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A literature review on the extensions of intuitionistic fuzzy sets
(World Scientific Publ Co Pte Ltd, 2020) Kahraman, Cengiz; Oztaysi, Basar; Onar, Sezi Cevik; Otay, Irem
Intuitionistic fuzzy sets (Atanassov, 1986) are the sets whose elements have degrees of membership and non-membership satisfying the condition that their sum is at most equal to one. Thus, an expert can express his/her hesitancy through IFS whereas it is not possible with ordinary fuzzy sets. This paper presents a literature review on intuitionistic fuzzy sets based on some classifications with respect to type of intuitionistic fuzzy numbers. We use graphical and tabular illustrations for a better visualization of the review. We also propose a new extension of IFS whose name is q-Spherical fuzzy sets.
A novel interval valued circular intuitionistic fuzzy AHP methodology: Application in digital transformation project selection
(Elsevier Science Inc, 2023) Otay, Irem; Onar, Sezi Cevik; Oztaysi, Basar; Kahraman, Cengiz
Since its first introduction, ordinary fuzzy sets have been extended to new types of fuzzy sets as a tool of artificial intelligence techniques. One of the recently introduced fuzzy sets, Circular Intuitionistic Fuzzy (CIF) sets enable us to take into account instability of the membership and non-membership degrees with a circular area & its radius. In this study, we first introduce Interval Valued CIF (IVCIF) sets and their arithmetic operations to better incorporate the uncertainty and cover a broader domain. Then, we introduce a novel IVCIF Analytic Hierarchy Process (AHP) method and apply it to evaluate Digital Transformation (DT) projects with complex nature. DT projects requiring fundamental changes in processes, business models and cultures of the com-panies, contribute a significant value to the companies and increase their market shares; so that they can achieve long term success and competitive advantage. On the other hand, DT problems which are usually ill-defined and include incomplete information based on human judgments, necessitate fuzzy representation. For the success of a digital transformation and to contribute excellence in engineering applications, DT projects should be carefully analyzed. For these rea-sons, we focus on DT project evaluation problem in application. Also, sensitivity & comparative analyses are performed.
A novel pythagorean fuzzy AHP and TOPSIS method for the wind power farm location selection problem
(Ios Press, 2020) Otay, Irem; Jaller, Miguel
This paper proposes an Integrated Fuzzy Analytic Hierarchy Process (AHP) with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method using Pythagorean fuzzy sets for the wind farm location selection problem. The method combines the advantages of the two methodologies to consider uncertainties and lack of information in the decision-making process (human expert capacities) and enables better representation of membership and non-membership functions, and at the same time, allows for the evaluation of large numbers of alternatives and criteria. The authors implement the method to evaluate four potential sites near cities located in the west and north-west regions of Turkey, using seven main criteria and twenty-five sub-criteria. The analyses are based on the judgements of three experts/decision-makers. Moreover, the authors compare the results (site ranking) of the methodology, with those from a Pythagorean Fuzzy AHP and an interval-valued Type-2 fuzzy AHP method. With the additional consideration of the sub-criteria, the proposed method generates slight differences in the ranking compared to the previously evaluated methods.
A novel single-valued spherical fuzzy AHP-WASPAS methodology
(World Scientific Publ Co Pte Ltd, 2020) Otay, Irem; Kahraman, Cengiz; Oztaysi, Bapr; Onar, Sezi Cevik
Intuitionistic fuzzy sets are the main source of several recent extensions of the ordinary fuzzy sets such as Pythagorean fuzzy sets, picture fuzzy sets, neutrosophic sets and qrung orthopair fuzzy sets. In addition to these, one of the latest extensions of these types of fuzzy sets is Spherical fuzzy sets, which have been often employed in many multiattribute decision making applications in the literature. One of the advantages of Spherical fuzzy set is that it provides a larger domain for the definition of the parameters (membership & non-membership functions and hesitancy) and it allows the parameters to be defined independently. Analytic Hierarchy Process (AHP) is one of the multi-attribute decision making methods based on pairwise comparisons of criteria and alternatives, satisfying the consistency of each pairwise comparison matrix. WASPAS (The Weighted Aggregates Sum Product Assessment) being the integration of weighted product sum and simple additive weighting methods, has been recently introduced to the literature. Under impreciseness and vagueness, linguistic evaluations are generally preferred in a decision matrix. There are many fuzzy extensions of AHP & WASPAS methods such as intuitionistic fuzzy AHP, intuitionistic fuzzy WASPAS, and Pythagorean fuzzy AHP. However, there is no paper integrating AHP and WASPAS methods using Spherical fuzzy sets. Thus, this paper aims to contribute to the literature by developing an integration of Spherical fuzzy AHP &WASPAS methods. The proposed method is applied to solve outsource manufacturer evaluation and selection problem.
