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.

Present worth (PW) analysis is an important technique in engineering economics for investment analysis. The values of PW analysis parameters such as interest rate, first cost, salvage value and annual cash flow are generally estimated including some degree of uncertainty. In order to capture the vagueness in these parameters, fuzzy sets are often used in the literature. In this study, we introduce interval-valued intuitionistic fuzzy PW analysis and circular intuitionistic fuzzy PW analysis in order to handle the impreciseness in the estimation of PW analysis parameters. Circular intuitionistic fuzzy sets are the latest extension of intuitionistic fuzzy sets defining the uncertainty of membership and non-membership degrees through a circle whose radius is r. Thus, we develop new fuzzy extensions of PW analysis including the uncertainty of membership functions. The methods are given step by step and an application for water treatment device purchasing at a local municipality is illustrated in order to show their applicability. In addition, a multi-parameter sensitivity analysis is given. Finally, discussions and suggestions for future research are given in conclusion section.

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.

Spherical fuzzy sets theory is useful and advantageous for handling uncertainty and imprecision in multiple attribute decision-making problems by considering membership, non-membership, and indeterminacy degrees. In this paper, by extending the classical linear assignment method, we propose a novel method called the spherical fuzzy linear assignment method (SF-LAM) to solve multiple criteria group decision-making problems in the spherical fuzzy environment. A ranking procedure consisting of aggregation functions, score functions, accuracy functions, weighted rank frequency, and a binary mathematical model are presented to determine the criterion-wise preferences and various alternatives’ priority order. The proposed method’s applicability and validity are shown through the selection problem among wind power farm locations. The proposed method helps managers to find the best location to construct the wind power plant based on the determined criteria. Finally, a comparative analysis is performed between the proposed spherical fuzzy linear assignment (SF-LAM) model and the spherical fuzzy analytic hierarchy process (SF-AHP) and spherical fuzzy WASPAS methods.

Today energy demand in the world cannot be met based on the growing population of the countries. Exhaustible resources are not enough to supply this energy requirement. Furthermore, the pollution created by these sources is one of the most important issues for all living things. In this context, clean and sustainable energy alternatives need to be considered. In this study, a novel interval-valued neutrosophic (IVN) ELECTRE I method is conducted to select renewable energy alternative for a municipality. A new division operation and deneutrosophication method for interval-valued neutrosophic sets is proposed. A sensitivity analysis is also implemented to check the validity of the proposed method. The obtained results and the sensitivity analysis demonstrate that the given decision in the application is robust. The results of the proposed method determine that the wind power plant is the best alternative and our proposed method’s decisions are consistent and reliable through the results of comparative and sensitivity analyses.

Construction site selection is a complex problem involving many alternatives and conflicting criteria with vague and imprecise evaluations. Fuzzy multi-criteria decision-making methods are the most effective tools to obtain optimum solutions under possibilistic uncertainty. In this paper, a novel interval hesitant fuzzy CODAS method is proposed and applied to a residential construction site selection problem. A comparative analysis with ordinary fuzzy CODAS method is applied for validating the proposed method. Also, a sensitivity analysis is conducted for the stability of the ranking results of the interval hesitant fuzzy CODAS method. The results of the analyses demonstrate the effectiveness of our proposed method.

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.

Fuzzy sets can be used in many old-fashioned aspects of our lives in order to reach better performance and make fairer judgments. Evaluation through examination is typically conducted by educational centers, and multiple choice question (MCQ) exams are widely applied to score the examinees. Since scoring is potentially a difficult process to judge, we propose to evaluate examinees by fuzzy evaluation method. This method can overcome the main shortcoming of the classical MCQs, i.e. the random selection of the choices. The evaluation of the proposed fuzzy MCQ is more accurate and its ranking of examinees is fairer than classical MCQ.