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Symmetry
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Neutrosophic Theories Applied in Engineering
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Neutrosophic Theories Applied in Engineering

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (15 October 2017) | Viewed by 67672

Special Issue Editors

Prof. Dr. Florentin Smarandache

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Guest Editor
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
Interests: neutrosophic probability; neutrosophic statistics; neutrosophic algebraic structures; plithogenic set; unmatter; superluminal physics; paradoxism; quantum paradoxes
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jun Ye

E-Mail Website
Guest Editor
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
Interests: soft computing; fuzzy decision theory and method; robot intelligent control; pattern recognition and fault diagnosis; neutrosophic theory; rock mechanics; engineering modeling; optimization design
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Neutrosophic sets and logic are generalizations of fuzzy and intuitionistic fuzzy sets and logic.

Neutrosophic sets and logic are gaining significant attention in solving many real life decision making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. They have been applied in computational intelligence, multiple criteria decision making, image processing, medical diagnoses, etc.

This Special Issue invites original research papers that report on state-of-the-art and recent advancements in neutrosophic sets and logic in soft computing, artificial intelligence, big and small data mining, decision making problems, and practical achievements.

Prof. Dr. Florentin Smarandache
Prof. Jun Ye
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (15 papers)

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Research

1298 KiB  
Article
Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups
by Xiaohong Zhang, Florentin Smarandache and Xingliang Liang
Symmetry 2017, 9(11), 275; https://doi.org/10.3390/sym9110275 - 14 Nov 2017
Cited by 56 | Viewed by 4413
Abstract
The notions of the neutrosophic triplet and neutrosophic duplet were introduced by Florentin Smarandache. From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic [...] Read more.
The notions of the neutrosophic triplet and neutrosophic duplet were introduced by Florentin Smarandache. From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic duplet semi-groups, and cancellable neutrosophic triplet groups. First, some new properties of neutrosophic duplet semi-groups are funded, and the following important result is proven: there is no finite neutrosophic duplet semi-group. Second, the new concepts of weak neutrosophic duplet, weak neutrosophic duplet set, and weak neutrosophic duplet semi-group are introduced, some examples are given by using the mathematical software MATLAB (MathWorks, Inc., Natick, MA, USA), and the characterizations of cancellable weak neutrosophic duplet semi-groups are established. Third, the cancellable neutrosophic triplet groups are investigated, and the following important result is proven: the concept of cancellable neutrosophic triplet group and group coincide. Finally, the neutrosophic triplets and weak neutrosophic duplets in BCI-algebras are discussed. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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2360 KiB  
Article
A Retinal Vessel Detection Approach Based on Shearlet Transform and Indeterminacy Filtering on Fundus Images
by Yanhui Guo, Ümit Budak, Abdulkadir Şengür and Florentin Smarandache
Symmetry 2017, 9(10), 235; https://doi.org/10.3390/sym9100235 - 19 Oct 2017
Cited by 34 | Viewed by 5055
Abstract
A fundus image is an effective tool for ophthalmologists studying eye diseases. Retinal vessel detection is a significant task in the identification of retinal disease regions. This study presents a retinal vessel detection approach using shearlet transform and indeterminacy filtering. The fundus image’s [...] Read more.
A fundus image is an effective tool for ophthalmologists studying eye diseases. Retinal vessel detection is a significant task in the identification of retinal disease regions. This study presents a retinal vessel detection approach using shearlet transform and indeterminacy filtering. The fundus image’s green channel is mapped in the neutrosophic domain via shearlet transform. The neutrosophic domain images are then filtered with an indeterminacy filter to reduce the indeterminacy information. A neural network classifier is employed to identify the pixels whose inputs are the features in neutrosophic images. The proposed approach is tested on two datasets, and a receiver operating characteristic curve and the area under the curve are employed to evaluate experimental results quantitatively. The area under the curve values are 0.9476 and 0.9469 for each dataset respectively, and 0.9439 for both datasets. The comparison with the other algorithms also illustrates that the proposed method yields the highest evaluation measurement value and demonstrates the efficiency and accuracy of the proposed method. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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1688 KiB  
Article
Scale Effect and Anisotropy Analyzed for Neutrosophic Numbers of Rock Joint Roughness Coefficient Based on Neutrosophic Statistics
by Jiqian Chen, Jun Ye and Shigui Du
Symmetry 2017, 9(10), 208; https://doi.org/10.3390/sym9100208 - 01 Oct 2017
Cited by 172 | Viewed by 4208
Abstract
In rock mechanics, the study of shear strength on the structural surface is crucial to evaluating the stability of engineering rock mass. In order to determine the shear strength, a key parameter is the joint roughness coefficient (JRC). To express and analyze JRC [...] Read more.
