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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. [ABSTRACT FROM AUTHOR]

The direct assignment of decimal numbers for membership and non-membership degrees of an element in intuitionistic fuzzy sets is not practical. The problem is that the expert cannot assign the same values to the degrees of membership, non-membership and hesitancy in decimal numbers for the same proposition in every attempt. Rather than the former, the assignment of proportional relationships between membership and non-membership degrees is more appropriate. We propose proportion-based models for intuitionistic fuzzy sets that include arithmetic and aggregation operators. Proportional intuitionistic fuzzy (PIF) sets require only the proportion relations between an intuitionistic fuzzy set's parameters. These models will make it easier to define intuitionistic fuzzy sets with more accurate data that better represents expert judgments. We transform AHP method, one of the traditional multi-criteria decision making methods, to PIF AHP using PIF sets. We compare the proposed PIF AHP method by interval-valued intuitionistic fuzzy AHP method existing in the literature. A wind turbine selection problem is handled to show the validity of the proposed PIF AHP method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Process capability analysis (PCA) is a tool for measuring a process's ability to meet specification limits (SLs), which the customers define. Process capability indices (PCIs) are used for establishing a relationship between SLs and the considered process's ability to meet these limits as an index. PCA compares the output of a process with the SLs through these capability indices. If the customers' needs contain vague or imprecise terms, the classical methods are inadequate to solve the problem. In such cases, the information can be processed by the fuzzy set theory. Recently, ordinary fuzzy sets have been extended to several new types of fuzzy sets such as intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets. In this paper, a new extension of intuitionistic fuzzy sets, which is called penthagorean fuzzy sets, is proposed, and penthagorean fuzzy PCIs are developed. The design of production processes for COVID-19 has gained tremendous importance today. Surgical mask production and design have been chosen as the application area of the penthagorean fuzzy PCIs developed in this paper. PCA of the two machines used in surgical mask production has been handled under the penthagorean fuzzy environment. [ABSTRACT FROM AUTHOR]

Autonomous vehicles are one of the emergent advances of the new technology era that has the prospective to redesign transportation structures. Understanding and measuring the limitations of adopting autonomous vehicles and selecting the best autonomous vehicle based on different aspects is crucial for enhancing the adoption process. Defining the criteria and the appropriate evaluation methodology is very important for selecting the best autonomous vehicles. However, this selection process is a human judgment-based process where both benefit and cost criteria with imprecise linguistic assessments should be considered. The KEmeny Median Indicator Ranks Accordance (KEMIRA) method is a method that enables ranking the benefit and cost criteria independently. In this paper, a new KEMIRA method based on hesitant fuzzy linguistic term sets is defined. Hesitant Fuzzy Linguistic Term Sets (HFLTS) are newly utilized to represent the hesitancy of the decision-makers. The proposed new KEMIRA is approach the first study that defines the alternative scores and weights of the criteria via HFLTS. The computational steps of the new model are applied to autonomous vehicle selection. A real application is employed to show the applicability of the new KEMIRA method. [ABSTRACT FROM AUTHOR]

A circular intuitionistic fuzzy set (CIFS) recently introduced by Atanassov as a new extension of intuitionistic fuzzy sets is represented by a circle whose radius is r and whose center is composed of membership and non-membership degrees. The idea is similar to type-2 fuzzy sets, which are based on the fuzziness of membership functions with a third dimension. CIFSs help us define membership functions more flexibly, taking into account the vagueness in membership and non-membership degrees. In this study, TOPSIS, which is a multi-criteria decision-making (MCDM) method, is developed under circular intuitionistic fuzzy environment. The proposed CIF-TOPSIS method is applied to determine the most appropriate pandemic hospital location selection problem. Then, a sensitivity analysis based on criteria weights and the weight of the decision maker's optimistic and pessimistic attitudes are conducted to check the robustness of the decisions given by the proposed approach. A comparative analysis with the single-valued intuitionistic fuzzy TOPSIS, Pythagorean fuzzy TOPSIS, picture fuzzy TOPSIS methods is also performed to verify the developed approach and to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

