Synergic ranking of fuzzy Z-numbers based on vectorial distance and spread for application in decision-making

Decision science has a wide range of applications in daily life. Decision information is usually incomplete and partially reliable. In the fuzzy set theory, Z-numbers are introduced to handle this situation because they contain the restriction and reliability components, which complement the impaired information. The ranking of Z-numbers is a challenging task since they are composed of pairs of fuzzy numbers. In this research, the vectorial distance and spread of Z-numbers were proposed synergically, in which the vectorial distance measures how much the fuzzy numbers are apart from the origin, which was set as a relative point, and their spreads over a horizontal axis. Furthermore, a ranking method based on the convex compound was proposed to combine the restriction and reliability components of Z-numbers. The proposed ranking method was validated using several empirical examples and a comparative analysis was conducted. The application of the proposed ranking method in decision-making was illustrated via the development of the Analytic Hierarchy Process-Weighted Aggregated Sum Product Assessment (AHP-WASPAS) model to solve the prioritization of public services for the implementation of Industry 4.0 tools. Sensitivity analysis was also conducted to evaluate the performance of the proposed model and the results showed that the proposed model has improved its consistency from 66.67% of the existing model to 83.33%. This research leads to a future direction of the application of ranking based on the vectorial distance and spread in multi-criteria decision-making methods, which use Z-numbers as linguistic values

Synergic ranking of fuzzy Z-numbers based on vectorial distance and spread for application in decision-making

Decision science has a wide range of applications in daily life. Decision information is usually incomplete and partially reliable. In the fuzzy set theory, Z-numbers are introduced to handle this situation because they contain the restriction and reliability components, which complement the impaired information. The ranking of Z-numbers is a challenging task since they are composed of pairs of fuzzy numbers. In this research, the vectorial distance and spread of Z-numbers were proposed synergically, in which the vectorial distance measures how much the fuzzy numbers are apart from the origin, which was set as a relative point, and their spreads over a horizontal axis. Furthermore, a ranking method based on the convex compound was proposed to combine the restriction and reliability components of Z-numbers. The proposed ranking method was validated using several empirical examples and a comparative analysis was conducted. The application of the proposed ranking method in decision-making was illustrated via the development of the Analytic Hierarchy Process-Weighted Aggregated Sum Product Assessment (AHP-WASPAS) model to solve the prioritization of public services for the implementation of Industry 4.0 tools. Sensitivity analysis was also conducted to evaluate the performance of the proposed model and the results showed that the proposed model has improved its consistency from 66.67% of the existing model to 83.33%. This research leads to a future direction of the application of ranking based on the vectorial distance and spread in multi-criteria decision-making methods, which use Z-numbers as linguistic values

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

TOPSIS-RTCID for range target-based criteria and interval data

[EN] The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is receiving considerable attention as an essential decision analysis technique and becoming a leading method. This paper describes a new version of TOPSIS with interval data and capability to deal with all types of criteria. An improved structure of the TOPSIS is presented to deal with high uncertainty in engineering and engineering decision-making. The proposed Range Target-based Criteria and Interval Data model of TOPSIS (TOPSIS-RTCID) achieves the core contribution in decision making theories through a distinct normalization formula for cost and benefits criteria in scale of point and range target-based values. It is important to notice a very interesting property of the proposed normalization formula being opposite to the usual one. This property can explain why the rank reversal problem is limited. The applicability of the proposed TOPSIS-RTCID method is examined with several empirical litreture’s examples with comparisons, sensitivity analysis, and simulation. The authors have developed a new tool with more efficient, reliable and robust outcomes compared to that from other available tools. The complexity of an engineering design decision problem can be resolved through the development of a well-structured decision making method with multiple attributes. Various decision approches developed for engineering design have neglected elements that should have been taken into account. Through this study, engineering design problems can be resolved with greater reliability and confidence.Jahan, A.; Yazdani, M.; Edwards, K. (2021). TOPSIS-RTCID for range target-based criteria and interval data. International Journal of Production Management and Engineering. 9(1):1-14. https://doi.org/10.4995/ijpme.2021.13323OJS11491Ahn, B.S. (2017). 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Multi-criteria decision making with linguistic labels: a comparison of two methodologies applied to energy planning

This paper compares two multi-criteria decision making (MCDM) approaches based on linguistic label assessment. The first approach consists of a modified fuzzy TOPSIS methodology introduced by Kaya and Kahraman in 2011. The second approach, introduced by Agell et al. in 2012, is based on qualitative reasoning techniques for ranking multi-attribute alternatives in group decision-making with linguistic labels. Both approaches are applied to a case of assessment and selection of the most suitable types of energy in a geographical area.Peer ReviewedPostprint (published version

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