Search Results (15)

Sets, probability, and neutrosophic logic are all topics covered by neutrosophy. Moreover, the classical set, fuzzy set, and intuitionistic fuzzy set are generalized using the neutrosophic set. A neutrosophic set is a mathematical concept used to solve problems with inconsistent, ambiguous, and inaccurate data. In this article, we demonstrate some basic fixed-point theorems for any even number of compatible mappings in complete neutrosophic metric spaces. Our primary findings expand and generalize the findings previously established in the literature. Full article

The impact of neutrosophy has increased rapidly in many areas of science and technology in recent years. Furthermore, numerous applications of the neutrosophic theory have become more usual. We aim to use neutrosophy to enhance Dai–Liao conjugate gradient (CG) iterative method. In particular, we suggest and explore a new neutrosophic logic system intended to compute the essential parameter t required in Dai–Liao CG iterations. Theoretical examination and numerical experiments signify the effectiveness of the introduced method for controlling t. By incorporation of the neutrosophy in the Dai–Liao conjugate gradient principle, we established novel Dai–Liao CG iterations for solving large-scale unconstrained optimization problems. Global convergence is proved under standard assumptions and with the use of the inexact line search. Finally, computational evidence shows the computational effectiveness of the proposed fuzzy neutrosophic Dai–Liao CG method. Full article

The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we propose and investigate an improvement of line search methods for solving unconstrained nonlinear optimization models. The improvement is based on the application of symmetry involved in neutrosophic logic in determining appropriate step size for the class of descent direction methods. Theoretical analysis is performed to show the convergence of proposed iterations under the same conditions as for the related standard iterations. Mutual comparison and analysis of generated numerical results reveal better behavior of the suggested iterations compared with analogous available iterations considering the Dolan and Moré performance profiles and statistical ranking. Statistical comparison also reveals advantages of the neutrosophic improvements of the considered line search optimization methods. Full article

Skin lesion segmentation is the first and indispensable step of malignant melanoma recognition and diagnosis. At present, most of the existing skin lesions segmentation techniques often used traditional methods like optimum thresholding, etc., and deep learning methods like U-net, etc. However, the edges of skin lesions in malignant melanoma images are gradually changed in color, and this change is nonlinear. The existing methods can not effectively distinguish banded edges between lesion areas and healthy skin areas well. Aiming at the uncertainty and fuzziness of banded edges, the neutrosophic set theory is used in this paper which is better than fuzzy theory to deal with banded edge segmentation. Therefore, we proposed a neutrosophy domain-based segmentation method that contains six steps. Firstly, an image is converted into three channels and the pixel matrix of each channel is obtained. Secondly, the pixel matrixes are converted into Neutrosophic Set domain by using the neutrosophic set conversion method to express the uncertainty and fuzziness of banded edges of malignant melanoma images. Thirdly, a new Neutrosophic Entropy model is proposed to combine the three memberships according to some rules by using the transformations in the neutrosophic space to comprehensively express three memberships and highlight the banded edges of the images. Fourthly, the feature augment method is established by the difference of three components. Fifthly, the dilation is used on the neutrosophic entropy matrixes to fill in the noise region. Finally, the image that is represented by transformed matrix is segmented by the Hierarchical Gaussian Mixture Model clustering method to obtain the banded edge of the image. Qualitative and quantitative experiments are performed on malignant melanoma image dataset to evaluate the performance of the NeDSeM method. Compared with some state-of-the-art methods, our method has achieved good results in terms of performance and accuracy. Full article

Neutrosophy, the study of neutralities, is a new branch of Philosophy that has applications in many different fields of science. Inspired by the idea of Neutrosophy, Smarandache introduced NeutroAlgebraicStructures (or NeutroAlgebras) by allowing the partiality and indeterminacy to be included in the structures’ operations and/or axioms. The aim of this paper is to combine the concept of Neutrosophy with hyperstructures theory. In this regard, we introduce NeutroSemihypergroups as well as NeutroH_v-Semigroups and study their properties by providing several illustrative examples. Full article

With increasing data on the Internet, it is becoming difficult to analyze every bit and make sure it can be used efficiently for all the businesses. One useful technique using Natural Language Processing (NLP) is sentiment analysis. Various algorithms can be used to classify textual data based on various scales ranging from just positive-negative, positive-neutral-negative to a wide spectrum of emotions. While a lot of work has been done on text, only a lesser amount of research has been done on audio datasets. An audio file contains more features that can be extracted from its amplitude and frequency than a plain text file. The neutrosophic set is symmetric in nature, and similarly refined neutrosophic set that has the refined indeterminacies $I_1$ and $I_2$ in the middle between the extremes Truth T and False F. Neutrosophy which deals with the concept of indeterminacy is another not so explored topic in NLP. Though neutrosophy has been used in sentiment analysis of textual data, it has not been used in speech sentiment analysis. We have proposed a novel framework that performs sentiment analysis on audio files by calculating their Single-Valued Neutrosophic Sets (SVNS) and clustering them into positive-neutral-negative and combines these results with those obtained by performing sentiment analysis on the text files of those audio. Full article

Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion of single-valued neutrosophic ideals sets in Šostak’s sense, which is considered as a generalization of fuzzy ideals in Šostak’s sense and intuitionistic fuzzy ideals. The concept of single-valued neutrosophic ideal open local function is also introduced for a single-valued neutrosophic topological space. The basic structure, especially a basis for such generated single-valued neutrosophic topologies and several relations between different single-valued neutrosophic ideals and single-valued neutrosophic topologies, are also studied here. Finally, for the purpose of symmetry, we also define the so-called single-valued neutrosophic relations. Full article

In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and the number of types of neutralities (sub-indeterminacies) may be any finite or infinite number. Full article

The notion of Neutrosophic triplet (NT) is a new theory in Neutrosophy. Also, the v-generalized metric is a specific form of the classical metrics. In this study, we introduced the notion of neutrosophic triplet v-generalized metric space (NTVGM), and we obtained properties of NTVGM. Also, we showed that NTVGM is different from the classical metric and neutrosophic triplet metric (NTM). Furthermore, we introduced completeness of NTVGM. Full article

The notions of neutrosophy, neutrosophic algebraic structures, neutrosophic duplet and neutrosophic triplet were introduced by Florentin Smarandache. In this paper, the neutrosophic duplets of $Z_{p^n}$ , $Z_{pq}$ and $Z_{p_1{p}_2\dots p_n}$ are studied. In the case of $Z_{p^n}$ and $Z_{pq}$ , the complete characterization of neutrosophic duplets are given. In the case of $Z_{p_1\dots p_n}$ , only the neutrosophic duplets associated with $p_i$ s are provided; $i=1,2,\dots ,n$ . Some open problems related to neutrosophic duplets are proposed. Full article

Neutrosphic triplet is a new theory in neutrosophy. In a neutrosophic triplet set, there is a neutral element and antielement for each element. In this study, the concept of neutrosophic triplet partial metric space (NTPMS) is given and the properties of NTPMS are studied. We show that both classical metric and neutrosophic triplet metric (NTM) are different from NTPM. Also, we show that NTPMS can be defined with each NTMS. Furthermore, we define a contraction for NTPMS and we give a fixed point theory (FPT) for NTPMS. The FPT has been revealed as a very powerful tool in the study of nonlinear phenomena. This study is also part of the “Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets” which is a special issue. Full article

In this paper, we present a deciding technique for robotic dexterous hand configurations. This algorithm can be used to decide on how to configure a robotic hand so it can grasp objects in different scenarios. Receiving as input, several sensor signals that provide information on the object’s shape, the DSmT decision-making algorithm passes the information through several steps before deciding what hand configuration should be used for a certain object and task. The proposed decision-making method for real time control will decrease the feedback time between the command and grasped object, and can be successfully applied on robot dexterous hands. For this, we have used the Dezert–Smarandache theory which can provide information even on contradictory or uncertain systems. Full article

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its shape detection performance, in this paper, we proposed neutrosophic Hough transform (NHT). As it was proved earlier, neutrosophy theory based image processing applications were successful in noisy environments. To this end, the Hough space is initially transferred into the NS domain by calculating the NS membership triples (T, I, and F). An indeterminacy filtering is constructed where the neighborhood information is used in order to remove the indeterminacy in the spatial neighborhood of neutrosophic Hough space. The potential peaks are detected based on thresholding on the neutrosophic Hough space, and these peak locations are then used to detect the lines in the image domain. Extensive experiments on noisy and noise-free images are performed in order to show the efficiency of the proposed NHT algorithm. We also compared our proposed NHT with traditional HT and fuzzy HT methods on variety of images. The obtained results showed the efficiency of the proposed NHT on noisy images. Full article

In the latest studies concerning the sentiment polarity of words, the authors mostly consider the positive and negative constructions, without paying too much attention to the neutral words, which can have, in fact, significant sentiment degrees. More precisely, not all the neutral words have zero positivity or negativity scores, some of them having quite important nonzero scores for these polarities. At this moment, in the literature, a word is considered neutral if its positive and negative scores are equal, which implies two possibilities: (1) zero positive and negative scores; (2) nonzero, but equal positive and negative scores. It is obvious that these cases represent two different categories of neutral words that must be treated separately by a sentiment analysis task. In this paper, we present a comprehensive study about the neutral words applied to English as is developed with the aid of SentiWordNet 3.0: the publicly available lexical resource for opinion mining. We designed our study in order to provide an accurate classification of the so-called “neutral words” described in terms of sentiment scores and using measures from neutrosophy theory. The intended scope is to fill the gap concerning the neutrality aspect by giving precise measurements for the words’ objectivity. Full article