Linguistic terms are quite suitable to make evaluations in multiple criteria decision making problems since humans prefer them rather than sharp evaluations. When linguistic evaluations are used in the decision matrix instead of exact numerical values, fuzzy set theory can capture the vagueness in the linguistic evaluations. Ordinary fuzzy sets have been extended to many new types of fuzzy sets such as intuitionistic fuzzy sets, neutrosophic sets, spherical fuzzy sets and picture fuzzy sets. Spherical fuzzy sets are an extension of picture fuzzy sets whose squared sum of their parameters is at most equal to one. This paper develops a novel spherical fuzzy CRiteria Importance Through Intercriteria Correlation (CRITIC) method and applies it for prioritizing supplier selection criteria. Supplier selection is one of the most critical aspects of any organization since any mistake in this process may cause poor supplier performance and inefficiencies in the business processes. Supplier selection is a multi-criteria decision making problem involving several conflicting criteria and alternatives. A numerical illustration of the proposed method is also given for this problem. [ABSTRACT FROM AUTHOR]

In Quality function deployment (QFD) approach, customers tend to express their needs in linguistic terms rather than exact numerical values and these needs generally contain vague and imprecise information. To overcome this challenge and to use the method more effectively for complex customer-oriented design problems, this paper introduces a novel intuitionistic Z-fuzzy QFD method based on Chebyshev's inequality (CI) and applies it for a new product design. CI provides the assignment of a more objective reliability function. The reliability value is based on the maximum probability obtained from CI. Then, the expected values of lower and upper bounds of interval-valued intuitionistic fuzzy (IVIF) numbers are determined. A competitive analysis among our firm and competitor firms and an integrative analysis for the different functions of QFD is presented. The proposed Z-fuzzy QFD method is applied to the design and development of a hand sanitizer for struggling with COVID-19. [ABSTRACT FROM AUTHOR]

Both national and international encouragements for research and development (R&D) projects have been growing worldwide. Since R&D projects include various uncertainties related to time, technology, finance, and knowledge, risk management studies are highly significant for the success of these projects. In risk management, all of the potential actions that might have negative impacts on the processes or outputs of a project should be determined, and if it is possible, their negative impacts should be reduced before the project starts. In this study, after risks in R&D projects are determined, the alternative projects are prioritized with respect to these risks by using an approach based on interval-valued intuitionistic fuzzy AHP and fuzzy information axiom. Interval-valued Intuitionistic Fuzzy Analytic Hierarchy Process (IVIF AHP) is used to determine the importance degrees of the determined risk factors while fuzzy information axiom is used to evaluate R&D projects considering these risk factors. It is revealed that the most important risk is "Abnormal changes in cost" while the least important one is "Deficiencies in contract articles". [ABSTRACT FROM AUTHOR]

The REGIME method is an easy to understand techniques which is based on pairwise comparisons and which can use qualitative data for decision making problems. The steps of the technique are simple and can be easily adopted to complex decision problems. Classical REGIME techniques use crisp numbers to evaluate qualitative evaluations. In this paper we propose Pythagorean Fuzzy REGIME (PF-REGIME) techniques which integrates Pythagorean Fuzzy Sets with REGIME technique. The proposed PF-REGIME is applied to waste disposal site selection problem. The decision model is constructed for three alternatives and five criteria in order to demonstrate the performance of the proposed PF-REGIME method. [ABSTRACT FROM AUTHOR]

Companies started to determine their strategies based on intelligent data analysis due to stagey enhance data production. Literature reviews show that the number of resources where demand estimation, location analysis, and decision-making technique applied together with the machine learning method is low in all sectors and almost none in the shopping mall domain. Within this study's scope, a new hybrid fuzzy prediction method has been developed that will estimate the customer numbers for shopping malls. This new methodology is applied to predict the number of visitors of three shopping malls on the Anatolian side of Istanbul. The forecasting study for corresponding shopping malls is made by using the daily signaling data from indoor base stations of large-scale technology and telecommunications services provider and the features to be used in machine learning models is determined by fuzzy multi criteria decision making method. Output revealed by the application of the fuzzy multi criteria decision making method enables the prioritization of features. [ABSTRACT FROM AUTHOR]

Milk-run is a delivery method allowing to move small quantities of a large number of different items with predictable lead times from various suppliers to a customer. The main goal is to minimize the transportation cost by minimizing the travel distance and by maximizing vehicle capacities. The effects of uncertainties in arrival times of vehicles and loading times of shipments should also be considered in modeling the milk-run problems. In this paper, a multi-objective linear programming model, an ordinary fuzzy multi-objective linear programming model and an intuitionistic fuzzy multi-objective linear programming model are proposed for the milk-run modeling under time window constraints. The proposed approaches are applied on the real-life data of Borusan Logistics which is one of the largest logistics firms in Turkey and the results are presented. [ABSTRACT FROM AUTHOR]