Informatica

The extensions of ordinary fuzzy sets are problematic because they require decimal numbers for membership, non-membership and indecision degrees of an element from the experts, which cannot be easily determined. This will be more difficult when three or more digits’ membership degrees have to be assigned. Instead, proportional relations between the degrees of parameters of a fuzzy set extension will make it easier to determine the membership, non-membership, and indecision degrees. The objective of this paper is to present a simple but effective technique for determining these degrees with several decimal digits and to enable the expert to assign more stable values when asked at different time points. Some proportion-based models for the fuzzy sets extensions, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets are proposed, including their arithmetic operations and aggregation operators. Proportional fuzzy sets require only the proportional relations between the parameters of the extensions of fuzzy sets. Their contribution is that these models will ease the use of fuzzy set extensions with the data better representing expert judgments. The imprecise definition of proportions is also incorporated into the given models. The application and comparative analyses result in that proportional fuzzy sets are easily applied to any problem and produce valid outcomes. Furthermore, proportional fuzzy sets clearly showed the role of the degree of indecision in the ranking of alternatives in binomial and trinomial fuzzy sets. In the considered car selection problem, it has been observed that there are minor changes in the ordering of intuitionistic and spherical fuzzy sets.

Modelling the reliability information in decision making process is an important issue to inclusively reflect the thoughts of decision makers. The Evaluation Based on Distance from Average Solution (EDAS) and Analytic Hierarchy Process (AHP) are frequently used MCDM methods, yet their fuzzy extensions in the literature are incapable of representing the reliability of experts’ fuzzy preferences, which may have important effects on the results. The first goal of this study is to extend the EDAS method by using Z-fuzzy numbers to reinforce its representation ability of fuzzy linguistic expressions. The second goal is to propose a decision making methodology for the solution of fuzzy MCDM problems by using Z-fuzzy AHP method for determining the criteria weights and Z-fuzzy EDAS method for the selection of the best alternative. The contribution of the study is to present an MCDM based decision support tool for the managers under vague and imprecise data, which also considers the reliability of these data. The applicability of the proposed model is presented with an application to wind energy investment problem aiming at the selection of the best wind turbine. Finally, the effectiveness and competitiveness of the proposed methodology is demonstrated by making a comparative analysis with the Z-fuzzy TOPSIS method. The results show that the proposed methodology can not only represent experts’ evaluation information extensively, but also reveal a logical and consistent sequence related to wind turbine alternatives using reliability information.

Innovations in technology emerged with digitalization affect all sectors, including supply chain and logistics. The term “digital supply chain” has arisen as a relatively new concept in the manufacturing and service sectors. Organizations planning to utilize the benefits of digitalization, especially in the supply chain area, have uncertainties on how to adapt digitalization, which criteria they will evaluate, what kind of strategies should be developed, and which should be given more importance. Multi-criteria decision making (MCDM) approaches can be addressed to determine the best strategy under various criteria in digital transformation. Because of the need to capture this uncertainty, fermatean fuzzy sets (FFSs) have been preferred in the study to widen the definition domain of uncertainty parameters. Interval-valued fermatean fuzzy sets (IVFFSs) are one of the most often used fuzzy set extensions to cope with uncertainty. Therefore, a new interval-valued fermatean fuzzy analytic hierarchy process (IVFF-AHP) method has been developed. After determining the main criteria and sub-criteria, the IVFF-AHP method has been used for calculating the criteria weights and ranking the alternatives. By determining the most important strategy and criteria, the study provides a comprehensive framework of digital transformation in the supply chain.

The 3D extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and neutrosophic sets (NS) aim to describe experts’ judgments more informatively and explicitly. In this paper, generalized three dimensional spherical fuzzy sets are presented with their arithmetic, aggregation, and defuzzification operations. Weighted Aggregated Sum Product ASsessment (WASPAS) is a combination of two well-known multi-criteria decision-making (MCDM) methods, which are weighted sum model (WSM) and weighted product model (WPM). The aim of this paper is to extend traditional WASPAS method to spherical fuzzy WASPAS (SF-WASPAS) method and to show its application with an industrial robot selection problem. Additionally, we present comparative and sensitivity analyses to show the validity and robustness of the given decisions.

In order to survive in the present day global competitive environment, it now becomes essential for the manufacturing organizations to take prompt and correct decisions regarding effective use of their scarce resources. Various multi-criteria decision-making (MCDM) methods are now available to help those organizations in choosing the best decisive course of actions. In this paper, the applicability of weighted aggregated sum product assessment (WASPAS) method is explored as an effective MCDM tool while solving eight manufacturing decision making problems, such as selection of cutting fluid, electroplating system, forging condition, arc welding process, industrial robot, milling condition, machinability of materials, and electro-discharge micro-machining process parameters. It is observed that this method has the capability of accurately ranking the alternatives in all the considered selection problems. The effect of the parameter λ on the ranking performance of WASPAS method is also studied.