Altun, Fatma; Köseoğlu, Ali; Şahin, Rıdvan

This study introduces a new set theory called bipolar fuzzy Z-number set that makes it possible to express an information both bipolar from positive and negative perspectives, and with the reliability of it. Then, besides basic set-theoretical operations and the score function, a new distance measure is also presented. Furthermore, a decision method integrating with regret theory is proposed. Additionally, to compute the weights of criteria under bipolar Z-number information, a method in which objective and subjective criterion weights are considered simultaneously is introduced by combining the weights found by SWARA and MEREC. Also, a model with standard deviation is developed to obtain decision maker’s weights. Finally, the problem of selection of paper raw material is handled to demonstrate stability and advantage of the proposed method.

Köseoğlu, Ali; Altun, Fatma; Şahin, Rıdvan

Failure mode risk prioritization is crucial in aircraft landing systems, where undetected or misjudged failures can lead to catastrophic outcomes. Effective risk analysis enables proactive maintenance and enhances aviation safety in such critical phases of flight. In this study, a novel hybrid decision-making framework is proposed to prioritize failure modes in aircraft landing systems by integrating the Multi-Attributive Border Approximation Area Comparison (MABAC) method with Prospect Theory under a q-Rung Orthopair Hesitant Fuzzy Set (q-ROHFS) environment. Traditional failure modes and effects analysis (FMEA) approaches often suffer from rigid weighting schemes, lack of sensitivity to expert hesitancy, and an inability to incorporate psychological factors such as risk aversion or subjective evaluations—especially in high-risk domains like aviation. To address these limitations, the proposed model incorporates human psychological behaviour and uncertainty in expert assessments. Prospect Theory is employed to capture decision makers’ risk attitudes and reference-dependent evaluations, while q-ROHFSs allow more flexible and comprehensive representation of hesitant and uncertain information. In this approach, Best-Worst Method (BWM) is used to determine the relative importance of risk factors for each decision maker, and their individual weights are obtained using TOPSIS-based similarity measures. A novel generalized q-ROHF Minkowski distance measure is also introduced and implemented to determine the weights of decision makers in the TOPSIS method, as well as to construct the prospect decision matrix and the distance matrix in the MABAC method, thereby enhancing computational precision. The applicability and effectiveness of the proposed method are demonstrated through a real-world case study on aircraft landing systems, and a sensitivity analysis is conducted to validate the robustness of the results. The findings highlight the method’s capability to reflect expert preferences more realistically and improve risk prioritization decisions in complex safety-critical systems.

Köseoğlu, Ali; Şahin, Rıdvan; Demir, Ümit

The Dempster–Shafer evidence theory is a very practical concept for handling uncertain information. The foundation of this theory lies in the basic probability assignment (BPA), which exclusively accounts for the degree of support attributed to focal elements (FEs). In this study, neutrosophic evidence sets (NESs) are defined to introduce additional probabilistic measures, aimed at addressing the uncertainty, imprecision, incompleteness, and inconsistency present in real-world information. The basic element of NESs is a neutrosophic basic probability assignment (NBPA), which consists of three components. The truth degree of FEs is represented by the first BPA, the second BPA represents the indeterminacy degree of FEs, and the last BPA characterizes the falsity degree of FEs. In NESs, each support degree of FEs is shown separately without any limitation. Therefore, the general concept of NESs is broader compared to traditional evidence sets and intuitionistic fuzzy evidence sets. Unlike the neutrosophic set (NS), the NBPA method assigns truth-support, uncertainty-support, and false-support degrees, as well as these support degrees, to single and multiple subsets in a discriminative framework. This paper aimed to develop some information measures for NESs, such as neutrosophic Deng entropy (NDE), neutrosophic cosine similarity measure, and neutrosophic Jousselme distance. Then, an improved method based on NDE and neutrosophic cosine similarity measure was established to combine contradictory evidence to increase the influence of reliable evidence on the one hand and to reduce the influence of unreliable evidence on the other hand. Finally, a case involving sensor data integration for target identification was studied to highlight the importance of these innovative ideas. The numerical example demonstrates that the proposed method provides more reliable and superior fusion performance compared to classical models, particularly in scenarios involving high conflict and uncertain information. However, the effectiveness of the method is partially influenced by the structure of the similarity matrix and the entropy parameters, which necessitates careful parameter tuning to achieve optimal results. These limitations are explicitly highlighted to serve as a guide for future improvements and broader applications of the method.