An Integrated Interval-Valued Picture Fuzzy CRITIC & TOPSIS Methodology: An Application to Disaster Debris Management
(Old City Publishing Inc, 2023) Oztaysi, Basar; Onar, Sezi Cevik; Otay, Irem; Kahraman, Cengiz
Picture fuzzy (PF) sets show the expert's opinion about an element's membership or non-membership in the set, as well as the expert's indecision about the element's membership in the set. Interval-valued PF sets (IVPFSs) offer more flexibility than single-valued PF sets in assigning the mentioned degrees. Picture fuzzy multi-criteria decision making methods or methodologies are superior to other methods or methodologies since they can take these opinions of the experts into account in the decision mechanism. CRITIC method is a criteria weighting method based on statistical terms such as correlation coefficients and standard deviations, which has become popular recently. In this paper, the PFCRITIC method will be used to calculate the weights of the criteria and the PF-TOPSIS method is used to rank the alternatives. The proposed multi-experts IVPF CRITIC&TOPSIS methodology is applied to the post-disaster location selection of debris waste sites in Istanbul. In the comparison analysis, the integrated methodology is compared with crisp TOPSIS method based on the same data. The results show that the integrated methodology gives a consistent ranking with slight differences in closeness coefficients.
Continuous Intuitionistic Fuzzy AHP & CODAS Methodology for Automation Degree Selection
(Old City Publishing Inc, 2024) Alkan, Nursah; Otay, Irem; Gul, Alize Yaprak; Demir, Zeynep Burcu Kizilkan; Dogan, Onur
The automotive industry's evolution thrives on technological innovation, prioritizing efficiency, safety, and sustainability. Recent improvements in autonomous driving and IoT integration have revolutionized vehicle design, safety, and maintenance with different automation degrees from partial human control to full automation. Selecting these automation degrees involves complicated Multi-Criteria Decision-Making (MCDM) encompassing technical feasibility, societal impact, and regulatory compliance. Utilizing Analytic Hierarchy Process (AHP) and Combinative Distance-Based Assessment (CODAS) offers a structured framework to navigate these complexities. AHP establishes criteria importance, while CODAS handles uncertainties, enabling informed decisions balancing technology with ethical, societal, and regulatory considerations. Fuzzy extensions further refine these methodologies, empowering the industry to adeptly address subjective perceptions and ambiguous data, enhancing the decision-making framework for automotive technology evolution. This paper navigates the intricate landscape of automation degree selection within the automotive industry evolution, employing a structured approach merging fuzzy AHP and fuzzy CODAS methods by utilizing Continuous Intuitionistic Fuzzy Set (CINFUS). This approach not only brings a new perspective to autonomous vehicles but also highlights the importance of choosing the right automation degree. Moreover, a sensitivity analysis involved adjusting the weights assigned to different criteria within the Continuous Intuitionistic Fuzzy (CINFU) AHP framework. By systematically altering these weights and observing their impact on the final automation degree selection, decision-makers can understand the sensitivity of the chosen automation degree to changes in priority among criteria.
Energy Management System Strategy Evaluation for E-Vehicles Using Proportional Pythagorean Fuzzy AHP
(Old City Publishing Inc, 2026) Otay, Irem; Sari, Irem Ucal; Tolga, A. Cagri; Cebi, Selcuk; Onar, Sezi Cevik; Oztaysi, Basar
The shift from conventional vehicles to electric vehicles (EVs) is essential for sustainability. Energy management strategies play a crucial role in this transition, as they affect battery performance, extend lifespan, and ensure cost-effectiveness. This study evaluates energy management system (EMS) strategies for EVs using the Proportional Pythagorean Fuzzy Analytical Hierarchy Process (PPF-AHP) to prioritize decision criteria. To achieve this, a decision model is constructed involving four main criteria-sustainability and resilience, cost efficiency, performance and reliability, and competitiveness-as well as sixteen sub-criteria. Then, pairwise evaluations from five experts are collected and aggregated leading to the prioritization of decision criteria. In order to show the robustness of the methodology, the PPF-AHP results are compared with Buckley's Fuzzy AHP and Decomposed Fuzzy AHP.
