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.

Başkan, Elif; Şahin, Rıdvan; Kahraman, C.; Oztaysi, B.; Cebi, S.; Cevik Onar, S.; Tolga, C.; Ucal Sari, I.; Otay, I.

In this study, we present a new method for developing Basic Probability Assignment (BPA) using Linguistic Fuzzy Sets (LFS). Dempster-Shafer Theory (DST) is used to efficiently combine different data sources. The use of LFS provides a robust structure for managing uncertainty in decision making by representing knowledge in linguistic terms. However, effectively integrating multiple uncertain sources requires a strong probabilistic approach. To overcome this challenge, we propose a method to derive BPA values directly from linguistic terms, ensuring compatibility with the DST fusion rule. We then use the Dempster-Shafer combination rule to combine information from various sources, thereby improving the reliability of the decision-making process.

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.

Merdan, Mehmet; Merdan, Merve; Şahin, Rıdvan

In this study, solutions of random complex partial differential equations were found using the two-dimensional Sumudu transformation method(STM). The initial conditions of a deterministic equation or the non-homogeneous part of the equation are transformed into random variables to obtain a random complex partial differential equation. With the help of the properties of two-dimensional Sumudu and inverse Sumudu transformation, an approximate analytical solution of a complex partial differential equation with random constant coefficients was obtained by selecting a random variable with an initial condition of Normal and Gamma distribution. The probability characteristics of the resulting solutions, such as expected value and variance, were obtained and graphically shown with the help of the Maple package program.

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.

Şahin, Rıdvan

In order to handle simultaneously the cardinal and ordinal information in decision-making process, QUALIFLEX (QUALItative FLEXible multiple criteria method) is a very well-known decision-making approach. In this work, we extend the classical QUALIFLEX method to neutrosophic environment and develop a neutrosophic QUALIFLEX (N-QUALIFLEX) method that uses the newly defined distance-based comparison approach. It is highly effective in solving multi-criteria decision problems in which both ratings of alternatives on criteria and weights of criteria are single-valued neutrosophic numbers (SVNNs), and their aggregated values are single-valued neutrosophic hesitant fuzzy numbers (SVNHFNs). A neutrosophic hesitancy index (NHI) of a SVNHN is introduced based on degrees of the truth-membership, indeterminacy-membership and falsity-membership, which is used to measure the degree of hesitancy of SVNHN. Considering the NHIS of SVNHFNs, we propose a distance-based comparison approach to determine the magnitude of the SVNHFNs. Then, we apply the comparison approach to define the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index that are steps of the developed N-QUALIFLEX. By taking all possible permutations of alternatives with respect to the level of concordance/discordance into account, we determine the order of alternatives in final decision. Finally, a practical example on antivirus mask selection over the COVID-19 pandemic is provided to present the effectiveness and applicability of the proposed method, and a comparative study is conducted to show the advantages of the proposed method over other existing methods.

Şahin, Rıdvan; Küçük, Gökçe Dilek

Linguistic neutrosophic number (LNN) is a specific form of neutrosophic number whose elements are expressed by linguistic terms. Maclaurin symmetric mean (MSM) operator is one of the basic collection operators in the modern knowledge fusion theory. Its most important feature is to consider the interrelationships among multiple input arguments. Multiple attribute group decision-making (MAGDM) with linguistic neutrosophic information is considered. First, we present some basic concepts, then we combine the MSM operator with linguistic neutrosophic environment and develop a sequence of linguistic neutrosophic MSM operators which are the linguistic neutrosophic Maclaurin symmetric mean (LNMSM) operator, the weighted linguistic neutrosophic Maclaurin symmetric mean (WLNMSM) operator, linguistic neutrosophic dual Maclaurin symmetric mean (LNDMSM) operator, and the weighted linguistic neutrosophic dual Maclaurin symmetric mean (WLNDMSM) operator. We look into some features of them such as monotonicity, boundedness, and idempotency and then discuss some special situations of these operators. A new idea based on the WLNMSM operator is proposed to solve an MAGDM problem where evaluation information is composed of LNNs. It is worth mentioning that the weight information of the decision-makers (DMs) and the attributes are completely unknown. In conclusion, a comparison analysis is performed with the existing methods. The developed method is based on both the WLNMSM operator which considers the interrelationships among any number of input arguments and LNNs which is a combination of the neutrosophic numbers, linguistic variables. At the same time, it also has the advantages of mentioned components. So, it enables preventing the loss or distortion of the original decision information in the decision-making process.

Şahin, Rıdvan; Altun, Fatma

Recently, there has been great interest on single valued neutrosophic hesitant fuzzy set theory. When compared single valued neutrosophic set, it is more convenient for real life situations. But even in this case, there is still missing data for some decision problems. Probabilistic single valued neutrosophic hesitant fuzzy sets (PSVNHFSs) are defined to solve this problem. Even though it contains more information, it needs some improvements. In this paper, the modified PSVNHFS is defined and some improvements in the theory of PSVNHFS are proposed. Also, we improve some algebraic properties of this set theory and define a distance operator for PSVNHFSs. Then we introduce two aggregation operators called probabilistic single valued neutrosophic hesitant fuzzy weighted arithmetic average (PSVNHFWA) operator and probabilistic single valued neutrosophic hesitant fuzzy weighted geometric average (PSVNHFWG) operator related to algebraic properties presented in this paper. Also, we extend the MABAC method under the probabilistic single valued neutrosophic hesitant fuzzy set theory. Finally, we give an illustrative example to demonstrate the stability and reliability of the proposed theory.

