İlgi alanları

• MakaleAçık Erişim2026/r/gumushane/12178
  A novel decision-making approach based on regret theory under bipolar Z-number information

  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.

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• MakaleAçık Erişim2025/r/gumushane/13748
  A novel q-ROHFS prospect theory based MABAC method for failure mode risk prioritization in aircraft landing systems

  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.

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• MakaleAçık Erişim2024/r/gumushane/13956
  Aggregation operators of complex fuzzy Z-number sets and their applications in multi-criteria decision making

  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.

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• MakaleYalnız künye2020/r/gumushane/14901
  Decision making with MABAC method under probabilistic single-valued neutrosophic hesitant fuzzy environment

  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.

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• MakaleAçık Erişim2020/r/gumushane/14624
  Multi-criteria decision making approach based on PROMETHEE with probabilistic simplified neutrosophic sets

  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.

  İncele
• MakaleAçık Erişim2014/r/gumushane/15745
  On some geometric properties of a new paranormed sequence space

  Karakaya, Vatan; Altun, Fatma

  We introduce a new sequence space which is defined by the operator W=(wnk) on the sequence space ℓ(p). We define a modular functional on this space and investigate structure of this space equipped with Luxemburg norm. Also we study some geometric properties which are called Kadec-Klee, k-NUC, and uniform Opial properties and prove that this new space possesses these properties.

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