Engineering economic analysis of solar energy investments using spherical fuzzy sets
(World Scientific Publ Co Pte Ltd, 2020) Onar, Sezi Cevik; Oztaysi, Bazar; Kahraman, Cengiz; Otay, Irem
Solar energy is a reliable energy source that is important for the environmental sustainability. Solar energy investments become crucial for the countries like Turkey that does not have natural fossil based fuels but has a great potential of solar energy. In order to give better solar energy investment decisions, the uncertainties and ambiguities inherit in the investment decisions should be considered. Spherical fuzzy sets enable us to deal with uncertainty and ambiguity. The membership, non-membership and the hesitancies are considered in Spherical fuzzy sets, In this study a Spherical fuzzy set based net present worth analysis is proposed to deal with uncertain solar energy investments. The applicability of the proposed model is shown by an application. In this application, a solar power plant investment is evaluated by using the proposed model.
Evaluating Hydrogen Production Technologies for Transportation in California Using Decomposed Fuzzy Sets
(Springer International Publishing Ag, 2024) Jaller, Miguel; Otay, Irem
Rapid decarbonization of our economies is imperative if we want to get a chance to curb climate change. Different nations and entities have been developing strategies and plans to decarbonize. The transportation sector, especially freight, is a vital component of everyday life, and the economy is one of the largest contributors to negative externalities such as greenhouse gases and local pollutants. It has also received increased pressure to mitigate its impacts. In California, for example, different policies are promoting the use of cleaner vehicle technologies and fuels. Battery electric and fuel cell (hydrogen) trucks are among the most prominent zero-emission truck technologies for transitioning various freight vocations. Today, technologies and fuels are at different stages of market readiness for mass adoption, and research is trying to identify the best uses for each technology. However, there has been a realization that the supporting infrastructure will play a key role in determining the various options' technical, operational, and financial viability. For hydrogen, there are various production processes with different costs, environmental impacts, technical requirements, and uncertainties, and there is an urgency to invest in developing those technologies and increasing production capacity. Therefore, this paper evaluates different hydrogen production technologies (e.g., electrolysis, biomass gasification, steam methane reforming, pyrolysis, and water splitting) and their potential role in California plans. The study implements an expert-based assessment using the Decomposed Fuzzy Sets (DFS)-based Analytic Hierarchy Process (AHP) methodology to evaluate the technologies' performance against various criteria (environmental, economic, technical, transport and delivery, and social). The study's results provide additional information to address a real-life hydrogen production technologies prioritization problem and perform sensitivity analysis to test the robustness and applicability of the method.
Financial Performance Evaluation of Leading Retail Companies in BIST Utilizing Decomposed Fuzzy TOPSIS
(Springer International Publishing Ag, 2024) Barutbas, Kaan; Bulut, Bayram; Otay, Irem
Evaluation of the financial performance of companies has a wide range of applications and indicators. The evaluation process has become much more complicated and crucial especially during and after the pandemics. Fuzzy sets were first introduced to be able to cope with uncertainty and vagueness in real-world applications. Since its introduction, various extensions of fuzzy sets have developed. In this paper, decomposed fuzzy sets (DFS) which were recently proposed fuzzy set extensions have been utilized. In this study, the Decomposed Fuzzy Technique for Order Preference by Similarities to Ideal Solution (DF TOPSIS) has been applied to assess leading retail companies in Borsa Istanbul (BIST). According to this approach, the criteria set has been determined by literature review and experts' opinions and the leading companies in ISE have been evaluated based on the determined criteria set. Considering the vagueness and imprecise information in the decision-making environment, we believe this study will create a strong roadmap for those such as stakeholders and investors who are interested in analyzing the financial performance of the companies.
Indoor location tracking technology evaluation by using spherial fuzzy TOPSIS method
(World Scientific Publ Co Pte Ltd, 2020) Oztaysi, Basar; Kahraman, Cengiz; Onar, Sezi Cevik; Otay, Irem
With the emerging technologies, collecting and processing data about the behaviors of customers or employees in a specific location has become possible. The purpose of this paper is to evaluate existing data collection technologies. Technology evaluation problem is handled as a multi-criteria decision-making (MCDM) problem. In this manner, a decision model containing four criteria and four alternatives are formed. In this study, we use Spherical Fuzzy TOPSIS method to solve the technology selection problem.
Industry 4.0 project prioritization by using spherical fuzzy analytic hierarchy process
(World Scientific Publ Co Pte Ltd, 2020) Oztaysi, Basar; Onar, Sezi Cevik; Kahraman, Cengiz; Otay, Irem
Industry 4.0, indicated as the Fourth Industrial Revolution, also pointed out as integrated industry, smart manufacturing and industrial internet of things, has taken a great attention in terms of the potential to reflect entire industries' actions by transforming the production to a fully automated and self-coordinated digital system. This transformation process necessitates the significant amount of investments and resources to be additionally, adaptation to the current operational technologies to new initiatives could be problematic. In this study we focus on Industry 4.0 project prioritization by using Spherical Fuzzy Analytic Hierarchy Process. In the application part, we prioritize five projects according to four main project selection criteria.
