Guest Editors
Dr. S.A. Edalatpanah, Ayandegan Institute of Higher Education, Iran
Prof. Florentin Smarandache, University of New Mexico, United States
Summary
Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough studies have already been done. There are various ways such as fuzzy and intuitionistic fuzzy sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. The neutrosophic theory that was founded by Florentin Smarandache in 1998 constitutes a further generalization of fuzzy set, intuitionistic fuzzy set, picture fuzzy set, Pythagorean fuzzy set, spherical fuzzy set, etc. Since then, this logic has been applied in various domains of science and engineering. Furthermore, the plithogenic set (as a generalization of crisp, fuzzy, Intuitionistic fuzzy and neutrosophic sets) was introduced by Smarandache in 2017. The plithogenic set is a set whose elements are characterized by the attribute values.
The objective of this special issue is to compile new and recent developments in methodologies, techniques, and applications of Neutrosophic and plithogenic sets for various practical problems and demonstrate the challenging issues on these topics. We welcome authors to present state-of-the-art and recent advancements in neutrosophic and plithogenic techniques, methodologies, mixed approaches, and research directions pointing to unsolved issues. Potential topics include but are not limited to the following:
· Neutrosophic and plithogenic modelling
· Neutrosophic and plithogenic optimization
· Neutrosophic and plithogenic sets in multiple criteria decision making
· Neutrosophic and plithogenic sets in multiple objective decision making
· Neutrosophic and plithogenic sets in linear/ nonlinear systems
· Neutrosophic and plithogenic sets in Data Envelopment Analysis
· Neutrosophic and plithogenic sets in manufacturing
· Neutrosophic and plithogenic sets in lattice structure
· Neutrosophic and plithogenic sets in fault diagnosis
· Neutrosophic and plithogenic sets in Metaheuristic algorithms
· Neutrosophic and plithogenic sets in Artificial Intelligence
· Neutrosophic and plithogenic sets in neural networks and deep learning
· Neutrosophic and plithogenic sets in pattern recognition
· Neutrosophic and plithogenic sets in Virtual Reality
· Neutrosophic and plithogenic sets in big data and analytics
· Neutrosophic and plithogenic sets in image processing
· Neutrosophic and plithogenic sets in supply chain and logistics management
· Neutrosophic and plithogenic sets in information systems and e-Business
Keywords
Neutrosophic sets, plithogenic sets, optimization, decision making, big data, manufacturing, deep learning, image processing.
Published Papers
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Open Access
EDITORIAL
Introduction to the Special Issue on Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications
S. A. Edalatpanah, Florentin Smarandache
Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 817-819, 2023, DOI:10.32604/cmes.2022.024060
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract This article has no abstract.
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Open Access
ARTICLE
Neutrosophic κ-Structures in Ordered Semigroups
G. Muhiuddin, K. Porselvi, B. Elavarasan, D. Al-Kadi
Computer Modeling in Engineering & Sciences, Vol.131, No.2, pp. 979-999, 2022, DOI:10.32604/cmes.2022.018615
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract In general, ordered algebraic structures, particularly ordered semigroups, play an important role in fuzzification in
many applied areas, such as computer science, formal languages, coding theory, error correction, etc. Nowadays,
the concept of ambiguity is important in dealing with a variety of issues related to engineering modeling problems,
network theory, decision-making problems in real-life situations, and so on. Several theories have been developed
by various researchers to overcome the difficulties that arise from uncertainty, including fuzzy sets, intuitionistic
fuzzy sets, probability, soft sets, neutrosophic sets, and many more. In this paper, we focus solely on neutrosophic set
theory. In ordered…
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Open Access
ARTICLE
A New Approach to Vague Soft Bi-Topological Spaces
Arif Mehmood, Saleem Abdullah, Choonkil Park
Computer Modeling in Engineering & Sciences, Vol.131, No.1, pp. 411-428, 2022, DOI:10.32604/cmes.2022.016967
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract Fuzzy soft topology considers only membership value. It has nothing to do with the non-membership value. So an extension was needed in this direction. Vague soft topology addresses both membership and non-membership values simultaneously. Sometimes vague soft topology (single structure) is unable to address some complex structures. So an extension to vague soft bi-topology (double structure) was needed in this direction. To make this situation more meaningful, a new concept of vague soft bi-topological space is introduced and its structural characteristics are attempted with a new definition. In this article, new concept of vague soft bi-topological space (VSBTS) is initiated…
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Open Access
ARTICLE
A New Attempt to Neutrosophic Soft Bi-Topological Spaces
Arif Mehmood, Muhammad Aslam, Muhammad Imran Khan, Humera Qureshi, Choonkil Park, Jung Rye Lee
Computer Modeling in Engineering & Sciences, Vol.130, No.3, pp. 1565-1585, 2022, DOI:10.32604/cmes.2022.018518
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract In this article, new generalized neutrosophic soft *
b open set is introduced in neutrosophic soft bi-topological structurers (NSBTS) concerning soft points of the space. This new set is produced by making the marriage of soft semi-open set with soft pre-open set in neutrosophic soft topological structure. An ample of results are investigated in NSBTS on the basis of this new neutrosophic soft *
b open set. Proper examples are settled for justification of these results. The non-validity of some results is vindicated with examples.