In rock mechanics, the study of shear strength on the structural surface is crucial to evaluating the stability of engineering rock mass. In order to determine the shear strength, a key parameter is the joint roughness coefficient (JRC). To express and analyze JRC values, Ye et al. have proposed JRC neutrosophic numbers (JRC-NNs) and fitting functions of JRC-NNs, which are obtained by the classical statistics and curve fitting in the current method. Although the JRC-NNs and JRC-NN functions contain much more information (partial determinate and partial indeterminate information) than the crisp JRC values and functions in classical methods, the JRC functions and the JRC-NN functions may also lose some useful information in the fitting process and result in the function distortion of JRC values. Sometimes, some complex fitting functions may also result in the difficulty of their expressions and analyses in actual applications. To solve these issues, we can combine the neutrosophic numbers with neutrosophic statistics to realize the neutrosophic statistical analysis of JRC-NNs for easily analyzing the characteristics (scale effect and anisotropy) of JRC values. In this study, by means of the neutrosophic average values and standard deviations of JRC-NNs, rather than fitting functions, we directly analyze the scale effect and anisotropy characteristics of JRC values based on an actual case. The analysis results of the case demonstrate the feasibility and effectiveness of the proposed neutrosophic statistical analysis of JRC-NNs and can overcome the insufficiencies of the classical statistics and fitting functions. The main advantages of this study are that the proposed neutrosophic statistical analysis method not only avoids information loss but also shows its simplicity and effectiveness in the characteristic analysis of JRC. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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1186 KiB  
Article
Forecasting Model Based on Neutrosophic Logical Relationship and Jaccard Similarity
by Hongjun Guan, Shuang Guan and Aiwu Zhao
Symmetry 2017, 9(9), 191; https://doi.org/10.3390/sym9090191 - 11 Sep 2017
Cited by 16 | Viewed by 4319
Abstract
The daily fluctuation trends of a stock market are illustrated by three statuses: up, equal, and down. These can be represented by a neutrosophic set which consists of three functions—truth-membership, indeterminacy-membership, and falsity-membership. In this paper, we propose a novel forecasting model based [...] Read more.
The daily fluctuation trends of a stock market are illustrated by three statuses: up, equal, and down. These can be represented by a neutrosophic set which consists of three functions—truth-membership, indeterminacy-membership, and falsity-membership. In this paper, we propose a novel forecasting model based on neutrosophic set theory and the fuzzy logical relationships between the status of historical and current values. Firstly, the original time series of the stock market is converted to a fluctuation time series by comparing each piece of data with that of the previous day. The fluctuation time series is then fuzzified into a fuzzy-fluctuation time series in terms of the pre-defined up, equal, and down intervals. Next, the fuzzy logical relationships can be expressed by two neutrosophic sets according to the probabilities of different statuses for each current value and a certain range of corresponding histories. Finally, based on the neutrosophic logical relationships and the status of history, a Jaccard similarity measure is employed to find the most proper logical rule to forecast its future. The authentic Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) time series datasets are used as an example to illustrate the forecasting procedure and performance comparisons. The experimental results show that the proposed method can successfully forecast the stock market and other similar kinds of time series. We also apply the proposed method to forecast the Shanghai Stock Exchange Composite Index (SHSECI) to verify its effectiveness and universality. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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14798 KiB  
Article
An Efficient Image Segmentation Algorithm Using Neutrosophic Graph Cut
by Yanhui Guo, Yaman Akbulut, Abdulkadir Şengür, Rong Xia and Florentin Smarandache
Symmetry 2017, 9(9), 185; https://doi.org/10.3390/sym9090185 - 06 Sep 2017
Cited by 17 | Viewed by 4638
Abstract
Segmentation is considered as an important step in image processing and computer vision applications, which divides an input image into various non-overlapping homogenous regions and helps to interpret the image more conveniently. This paper presents an efficient image segmentation algorithm using neutrosophic graph [...] Read more.