Interval-Valued Proportional Intuitionistic Fuzzy AHP & EDAS Methodology: Evaluation of Low-Cost Airlines in Europe
(Springer International Publishing Ag, 2025) Bulut, Bayram; Barutbas, Kaan; Otay, Irem
This study introduces an integrated Multi Criteria Decision Making (MCDM) methodology which combines the Evaluation Based on Distance from Average Solution (EDAS) method and Analytic Hierarchy Process (AHP) methods by utilizing Interval-Valued Proportional Intuitionistic Fuzzy Sets (IVPIFSs) for the first time in the literature. The proposed methodology is used to assess lowcost airlines in Europe. While Interval-Valued Proportional Intuitionistic Fuzzy (IVPIF) AHP method incorporates experts' hesitant judgments to calculate the relative weights of evaluation criteria, IVPIF EDAS technique ranks alternatives according to their performances on the considered criteria set. Through the resolution of ambiguous and contradictory data in airlines' evaluations, the suggested integrated framework improves the reliability of decision-making processes. The model's ability to rank carriers scrutinizing a variety of criteria such as on-time performance, cost effectiveness, and service quality, is demonstrated through a case study involving significant European low-cost airlines. The proposed methodology is realized successfully to the problem and the findings provide valuable insights to travelers, stakeholders, and related actors based on the airline service strategies in the low-cost aviation sector.
Interval-Valued Pythagorean Fuzzy AHP&TOPSIS for ERP Software Selection
(Springer International Publishing Ag, 2022) Dalyan, Tugba; Otay, Irem; Gulada, Mehmet
The selection of an Enterprise Resource Planning (ERP) system is considerably important since it has effects on the productivity of companies. This paper aims to choose the best decision for ERP software over many conflicting criteria by using Pythagorean fuzzy (PF) Analytic Hierarchy Process (AHP) that integrated with Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. The proposed model includes a hierarchical structure with four main criteria which are finance, technology, usability and corporate, twenty two sub-criteria and several alternatives. In this study, the evaluations are expressed using interval-valued PF sets that consist of membership and non-membership values, where the square sum of these degrees is at most 1. The weights of the criteria are computed using interval-valued PF AHP. Then, fuzzy TOPSIS method is utilized to evaluate alternatives by considering distances of alternatives to negative and positive ideal solutions (NIS, PIS), respectively. This attempt using interval-valued PF AHP-TOPSIS is deemed to be a significant contribution toward ERP selection problem.
Multi-expert disaster risk management & response capabilities assessment using interval-valued intuitionistic fuzzy sets
(Ios Press, 2020) Otay, Irem; Jaller, Miguel
This study focuses on the evaluation of disaster risk management and response (DRMR) processes and capabilities using a multi-expert multi-criteria decision making (MCDM) framework. The proposed framework considers four sets of evaluation and performance criteria: risk knowledge and organization, risk reduction, disaster response management, and disaster response support; and 22 sub-criteria such as regulating risk management, financial management, energy, and public safety. To contend with random perception and utility, lack of information and subjectivity in the human (expert) judgment processes that could be present in expert-based models, the authors propose an interval-valued intuitionistic fuzzy sets (IVIFSs) approach. IVIFSs can handle high levels of uncertainty and define appropriate membership functions. Specifically, the proposed approach incorporates score judgement and possibility degree matrices, and estimates the local and global weights for each assessment criteria. And finally, evaluates the overall performances of the alternatives using intuitionistic fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) approach. The authors implemented the framework to the Atlantico State of Colombia, and assessed the disaster risk management and response processes for each for the State's 23 municipalities. The authors discuss sensitivity analysis that illustrates the robustness of the results.
Proportional Spherical Fuzzy AHP & COPRAS: Evaluation of Intelligent Strategies for Smart Cities
(Springer International Publishing Ag, 2025) Otay, Irem; Kahraman, Cengiz
Evaluation of smart cities involves many intangible criteria that are difficult to handle with classical sets. Inclusion of these intangible criteria in the numerical decision making models can be managed successfully through fuzzy set theory. In this study, an integrated Multi Criteria Decision Making (MCDM) methodology is proposed using proportional spherical fuzzy sets to prioritize smart city strategies. This methodology consists of fuzzy Analytic Hierarchy Process (AHP) to obtain weights and fuzzy COmplex PRoportional ASsessment (COPRAS) methods to evaluate alternative intelligence-based smart city strategies. The proposed methodology takes advantage of utilizing COPRAS method which defines a solution considering the ratio to the ideal solution and the ratio with the ideal-worst solution. The proposed fuzzy methodology is successfully applied to the considered problem.