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Open Access
ARTICLE
Dombi-Normalized Weighted Bonferroni Mean Operators with Novel Multiple-Valued Complex Neutrosophic Uncertain Linguistic Sets and Their Application in Decision Making
Tahir Mahmood, Zeeshan Ali, Dulyawit Prangchumpol, Thammarat Panityakul
Computer Modeling in Engineering & Sciences, Vol.130, No.3, pp. 1587-1623, 2022, DOI:10.32604/cmes.2022.017998
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract Although fuzzy set concepts have evolved, neutrosophic sets are attracting more attention due to the greater power of the structure of neutrosophic sets. The ability to account for components that are true, false or neither true nor false is useful in the resolution of real-life problems. However, simultaneous variations render neutrosophic sets unsuitable in specific circumstances. To enable the management of these sorts of issues, we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multi-valued complex neutrosophic uncertain linguistic sets. Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of…
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Open Access
ARTICLE
On Single Valued Neutrosophic Regularity Spaces
Yaser Saber, Fahad Alsharari, Florentin Smarandache, Mohammed Abdel-Sattar
Computer Modeling in Engineering & Sciences, Vol.130, No.3, pp. 1625-1648, 2022, DOI:10.32604/cmes.2022.017782
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract This article aims to present new terms of single-valued neutrosophic notions in the Šostak
sense, known as single-valued neutrosophic regularity spaces. Concepts such as
r-single-valued neutrosophic semi £-open,
r-single-valued neutrosophic pre-£-open,
r-single valued neutrosophic regular-£-open and
r-single valued neutrosophic α£-open are defined and their properties are studied as well as the relationship between them. Moreover, we introduce the
concept of
r-single valued neutrosophic θ£-cluster point and
r-single-valued neutrosophic γ £-cluster point,
r-θ£-closed, and θ£-closure operators and study some of their properties. Also, we present and investigate the notions of
r-single-valued neutrosophic θ£-connectedness and
r-single valued neutrosophic δ£-connectedness and investigate relationship…
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Open Access
ARTICLE
Sine Trigonometry Operational Laws for Complex Neutrosophic Sets and Their Aggregation Operators in Material Selection
D. Ajay, J. Aldring, G. Rajchakit, P. Hammachukiattikul, N. Boonsatit
Computer Modeling in Engineering & Sciences, Vol.130, No.2, pp. 1033-1076, 2022, DOI:10.32604/cmes.2022.018267
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract In this paper, sine trigonometry operational laws (ST-OLs) have been extended to neutrosophic sets (NSs) and the
operations and functionality of these laws are studied. Then, extending these ST-OLs to complex neutrosophic sets
(CNSs) forms the core of this work. Some of the mathematical properties are proved based on ST-OLs. Fundamental
operations and the distance measures between complex neutrosophic numbers (CNNs) based on the ST-OLs are
discussed with numerical illustrations. Further the arithmetic and geometric aggregation operators are established
and their properties are verified with numerical data. The general properties of the developed sine trigonometry
weighted averaging/geometric aggregation operators for…
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Open Access
ARTICLE
On Some Properties of Neutrosophic Semi Continuous and Almost Continuous Mapping
Bhimraj Basumatary, Nijwm Wary, Jeevan Krishna Khaklary, Usha Rani Basumatary
Computer Modeling in Engineering & Sciences, Vol.130, No.2, pp. 1017-1031, 2022, DOI:10.32604/cmes.2022.018066
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract The neutrality’s origin, character, and extent are studied in the Neutrosophic set. The neutrosophic set is an essential issue to research since it opens the door to a wide range of scientific and technological applications. The neutrosophic set can find its spot to research because the universe is filled with indeterminacy. Neutrosophic set is currently being developed to express uncertain, imprecise, partial, and inconsistent data. Truth membership function, indeterminacy membership function, and falsity membership function are used to express a neutrosophic set in order to address uncertainty. The neutrosophic set produces more rational conclusions in a variety of practical problems.…
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Open Access
ARTICLE
Decision-Making Problems under the Environment of m-Polar Diophantine Neutrosophic N-Soft Set