Segmentation is considered as an important step in image processing and computer vision applications, which divides an input image into various non-overlapping homogenous regions and helps to interpret the image more conveniently. This paper presents an efficient image segmentation algorithm using neutrosophic graph cut (NGC). An image is presented in neutrosophic set, and an indeterminacy filter is constructed using the indeterminacy value of the input image, which is defined by combining the spatial information and intensity information. The indeterminacy filter reduces the indeterminacy of the spatial and intensity information. A graph is defined on the image and the weight for each pixel is represented using the value after indeterminacy filtering. The segmentation results are obtained using a maximum-flow algorithm on the graph. Numerous experiments have been taken to test its performance, and it is compared with a neutrosophic similarity clustering (NSC) segmentation algorithm and a graph-cut-based algorithm. The results indicate that the proposed NGC approach obtains better performances, both quantitatively and qualitatively. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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1385 KiB  
Article
NS-k-NN: Neutrosophic Set-Based k-Nearest Neighbors Classifier
by Yaman Akbulut, Abdulkadir Sengur, Yanhui Guo and Florentin Smarandache
Symmetry 2017, 9(9), 179; https://doi.org/10.3390/sym9090179 - 02 Sep 2017
Cited by 62 | Viewed by 5481
Abstract
k-nearest neighbors (k-NN), which is known to be a simple and efficient approach, is a non-parametric supervised classifier. It aims to determine the class label of an unknown sample by its k-nearest neighbors that are stored in a training [...] Read more.
k-nearest neighbors (k-NN), which is known to be a simple and efficient approach, is a non-parametric supervised classifier. It aims to determine the class label of an unknown sample by its k-nearest neighbors that are stored in a training set. The k-nearest neighbors are determined based on some distance functions. Although k-NN produces successful results, there have been some extensions for improving its precision. The neutrosophic set (NS) defines three memberships namely T, I and F. T, I, and F shows the truth membership degree, the false membership degree, and the indeterminacy membership degree, respectively. In this paper, the NS memberships are adopted to improve the classification performance of the k-NN classifier. A new straightforward k-NN approach is proposed based on NS theory. It calculates the NS memberships based on a supervised neutrosophic c-means (NCM) algorithm. A final belonging membership U is calculated from the NS triples as U = T + I − F . A similar final voting scheme as given in fuzzy k-NN is considered for class label determination. Extensive experiments are conducted to evaluate the proposed method’s performance. To this end, several toy and real-world datasets are used. We further compare the proposed method with k-NN, fuzzy k-NN, and two weighted k-NN schemes. The results are encouraging and the improvement is obvious. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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275 KiB  
Article
Vector Similarity Measures between Refined Simplified Neutrosophic Sets and Their Multiple Attribute Decision-Making Method
by Jiqian Chen, Jun Ye and Shigui Du
Symmetry 2017, 9(8), 153; https://doi.org/10.3390/sym9080153 - 11 Aug 2017
Cited by 25 | Viewed by 4188
Abstract
A refined single-valued/interval neutrosophic set is very suitable for the expression and application of decision-making problems with both attributes and sub-attributes since it is described by its refined truth, indeterminacy, and falsity degrees. However, existing refined single-valued/interval neutrosophic similarity measures and their decision-making [...] Read more.
