrees for the environmental priorities of green project investments. The main novelty of the study stems from its proposed integrated model by equipping the Multi-SWARA, and TOPSIS based on the q-ROFSs technique with the golden cut. A set of criteria is identified for measuring the green projects’ environmental priorities while several project alternatives are also determined with the supporting literature. Appropriately, the extensions of Multi-SWARA and TOPSIS methods have been applied for weighting and ranking the factors, respectively, in the integrated approach. Additionally, a comparative evaluation is performed with the help of VIKOR method to rank the alternatives. Besides, the sensitivity analysis is applied to illustrate the coherency of the weighting results in the decision-making approach. Accordingly, 5 cases are considered to measure the effects of changing weight results. It is defined that this model is coherent and could be extended for further studies. It is concluded that the reduction of emissions is the most essential item for the environmental priorities of green project investments. Pollution control, waste management and eco-friendly transportation activities are the most critical alternatives. Therefore, this study recommends that investors of green projects should prioritize the strategies of minimizing carbon emissions problem. In this context, investing in renewable energy technologies will help green project investors solve this problem.WOS:0007974148000012-s2.0-8513083050

Developing an integrated AHP and Intuitionistic FuzzyTOPSIS methodology

U ovom se istraživanju daje pregled analitičkog hijerarhijskog postupka (AHP) i intuicijskih FuzzyTOPSIS (IFT) metoda. Rad se bavi procjenom metodologije zasnovane na AHP-IFT gdje se nesigurnosti opisuju lingvističkim vrijednostima. Najprije se problem izbora dobavljača formulira primjenom AHP, a zatim se koristi za određivanje težina kriterija. Kasnije se IFT koristi za postizanje rangiranja među alternativama temeljenim na mišljenju donositelja odluka (DMs). Ovaj model omogućuje točnu i laku klasifikaciju svojstava dobavljača prema tome kako su rangirani u hibridnom modelu. Daje se numerički primjer kako bi se objasnio glavni dobiveni rezultat u radu.This research gives an overview of the Analytic Hierarchy Process (AHP) and Intuitionistic FuzzyTOPSIS (IFT) methods. This study deals with an evaluation methodology based on the AHP-IFT where the uncertainties are handled with linguistic values. First, the supplier selection problem is formulated using AHP and, then, it is used to determine the weights of the criteria. Later, IFT is used to obtain full- ranking among alternatives based on opinion of the Decision Makers (DMs). The present model provides an accurate and easy classification in supplier attributes by those that have been prioritized in the hybrid model. A numerical example is given to clarify the main developed result in this paper

Developing an integrated AHP and Intuitionistic FuzzyTOPSIS methodology

U ovom se istraživanju daje pregled analitičkog hijerarhijskog postupka (AHP) i intuicijskih FuzzyTOPSIS (IFT) metoda. Rad se bavi procjenom metodologije zasnovane na AHP-IFT gdje se nesigurnosti opisuju lingvističkim vrijednostima. Najprije se problem izbora dobavljača formulira primjenom AHP, a zatim se koristi za određivanje težina kriterija. Kasnije se IFT koristi za postizanje rangiranja među alternativama temeljenim na mišljenju donositelja odluka (DMs). Ovaj model omogućuje točnu i laku klasifikaciju svojstava dobavljača prema tome kako su rangirani u hibridnom modelu. Daje se numerički primjer kako bi se objasnio glavni dobiveni rezultat u radu.This research gives an overview of the Analytic Hierarchy Process (AHP) and Intuitionistic FuzzyTOPSIS (IFT) methods. This study deals with an evaluation methodology based on the AHP-IFT where the uncertainties are handled with linguistic values. First, the supplier selection problem is formulated using AHP and, then, it is used to determine the weights of the criteria. Later, IFT is used to obtain full- ranking among alternatives based on opinion of the Decision Makers (DMs). The present model provides an accurate and easy classification in supplier attributes by those that have been prioritized in the hybrid model. A numerical example is given to clarify the main developed result in this paper

A comprehensive review of hybrid game theory techniques and multi-criteria decision-making methods

More studies trend to hybrid the game theory technique with the multi-criteria decision-making (MCDM) method to aid real-life problems. This paper provides a comprehensive review of the hybrid game theory technique and MCDM method. The fundamentals of game theory concepts and models are explained to make game theory principles clear to the readers. Moreover, the definitions and models are elaborated and classified to the static game, dynamic game, cooperative game and evolutionary game. Therefore, the hybrid game theory technique and MCDM method are reviewed and numerous applications studied from the past works of literature are highlighted. The result of the previous studies shows that the fundamental elements for both frameworks were studied in various ways with most of the past studies tend to integrate the static game with AHP and TOPSIS methods. Also, the integration of game theory techniques and MCDM methods was studied in various applications such as politics, economy, supply chain, engineering, water management problem, allocation problem and telecommunication network selection. The main contribution of the recent studies of employment between game theory technique and MCDM method are analyzed and discussed in detail which includes static and dynamic games in the non-cooperative game, cooperative game, both non-cooperative and cooperative games and evolutionary gam

Sustainability performance assessment with intuitionistic fuzzy composite metrics and its application to the motor industry

The performance assessment of companies in terms of sustainability requires to find a balance between multiple and possibly conflicting criteria. We here rely on composite metrics to rank a set of companies within an industry considering environmental, social and corporate governance criteria. To this end, we connect intuitionistic fuzzy sets and composite programming to propose novel composite metrics. These metrics allow to integrate important environmental, social and governance principles with the gradual membership functions of fuzzy set theory. The main result of this paper is a sustainability assessment method to rank companies within a given industry. In addition to consider multiple objectives, this method integrates two important social principles such as maximum utility and fairness. A real-world example is provided to describe the application of our sustainability assessment method within the motor industry. A further contribution of this paper is a multicriteria generalization of the concept of magnitude of a fuzzy number