Shouzhen Zeng, Shahbaz Ali, Muhammad Khalid Mahmood, Florentin Smarandache, Daud Ahmad
Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 581-606, 2022, DOI:10.32604/cmes.2022.017397
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract Fuzzy models are present everywhere from natural to artificial structures, embodying the dynamic processes in
physical, biological, and social systems. As real-life problems are often uncertain on account of inconsistent and
indeterminate information, it seems very demanding for an expert to solve those problems using a fuzzy model.
In this regard, we develop a hybrid new model m-polar Diophantine neutrosophic N-soft set which is based on
neutrosophic set and soft set. Additionally, we define several different sorts of compliments on the proposed set.
A proposed set is a generalized form of fuzzy, soft, Pythagorean fuzzy, Pythagorean fuzzy soft, and Pythagorean…
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Open Access
ARTICLE
New Concepts on Quadripartitioned Bipolar Single Valued Neutrosophic Graph
S. Satham Hussain, G. Muhiuddin, N. Durga, D. Al-Kadi
Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 559-580, 2022, DOI:10.32604/cmes.2022.017032
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract The partition of indeterminacy function of the neutrosophic set into the contradiction part and the ignorance part represent the quadripartitioned single valued neutrosophic set. In this work, the new concept of quadripartitioned bipolar single valued neutrosophic graph is established, and the operations on it are studied. The Cartesian product, cross product, lexicographic product, strong product and composition of quadripartitioned bipolar single valued neutrosophic graph are investigated. The proposed concepts are illustrated with examples.
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Open Access
ARTICLE
Using Sieve of Eratosthenes for the Factor Analysis of Neutrosophic Form of the Five Facet Mindfulness Questionnaire as an Alternative Confirmatory Factor Analysis
Volkan Duran, Selçuk Topal, Florentin Smarandache, Said Broumi
Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 953-971, 2021, DOI:10.32604/cmes.2021.016696
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract In this study, the Five Facet Mindfulness Questionnaire which was adapted from the short form of the Five Facet
Mindfulness Questionnaire was evaluated and this scale into neutrosophic form was converted and the results of the
scale were compared for proposing new type confirmatory analysis procedure as well as developing neutrosophic
scales. The exploratory factor analysis was used in the analysis of the data. Besides, test results were analyzed
for Kaiser–Meyer–Olkin and Bartlett values, common factor variance values, scree plot graphs, and the principal
component analysis results. The sample of the study consists of 194 students in mathematics departments at…
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Open Access
ARTICLE
Neutrosophic Mathematical Programming for Optimization of Multi-Objective Sustainable Biomass Supply Chain Network Design
Mohammad Fallah, Hamed Nozari
Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 927-951, 2021, DOI:10.32604/cmes.2021.017511
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract In this paper, a multi-objective sustainable biomass supply chain network under uncertainty is designed by neutrosophic programming method. In this method, for each objective function of the problem, three functions of
truth membership, non-determination and falsehood are considered. Neutrosophic programming method in this
paper simultaneously seeks to optimize the total costs of the supply chain network, the amount of greenhouse gas
emissions, the number of potential people hired and the time of product transfer along the supply chain network. To
achieve the stated objective functions, strategic decisions such as locating potential facilities and tactical decisions
such as optimal product flow…
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Open Access
ARTICLE
A New Method to Evaluate Linear Programming Problem in Bipolar Single-Valued Neutrosophic Environment
Jamil Ahmed, Majed G. Alharbi, Muhammad Akram, Shahida Bashir
Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 881-906, 2021, DOI:10.32604/cmes.2021.017222
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract A bipolar single-valued neutrosophic set can deal with the hesitation relevant to the information of any decision
making problem in real life scenarios, where bipolar fuzzy sets may fail to handle those hesitation problems. In