A refined single-valued/interval neutrosophic set is very suitable for the expression and application of decision-making problems with both attributes and sub-attributes since it is described by its refined truth, indeterminacy, and falsity degrees. However, existing refined single-valued/interval neutrosophic similarity measures and their decision-making methods are scarcely studied in existing literature and cannot deal with this decision-making problem with the weights of both attributes and sub-attributes in a refined interval and/or single-valued neutrosophic setting. To solve the issue, this paper firstly introduces a refined simplified neutrosophic set (RSNS), which contains the refined single-valued neutrosophic set (RSVNS) and refined interval neutrosophic set (RINS), and then proposes vector similarity measures of RSNSs based on the Jaccard, Dice, and cosine measures of simplified neutrosophic sets in vector space, and the weighted Jaccard, Dice, and cosine measures of RSNSs by considering weights of both basic elements and sub-elements in RSNS. Further, a decision-making method with the weights of both attributes and sub-attributes is developed based on the weighted Jaccard, Dice, and cosine measures of RSNSs under RSNS (RINS and/or RSVNS) environments. The ranking order of all the alternatives and the best one can be determined by one of weighted vector similarity measures between each alternative and the ideal solution (ideal alternative). Finally, an actual example on the selecting problem of construction projects illustrates the application and effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
408 KiB  
Article
Evaluating Investment Risks of Metallic Mines Using an Extended TOPSIS Method with Linguistic Neutrosophic Numbers
by Weizhang Liang, Guoyan Zhao and Hao Wu
Symmetry 2017, 9(8), 149; https://doi.org/10.3390/sym9080149 - 08 Aug 2017
Cited by 52 | Viewed by 4221
Abstract
The investment in and development of mineral resources play an important role in the national economy. A good mining project investment can improve economic efficiency and increase social wealth. Faced with the complexity and uncertainty of a mine’s circumstances, there is great significance [...] Read more.
The investment in and development of mineral resources play an important role in the national economy. A good mining project investment can improve economic efficiency and increase social wealth. Faced with the complexity and uncertainty of a mine’s circumstances, there is great significance in evaluating investment risk scientifically. In order to solve practical engineering problems, this paper presents an extended TOPSIS method combined with linguistic neutrosophic numbers (LNNs). Firstly, considering that there are several qualitative risk factors of mining investment projects, the paper describes evaluation information by means of LNNs. The advantage of LNNs is that major original information is reserved with linguistic truth, indeterminacy, and false membership degrees. After that, a number of distance measures are defined. Furthermore, a common status is that the decision makers can’t determine the importance degrees of every risk factor directly for a few reasons. With respect to this situation, the paper offers a weight model based on maximizing deviation to obtain the criteria weight vector objectively. Subsequently, a decision-making approach through improving classical TOPSIS with LNNs comes into being. Next, a case study of the proposed method applied in metallic mining projects investment is given. Some comparison analysis is also submitted. At last, the discussions and conclusions are finished. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
871 KiB  
Article
A Novel Neutrosophic Weighted Extreme Learning Machine for Imbalanced Data Set
by Yaman Akbulut, Abdulkadir Şengür, Yanhui Guo and Florentin Smarandache
Symmetry 2017, 9(8), 142; https://doi.org/10.3390/sym9080142 - 03 Aug 2017
Cited by 13 | Viewed by 5398
Abstract
Extreme learning machine (ELM) is known as a kind of single-hidden layer feedforward network (SLFN), and has obtained considerable attention within the machine learning community and achieved various real-world applications. It has advantages such as good generalization performance, fast learning speed, and low [...] Read more.
Extreme learning machine (ELM) is known as a kind of single-hidden layer feedforward network (SLFN), and has obtained considerable attention within the machine learning community and achieved various real-world applications. It has advantages such as good generalization performance, fast learning speed, and low computational cost. However, the ELM might have problems in the classification of imbalanced data sets. In this paper, we present a novel weighted ELM scheme based on neutrosophic set theory, denoted as neutrosophic weighted extreme learning machine (NWELM), in which neutrosophic c-means (NCM) clustering algorithm is used for the approximation of the output weights of the ELM. We also investigate and compare NWELM with several weighted algorithms. The proposed method demonstrates advantages to compare with the previous studies on benchmarks. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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214 KiB  
Article
Another Note on Paraconsistent Neutrosophic Sets
by Francisco Gallego Lupiáñez
Symmetry 2017, 9(8), 140; https://doi.org/10.3390/sym9080140 - 02 Aug 2017
Cited by 1 | Viewed by 2815
Abstract
In an earlier paper, we proved that Smarandache’s definition of neutrosophic paraconsistent topology is neither a generalization of Çoker’s intuitionistic fuzzy topology nor a generalization of Smarandache’s neutrosophic topology. Recently, Salama and Alblowi proposed a new definition of neutrosophic topology, that generalizes Çoker’s [...] Read more.
