Linguistic neutrosophic numbers (LNN) is presented by Fang and Ye in 2017, which can describe the truth, falsity, and indeterminacy linguistic information independently. In this paper, the LNN and the Bonferroni mean operator are merged together to propose a LNN normalized weighted Bonferroni mean (LNNNWBM) operator and a LNN normalized weighted geometric Bonferroni mean (LNNNWGBM) operator and the properties of these two operators are proved. Further, multi-attribute group decision methods are introduced based on the proposed LNNNWBM and LNNNWGBM operators, and then an example is provided to demonstrate the application and validity of the proposed methods. In addition, in order to consider the effect of the parameters p and q on the decision results, different pairs of parameter values are employed to verify the decision results.
Based on the multiplicity evaluation in some real situations, this paper firstly introduces a single-valued neutrosophic multiset (SVNM) as a subclass of neutrosophic multiset (NM) to express the multiplicity information and the operational relations of SVNMs. Then, a cosine measure between SVNMs and weighted cosine measure between SVNMs are presented to measure the cosine degree between SVNMs, and their properties are investigated. Based on the weighted cosine measure of SVNMs, a multiple attribute decision-making method under a SVNM environment is proposed, in which the evaluated values of alternatives are taken in the form of SVNMs. The ranking order of all alternatives and the best one can be determined by the weighted cosine measure between every alternative and the ideal alternative. Finally, an actual application on the selecting problem illustrates the effectiveness and application of the proposed method.
Abstract:Visual object tracking is a critical task in computer vision. Challenging things always exist when an object needs to be tracked. For instance, background clutter is one of the most challenging problems. The mean-shift tracker is quite popular because of its efficiency and performance in a range of conditions. However, the challenge of background clutter also disturbs its performance. In this article, we propose a novel weighted histogram based on neutrosophic similarity score to help the mean-shift tracker discriminate the target from the background. Neutrosophic set (NS) is a new branch of philosophy for dealing with incomplete, indeterminate, and inconsistent information. In this paper, we utilize the single valued neutrosophic set (SVNS), which is a subclass of NS to improve the mean-shift tracker. First, two kinds of criteria are considered as the object feature similarity and the background feature similarity, and each bin of the weight histogram is represented in the SVNS domain via three membership functions T(Truth), I(indeterminacy), and F(Falsity). Second, the neutrosophic similarity score function is introduced to fuse those two criteria and to build the final weight histogram. Finally, a novel neutrosophic weighted mean-shift tracker is proposed. The proposed tracker is compared with several mean-shift based trackers on a dataset of 61 public sequences. The results revealed that our method outperforms other trackers, especially when confronting background clutter.
Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations based on the Einstein operation. Then, we analyze some of the relationships between these operations. For LNN aggregation problems, we put forward two kinds of LNN aggregation operators, one is the LNN Einstein weighted average operator and the other is the LNN Einstein geometry (LNNEWG) operator. Then we present a method for solving decision-making problems based on LNNEWA and LNNEWG operators in the linguistic neutrosophic environment. Finally, we apply an example to verify the feasibility of these two methods.
A neutrosophic uncertain linguistic variable is composed of an uncertain linguistic variable and a neutrosophic number, which has more advantages than both of uncertain linguistic variable and neutrosophic number in expression. Therefore, the decision-making theory and its related methods based on neutrosophic uncertain linguistic variables have received wide attention of scholars. This paper mainly studies the new expression and operations of single value neutrosophic uncertain linguistic variables and its application in multiple attribute group decision-making (MAGDM). First, a new form of single value neutrosophic uncertain linguistic set (NFSVNULS) and its operational rules are defined. Then, a new form of single value neutrosophic uncertain linguistic variable weighted arithmetic average (NFSVNULVWAA) operator and a new form of single value neutrosophic uncertain linguistic variable weighted geometric average (NFSVNULVWGA) operator are proposed. Furthermore, a MAGDM method based on the proposed aggregation operators is put forward. Finally, an example of investment is used to demonstrate the feasibility and effectiveness of the proposed method.
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