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.

AtıfScopus1·WoS1·OpenAlex2

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Şahin, Rıdvan

Graph theory that can be used to describe the relationships among several individuals has numerous applications in diverse fields such as modern sciences and technology, database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capturing. As a generalization of fuzzy set (FS) and intuitionistic fuzzy set (IFS), the concept of neutrosophic set is a more functional tool for handling indeterminate, inconsistent and uncertain information that exist in real life compared to FSs and IFSs. In this paper, we apply the graph theory to the single-valued neutrosophic sets and investigate a new kind of graph structure which is called single-valued neutrosophic graphs and is generalized the results concerning crisp graphs, fuzzy graphs and intuitionistic fuzzy graphs. Then we describe some of their theoretical properties, such as the Cartesian product, composition, union and join. By applying two different procedures to solve single-valued neutrosophic decision-making problems, a neutrosophic graph-based multicriteria decision-making model is developed to consider relationships among the multi-input arguments which cannot be handled well by means of the existing methods. Finally, two illustrative examples are given to demonstrate the applicability, feasibility, effectiveness and advantages of these two proposed approaches.

AtıfScopus38·WoS21·OpenAlex31

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Broumi, Said; Bakali, Assia; Talea, Mohamed; Smarandache, Florentin; Krishnan Kishore, K.P.; Şahin, Rıdvan

This paper provides a research of the shortest neutrosophic path with interval valued neutrosophic numbers on a network. The suggested algorithm also provides the shortest path length utilizing ranking function from the source node to the destination node. Each of the arc lengths is attributed to an interval valued neutrosophic number. Lastly, we provide a numerical example to illustrate the suggested approach.

AtıfScopus16·OpenAlex11

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Şahin, Rıdvan

Normal neutrosophic set, which allows a combination of the normal fuzzy number and the neutrosophic number, is a powerful tool for handling the incompleteness, indeterminacy and inconsistency of evaluation information. Based on the opinion of prioritized aggregation operators developed to describe the prioritization relationships among several attributes, this paper investigates some prioritized aggregation operators for aggregating the normal neutrosophic information, such as normal neutrosophic prioritized weighted averaging operator and normal neutrosophic prioritized weighted geometric operator, and then extends these operators to the generalized prioritized weighted aggregation operators, including normal neutrosophic generalized prioritized weighted averaging operator and normal neutrosophic generalized prioritized weighted geometric operator, respectively. They can take into account the prioritization facts in the aggregated information. Moreover, some of their desirable properties are investigated in detail. A multiple attribute decision-making method is developed for solving a kind of problems in which the decision attributes have different priority level commonly and they take the form of normal neutrosophic numbers. Finally, an illustrative example based on the prioritization relationship over the evaluation data is given to depict the effectiveness and feasibility of the developed decision-making method, which are then compared to the existing approaches.

AtıfScopus14·WoS18·OpenAlex20

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Şahin, Rıdvan; Liu, Peide

Simplified neutrosophic set (SNS) is an appropriate tool used to express the incompleteness, indeterminacy and uncertainty of the evaluation objects in decision-making process. In this study, we define the concept of possibility SNS including two types of information such as the neutrosophic performance provided from the evaluation objects and its possibility degree using a value ranging from zero to one. Then by extending the existing neutrosophic information, aggregation models for SNSs that cannot be used effectively to fusion the two different information described above, we propose two novel neutrosophic aggregation operators considering possibility, which are named as a possibility-induced simplified neutrosophic weighted arithmetic averaging operator and possibility-induced simplified neutrosophic weighted geometric averaging operator, and discuss their properties. Moreover, we develop a useful method based on the proposed aggregation operators for solving a multi-criteria group decision-making problem with the possibility simplified neutrosophic information, in which the weights of decision-makers and decision criteria are calculated based on entropy measure. Finally, a practical example is utilised to show the practicality and effectiveness of the proposed method.

AtıfScopus32·WoS28·OpenAlex33

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Şahin, Rıdvan; Liu, Peide

As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS. Correlation and correlation coefficient have been applied widely in many research domains and practical fields. This paper, motivated by the idea of correlation coefficients derived for HFSs, IFSs, DHFSs and SVNSs, focuses on the correlation and correlation coefficient of SVNHFSs and investigates their some basic properties in detail. By using the weighted correlation coefficient information between each alternative and the optimal alternative, a decision-making method is established to handling the single-valued neutrosophic hesitant fuzzy information. Finally, an effective example is used to demonstrate the validity and applicability of the proposed approach in decision making, and the relationship between the each existing method and the developed method is given as a comparison study.

AtıfScopus118·WoS94·OpenAlex108

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Şahin, Rıdvan

The neutrosophic set model is an important tool for dealing with real scientific and engineering applications because it can handle not only incomplete information but also the inconsistent information and indeterminate information which exist commonly in real situations. In this paper, we firstly propose two practical techniques converting an interval neutrosophic set into a fuzzy set and a single-valued neutrosophic set, respectively. Then, we define the interval neutrosophic cross-entropy in two different ways, which are based on extension of fuzzy cross-entropy and single-valued neutrosophic cross-entropy. Additionally, two multicriteria decision-making methods using the interval neutrosophic cross-entropy between an alternative and the ideal alternative are developed in order to determine the order of the alternatives and choose most preferred one(s). Finally, an illustrative example is presented to verify the proposed methods and to demonstrate their effectiveness and practicality.

AtıfScopus65·WoS62·OpenAlex72

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Şahin, Rıdvan; Liu, Peide

This paper develops a method for solving the multiple attribute decision-making problems with the single-valued neutrosophic information or interval neutrosophic information. We first propose two discrimination functions referred to as score function and accuracy function for ranking the neutrosophic numbers. An optimization model to determine the attribute weights that are partly known is established based on the maximizing deviation method. For the special situations where the information about attribute weights is completely unknown, we propose another optimization model. A practical and useful formula which can be used to determine the attribute weights is obtained by solving a proposed nonlinear optimization problem. To aggregate the neutrosophic information corresponding to each alternative, we utilize the neutrosophic weighted averaging operators which are the single-valued neutrosophic weighted averaging operator and the interval neutrosophic weighted averaging operator. Thus, we can determine the order of alternatives and choose the most desirable one(s) based on the score function and accuracy function. Finally, some illustrative examples are presented to verify the proposed approach and to present its effectiveness and practicality.

AtıfScopus151·WoS130·OpenAlex148

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Şahin, Rıdvan

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and efficiency of our accuracy function are provided by giving related examples. A fuzzy multicriteria decision making method is established to select the best alternative in multicriteria decision making process which is taken as interval-valued intuitionistic fuzzy set of criterion values for alternatives. While aggregating the interval-valued intuitionistic fuzzy information corresponding to each alternative, we utilize the interval-valued intuitionistic fuzzy weighted aggregation operators. Then the accuracy degree of the aggregated interval-valued intuitionistic fuzzy information is computed via the new proposed accuracy function. Thus, we can rank all the alternatives according to the accuracy function and choose the optimal one(s). Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach.

AtıfScopus76·WoS61·OpenAlex83

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