In an earlier paper, we proved that Smarandache’s definition of neutrosophic paraconsistent topology is neither a generalization of Çoker’s intuitionistic fuzzy topology nor a generalization of Smarandache’s neutrosophic topology. Recently, Salama and Alblowi proposed a new definition of neutrosophic topology, that generalizes Çoker’s intuitionistic fuzzy topology. Here, we study this new definition and its relation to Smarandache’s paraconsistent neutrosophic sets. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
787 KiB  
Article
Merger and Acquisition Target Selection Based on Interval Neutrosophic Multigranulation Rough Sets over Two Universes
by Chao Zhang, Deyu Li, Arun Kumar Sangaiah and Said Broumi
Symmetry 2017, 9(7), 126; https://doi.org/10.3390/sym9070126 - 21 Jul 2017
Cited by 19 | Viewed by 4513
Abstract
As a significant business activity, merger and acquisition (M&A) generally means transactions in which the ownership of companies, other business organizations or their operating units are transferred or combined. In a typical M&A procedure, M&A target selection is an important issue that tends [...] Read more.
As a significant business activity, merger and acquisition (M&A) generally means transactions in which the ownership of companies, other business organizations or their operating units are transferred or combined. In a typical M&A procedure, M&A target selection is an important issue that tends to exert an increasingly significant impact on different business areas. Although some research works based on fuzzy methods have been explored on this issue, they can only deal with incomplete and uncertain information, but not inconsistent and indeterminate information that exists universally in the decision making process. Additionally, it is advantageous to solve M&A problems under the group decision making context. In order to handle these difficulties in M&A target selection background, we introduce a novel rough set model by combining interval neutrosophic sets (INSs) with multigranulation rough sets over two universes, called an interval neutrosophic (IN) multigranulation rough set over two universes. Then, we discuss the definition and some fundamental properties of the proposed model. Finally, we establish decision making rules and computing approaches for the proposed model in M&A target selection background, and the effectiveness of the decision making approach is demonstrated by an illustrative case analysis. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
613 KiB  
Article
Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making
by Zhikang Lu and Jun Ye
Symmetry 2017, 9(7), 121; https://doi.org/10.3390/sym9070121 - 18 Jul 2017
Cited by 57 | Viewed by 4189
Abstract
The neutrosophic cubic set can contain much more information to express its interval neutrosophic numbers and single-valued neutrosophic numbers simultaneously in indeterminate environments. Hence, it is a usual tool for expressing much more information in complex decision-making problems. Unfortunately, there has been no [...] Read more.
The neutrosophic cubic set can contain much more information to express its interval neutrosophic numbers and single-valued neutrosophic numbers simultaneously in indeterminate environments. Hence, it is a usual tool for expressing much more information in complex decision-making problems. Unfortunately, there has been no research on similarity measures of neutrosophic cubic sets so far. Since the similarity measure is an important mathematical tool in decision-making problems, this paper proposes three cosine measures between neutrosophic cubic sets based on the included angle cosine of two vectors, distance, and cosine functions, and investigates their properties. Then, we develop a cosine measures-based multiple attribute decision-making method under a neutrosophic cubic environment in which, from the cosine measure between each alternative (each evaluated neutrosophic cubic set) and the ideal alternative (the ideal neutrosophic cubic set), the ranking order of alternatives and the best option can be obtained, corresponding to the cosine measure values in the decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to illustrate the application and feasibility of the developed decision-making method. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
782 KiB  
Article
A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application
by Zhi-Lian Guo, Yan-Ling Liu and Hai-Long Yang
Symmetry 2017, 9(7), 119; https://doi.org/10.3390/sym9070119 - 17 Jul 2017
Cited by 17 | Viewed by 3680
Abstract
In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment. Firstly, based on the ( α , β , γ ) -cut relation [...] Read more.