q-spherical fuzzy sets and their usage in multi-attribute decision making
(World Scientific Publ Co Pte Ltd, 2020) Kahraman, Cengiz; Oztaysi, Basar; Onar, Sezi Cevik; Otay, Irem
Intuitionistic fuzzy sets (IFS) have been very popular in the literature after they were introduced by Atanassov (1986). Several extensions of IFS have been proposed such as Pythagorean fuzzy sets (PFS), fermatean fuzzy sets (FFS), q-rung orthopair fuzzy sets, picture fuzzy sets (PiFS), and spherical fuzzy sets (SFS). The main difference among these extensions is the number of independent membership function parameters such as membership degree, non-membership degree, and hesitancy degree. Similar to q-rung orthopair fuzzy sets, picture fuzzy sets can be extended to q-spherical fuzzy sets. This idea is handled in this paper and some operations of q-Spherical fuzzy sets are presented.
Score and accuracy functions for different types of spherical fuzzy sets
(World Scientific Publ Co Pte Ltd, 2020) Otay, Irem; Kahraman, Cengiz; Oztaysi, Basar; Onar, Sezi Cevik
Spherical fuzzy sets are the latest extension of the ordinary fuzzy sets, which are based on three independent parameters, namely membership degree, non-membership degree and hesitancy degree. The squared sum of these parameters must be equal or less than 1. Several papers have been published on the arithmetic operations, aggregation operators, defuzzification operations and many others in the literature. However, there are still gaps in these operations for different types of spherical fuzzy numbers such as triangular, trapezoidal, and left-right (LR) fuzzy numbers. In this paper, we focus on score and accuracy functions for several types of spherical fuzzy numbers by illustrating numerical examples.
Selection of learning analytics projects by using spherical fuzzy TOPSIS
(World Scientific Publ Co Pte Ltd, 2020) Onart, Sezi Cevik; Kahraman, Cengiz; Oztaysi, Basar; Otay, Irem
Learning analytics is the measurement of student progress by the collecting, analysis and reporting data in the learning environment. Learning analytics methods try to find out the dependent pattern in dataset gathered. Learning Analytics improve student outcomes in several ways, first, using learning analytics leads to measure student success correctly. With this information students can find accurate teaching techniques and support themselves. Also, it gives proper and faster feedback about learning technique to the stakeholders (principals, teachers, parents). The scope and the aim of learning analytic projects may differ for different organizations. Selecting the right learning analytic project is crucial for the overall success of the learning process. Despite their benefits, while selecting the learning analytic projects not only financial benefits but also various factors including Privacy, Access, Transparency, Security, Accuracy, Restrictions, and Ownership should be taken into account. Yet, evaluating these factors is not easy since they involve uncertainties. Therefore, the selection of learning analytic projects is a complex process that includes various uncertainties. In this study, we utilize an Spherical fuzzy TOPSIS approach for selecting Learning Analytics Projects This method enabled us defining the uncertainties with independent parameters.
Tech-center location selection by interval-valued spherical fuzzy AHP based MULTIMOORA methodology
(Springer, 2023) Otay, Irem
Intense market competition, changes in demand structure and acceleration in the technological developments have led companies to offer innovative and technology driven solutions in order to have competitive advantage and to survive in the market. In this aspect, tech-centers offering technological & innovative engineering solutions, and providing customized services to the needs of the companies, have taken attentions of academicians and practitioners. In this study, a tech-center location evaluation problem having a strategic and complex structure on the success and performance of the engineering companies, is analyzed. By considering inherent uncertainties and lack of information in the multi-criteria & multi-expert based tech-center location selection problem, the fuzzy set theory as a tool of artificial intelligence is employed. In the study, one of the recently proposed fuzzy sets namely Spherical fuzzy sets are used to handle uncertainty in a better way by incorporating a larger domain. According to the best knowledge of the authors, it is the first study concentrating on tech-centers and employing an integrated interval-valued Spherical fuzzy Analytic Hierarchy Process (AHP) & MULTIMOORA methodology to solve location selection problem of a tech-center. In the study, a novel defuzzification function is also presented. In the application section, a case of a company planning to launch a tech-center is analyzed. Moreover, sensitivity analysis is applied to test the applicability and robustness of the method. The results of the proposed multi-expert Spherical fuzzy methodology are also compared with the results of AHP & MULTIMOORA methodology utilizing interval-valued intuitionistic fuzzy sets.

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