Köseoğlu, Ali; Altun, Fatma; Şahin, Rıdvan

Fuzzy sets (FSs) are a flexible and powerful tool for reasoning about uncertain situations that cannot be adequately expressed by classical sets. However, these sets fall short in two areas. The first is the reliability of this tool. Z-numbers are an extension of fuzzy numbers that improve the representation of uncertainty by combining two important components: restriction and reliability. The second is the problems that need to be solved simultaneously. Complex fuzzy sets (CFSs) overcome this problem by adding a second dimension to fuzzy numbers and simultaneously adding connected elements to the solution. However, they are insufficient when it comes to problems involving these two areas. We cannot express real-life problems that need to be solved at the same time and require the reliability of the information given with any set approach given in the literature. Therefore, in this study, we propose the complex fuzzy Z-number set (CFZNS), a generalization of Z-numbers and CFS, which fills this gap. We provide the operational laws of CFZNS along with some properties. Additionally, we define two essential aggregation operators called complex fuzzy Z-number weighted averaging (CFZNWA) and complex fuzzy Z-number weighted geometric (CFZNWG) operators. Then, we present an illustrative example to demonstrate the proficiency and superiority of the proposed approach. Thus, we process multiple fuzzy expressions simultaneously and take into account the reliability of these fuzzy expressions in applications. Furthermore, we compare the results with the existing set operations to confirm the advantages and demonstrate the efficiency of the proposed approach. Considering the simultaneous expression of fuzzy statements, this study can serve as a foundation for new aggregation operators and decision-making problems and can be extended to many new applications such as pattern recognition and clustering.

Köseoğlu, Ali; Şahin, Rıdvan; Kahraman, C.; Cevik Onar, S.; Cebi, S.; Oztaysi, B.; Ucal Sari, I.; Tolga, A.C.

Fuzzy sets allow elements to have partial membership in a set, represented by a membership value between 0 and 1. This feature enables fuzzy sets to model imprecise or vague concepts. Decomposed fuzzy sets, an extension of fuzzy sets, have introduced a novel perspective in the literature by incorporating the Kano model into risk assessment. These sets have also paved the way for new approaches in decision-making methods, highlighting their functional and dysfunctional elements. In this paper, we propose a distance measure for decomposed fuzzy sets and subsequently extend the TODIM method based on this distance measure to DFSs. Then, we provide a numerical example to illustrate its effectiveness and practicality.

Köseoğlu, Ali; Şahin, Rıdvan

The use of fuzzy sets, intuitionistic fuzzy sets and neutrosophic sets can often handle with real-life problems that contain incomplete and uncertain information. The 0–1 scale is used to deal with such information which is graded symmetrically and uniformly but, some problems consist of unsymmetrical and non-uniform information. Although intuitionistic multiplicative set (IMS) is a powerful tool to deal with this kind of problems, due to the dependence of hesitant information to the membership and non-membership functions in IMS, it brings a restriction to decision-makers while working on the real-life problems such as applications of correlation coefficients and clustering. In this study, we propose novel correlation coefficients (CCs) of simplified neutrosophic multiplicative sets (SNMSs) which is defined recently by removing the shortages of IMSs. Firstly, we give SNMS-based operations, fulfil the deficiencies in the theoretical background of IMS and establish a theoretical structure for the SNMS. Then, we propose novel correlation coefficients (CC) of SNMS and show some of their important properties. Finally, we apply the CCs to a clustering problem to confirm the efficiency of the proposed SNMS and its correlation coefficients.

Köseoğlu, Ali; Şahin, Rıdvan; Merdan, Mehmet

Due to the technological developments around the world, the amount of information that researchers work on increases continuously. This information density contains incomplete and uncertain data that cannot be fully expressed with crisp numbers. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are useful tools to manage such information, but these concepts use a symmetrical and uniform scale to express data, whereas real-life problems contain nonsymmetrical and non-uniform information. Intuitionistic multiplicative sets (IMSs) are effective tools for dealing with these real-life problems. However, IMSs cannot handle real-life problems completely because indeterminate information depends on membership and non-membership information of IMSs, which is a restriction for decision makers and also for decision problems. To overcome this limitation, this paper generalizes the IMSs by using simplified neutrosophic set and introduces a novel approach that is called simplified neutrosophic multiplicative sets (SNMSs). Firstly, we define SNMS, show their set-based operations, and then give a description of simplified neutrosophic multiplicative numbers (SNMNs). Based on SNMNs, we develop two simplified neutrosophic multiplicative aggregation operators on SNMNs that are called simplified neutrosophic multiplicative weighted arithmetic average operator and simplified neutrosophic multiplicative weighted geometric average operator. Furthermore, we define some simplified neutrosophic multiplicative distance measures. Finally, using a model based on water-filling algorithm for determining criteria weights, we give a numerical example to demonstrate the effectiveness of the introduced concept with the proposed simplified neutrosophic multiplicative simplified neutrosophic multiplicative-TODIM method.