In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment. Firstly, based on the ( α , β , γ ) -cut relation R ˜ { ( α , β , γ ) } , we propose a rough set model in generalized single-valued neutrosophic approximation spaces. Then, some properties of the new rough set model are discussed. Furthermore, we obtain two extended models of the new rough set model—the degree rough set model and the variable precision rough set model—and study some of their properties. Finally, we explore an example to illustrate the validity of the new rough set model. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
258 KiB  
Article
Multiple Attribute Group Decision-Making Method Based on Linguistic Neutrosophic Numbers
by Zebo Fang and Jun Ye
Symmetry 2017, 9(7), 111; https://doi.org/10.3390/sym9070111 - 07 Jul 2017
Cited by 87 | Viewed by 4779
Abstract
Existing intuitionistic linguistic variables can describe the linguistic information of both the truth/membership and falsity/non-membership degrees, but it cannot represent the indeterminate and inconsistent linguistic information. To deal with the issue, this paper originally proposes the concept of a linguistic neutrosophic number (LNN), [...] Read more.
Existing intuitionistic linguistic variables can describe the linguistic information of both the truth/membership and falsity/non-membership degrees, but it cannot represent the indeterminate and inconsistent linguistic information. To deal with the issue, this paper originally proposes the concept of a linguistic neutrosophic number (LNN), which is characterized independently by the truth, indeterminacy, and falsity linguistic variables. Then, we define the basic operational laws of LNNs and the score and accuracy functions of LNN for comparing LNNs. Next, we develop an LNN-weighted arithmetic averaging (LNNWAA) operator and an LNN-weighted geometric averaging (LNNWGA) operator to aggregate LNN information and investigate their properties. Further, a multiple attribute group decision-making method based on the proposed LNNWAA or LNNWGA operator is established under LNN environment. Finally, an illustrative example about selecting problems of investment alternatives is presented to demonstrate the application and effectiveness of the developed approach. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
515 KiB  
Article
Solving Solar-Wind Power Station Location Problem Using an Extended Weighted Aggregated Sum Product Assessment (WASPAS) Technique with Interval Neutrosophic Sets
by Ru-xin Nie, Jian-qiang Wang and Hong-yu Zhang
Symmetry 2017, 9(7), 106; https://doi.org/10.3390/sym9070106 - 04 Jul 2017
Cited by 54 | Viewed by 4557
Abstract
As one of the promising renewable energy resources, solar-wind energy has increasingly become a regional engine in leading the economy and raising competitiveness. Selecting a solar-wind power station location can contribute to efficient utilization of resource and instruct long-term development of socio-economy. Since [...] Read more.
As one of the promising renewable energy resources, solar-wind energy has increasingly become a regional engine in leading the economy and raising competitiveness. Selecting a solar-wind power station location can contribute to efficient utilization of resource and instruct long-term development of socio-economy. Since the selection procedure consists of several location alternatives and many influential criteria factors, the selection can be recognized as a multiple criteria decision-making (MCDM) problem. To better express multiple uncertainty information during the selection procedure, fuzzy set theory is introduced to manage that issue. Interval neutrosophic sets (INSs), which are characterized by truth-membership, indeterminacy-membership and falsity-membership functions in the interval numbers (INs) form, are feasible in modeling more uncertainty of reality. In this paper, a newly extended weighted aggregated sum product assessment (WASPAS) technique, which involves novel three procedures, is utilized to handle MCDM issues under INSs environment. Some modifications are conducted in the extended method comparing with the classical WASPAS method. The most obvious improvement of the extended method relies on that it can generate more realistic criteria weight information by an objective and subjective integrated criteria weight determination method. A case study concerning solar-wind power station location selection is implemented to demonstrate the applicability and rationality of the proposed method in practice. Its validity and feasibility are further verified by a sensitivity analysis and a comparative analysis. These analyses effectively reveal that the extended WASPAS technique can well match the reality and appropriately handle the solar-wind power station location selection problem. Full article
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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