Altun, Fatma; Şahin, Rıdvan; Güler, Coşkun

Probabilistic simplified neutrosophic set (PSNS) is an important tool to describe the vagueness existing in the real life. In this study, we define a PSNS and discuss some of theoretical set operations of PSNSs. Also we propose the concepts of module on PSNSs, as well as inner product and projection operator between two PSNSs. In relation to this new set, we introduce a probabilistic simplified neutrosophic number (PSNN). A PSNN has three components which is called probabilistic-valued truth membership degree, probabilistic-valued indeterminacy membership degree and probabilistic-valued falsity membership degree, respectively. We give some of algebraic operational rules, a score function and an accuracy function on PSNNs. Furthermore, we introduce two aggregation operators called the probabilistic simplified neutrosophic weighted arithmetic average operator and the probabilistic simplified weighted geometric average operator on PSNNs. Furthermore, we determine weights of criteria with a method that is based on fuzzy measure and develop a method based on preference function to determine weight of each decision maker. We present an extended PROMETHEE method based on PSNSs for group decision problems. Finally, as an application of this theory, we give a practice on a multi-criteria group decision making problem based on PSNNs by using extended PROMETHEE method to ensure stability of the proposed method.

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.

Aydoğdu, Ali; Şahin, Rıdvan

Our aim in this work is to obtain two new entropy measures for single valued neutrosophic sets (SVNSs) and interval neutrosophic sets (INSs). Moreover, we give the essential properties of the proposed entropies. Finally, we introduce a numerical example to show that the entropy measures are more reliable and reasonable for representing the degree of uncertainty.

Şahin, Rıdvan

Interval neutrosophic number (INN), which is descripted by the degree of truth-membership, indeterminacy-membership and falsity-membership of an element, is a powerful information tool with many application areas. The purpose of this study is to develop an extended form of COPRAS (Complex Proportional Assessment) method used for solving the decision making problems in which all the data presented by decision makers is in the form of interval neutrosophic matrix presented by INNs, and the information about criterion weights is partially known or completely unknown. In order to accomplish this goal, a new score function and an accuracy function that consider the decision maker’s risk attitude are defined under a parameter called the risk index to determine the ordering of INNs. Then, based on Maclaurin symmetric mean (MSM) operator that can capture the interrelationships among multi-input arguments, some aggregation operators are defined, such as interval neutrosophic Maclaurin symmetric mean (INMSM) operator and interval neutrosophic weighted Maclaurin symmetric mean (INWMSM) operator. Moreover, some optimization models are established to determine the subjective and objective weights of decision criteria. A numerical problem is solved to demonstrate the effective and feasible structure of the developed method. Then, a sensitive analysis is conducted according to the decision maker’s risk attitude, and the advantages of the developed method are listed. Finally, a comparison analysis is provided to present the relationships among the developed method and existing methods, and some conclusions are given at the end of the study.

Şahin, Rıdvan; Zhang, Hong-yu

Induced Choquet integral is a powerful tool to deal with imprecise or uncertain nature. This study proposes a combination process of the induced Choquet integral and neutrosophic information. We first give the operational properties of simplified neutrosophic numbers (SNNs). Then, we develop some new information aggregation operators, including an induced simplified neutrosophic correlated averaging (I-SNCA) operator and an induced simplified neutrosophic correlated geometric (I-SNCG) operator. These operators not only consider the importance of elements or their ordered positions, but also take into account the interactions phenomena among decision criteria or their ordered positions under multiple decision-makers. Moreover, we present a detailed analysis of I-SNCA and I-SNCG operators, including the properties of idempotency, commutativity and monotonicity, and study the relationships among the proposed operators and existing simplified neutrosophic aggregation operators. In order to handle the multi-criteria group decision-making (MCGDM) situations where the weights of criteria and decision-makers usually correlative and the criterion values are considered as SNNs, an approach is established based on I-SNCA operator. Finally, a numerical example is presented to demonstrate the proposed approach and to verify its effectiveness and practicality.

Şahin, Rıdvan; Küçük, Gökçe Dilek

Simplified neutrosophic set is a convenient tool proposed for dealing with complex problems; it is effective in providing more data for decision-making process. In this study, we develop a simplified neutrosophic ordered weighted distance operator which combines the neutrosophic distance measures and the ordered weighted average distance in the same formulation. It is a new handy aggregation operator that considers the situations where the input data are represented in simplified neutrosophic numbers, and it also contains diverse distance aggregation operators. Parameterized families of simplified neutrosophic ordered weighted distance operator are handled. Moreover, we establish a new neutrosophic group decision-making method based on the simplified neutrosophic ordered weighted distance operator, which has 2 extended approaches for determining the weights of decision makers and decision attributes in decision-making process, respectively. Finally, an illustrative example demonstrates the application of the proposed method. The effectiveness and advantages of the proposed method are shown by the comparative analysis with existing relative methods.

Küçük, Gökçe Dilek; Şahin, Rıdvan

The simplified neutrosophic set (SNS) is a useful model to describe the indeterminacy information which widely exists in the real world. In this paper, we develop a multicriteria decision-making (MCDM) method under simplified neutrosophic environment in which the information about weights of criteria is completely unknown, and the decision criterion values take the form of simplified neutrosophic numbers (SNNs). In order to determine the weighting vector of the criteria, we establish an optimization model based on the basic ideal of the traditional gray relational analysis (GRA) method. By solving this model, we get a simple and exact formula which can be used to determine the criterion weights. Moreover, we utilize the dice similarity measure to determine the similarity measures between each alternative decision and the related ideal decisions. Then, based on the traditional GRA method and the technique for order preference by similarity to ideal solution (TOPSIS), some calculation steps are presented for solving a simplified neutrosophic multicriteria decision-making problem with completely unknown weight information. To avoid information loss, this model does not use the aggregation process of decision information. Comparisons of the suggested methodology with other methods are also made. Finally, a numerical example and an experimental analysis are proposed to illustrate the application of the proposed model.