this study, we first develop a new method for solving linear programming problems based on bipolar singlevalued neutrosophic sets. Further, we apply the score function to transform bipolar single-valued neutrosophic
problems into crisp linear programming problems. Moreover, we apply the proposed technique to solve fully bipolar
single-valued neutrosophic linear programming problems with non-negative triangular bipolar single-valued
neutrosophic numbers (
TBSvNNs) and non-negative trapezoidal bipolar single-valued neutrosophic…
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Open Access
ARTICLE
Investigation on the Indeterminate Information of Rock Joint Roughness through a Neutrosophic Number Approach
Changshuo Wang, Liangqing Wang, Shigui Du, Jun Ye, Rui Yong
Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 973-991, 2021, DOI:10.32604/cmes.2021.017453
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract To better estimate the rock joint shear strength, accurately determining the rock joint roughness coefficient (JRC) is the first step faced by researchers and engineers. However, there are incomplete, imprecise, and indeterminate problems during the process of calculating the JRC. This paper proposed to investigate the indeterminate information of rock joint roughness through a neutrosophic number approach and, based on this information, reported a method to capture the incomplete, uncertain, and imprecise information of the JRC in uncertain environments. The uncertainties in the JRC determination were investigated by the regression correlations based on commonly used statistical parameters, which demonstrated the…
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Open Access
ARTICLE
Novel Complex T-Spherical Dual Hesitant Uncertain Linguistic Muirhead Mean Operators and Their Application in Decision-Making
Shouzhen Zeng, Zeeshan Ali, Tahir Mahmood
Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 849-880, 2021, DOI:10.32604/cmes.2021.016727
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract In this manuscript, the theory of complex T-spherical dual hesitant uncertain linguistic set is discovered, which is the mixture of three different ideas like the complex T-spherical fuzzy set, dual hesitant fuzzy set, and uncertain linguistic set. The complex T-spherical dual hesitant uncertain linguistic set composes the uncertain linguistic set, truth grade, abstinence grade, and falsity grade. Whose real and imaginary parts are the subset of a unit interval, and some of their operational laws are also presented. The theory of complex T-spherical dual hesitant uncertain linguistic Muirhead mean operator, complex T-spherical dual hesitant uncertain linguistic weighted Muirhead mean operator,…
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Open Access
ARTICLE
An Improved Method Based on TODIM and TOPSIS for Multi-Attribute Decision-Making with Multi-Valued Neutrosophic Sets
Dongsheng Xu, Lijuan Peng
Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 907-926, 2021, DOI:10.32604/cmes.2021.016720
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract Due to the complexity of decision-making problems and the subjectivity of decision-makers in practical application, it is necessary to adopt different forms of information expression according to the actual situation of specific decision-making problems and choose the best method to solve them. Multi-valued neutrosophic set, as an extension of neutrosophic set, can more effectively and accurately describe incomplete, uncertain or inconsistent information. TODIM and TOPSIS methods are two commonly used multi-attribute decision-making methods, each of which has its advantages and disadvantages. This paper proposes a new method based on TODIM and TOPSIS to solve multi-attribute decision-making problems under multi-valued neutrosophic…
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ARTICLE
Weighted Parameterized Correlation Coefficients of Indeterminacy Fuzzy Multisets and Their Multicriteria Group Decision Making Method with Different Decision Risks
Cheng Du, Jun Ye
Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 341-354, 2021, DOI:10.32604/cmes.2021.016758
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract Real-life data introduce noise, uncertainty, and imprecision to statistical projects; it is advantageous to consider strategies to overcome these information expressions and processing problems. Neutrosophic (indeterminate) numbers can flexibly and conveniently represent the hybrid information of the partial determinacy and partial indeterminacy in an indeterminate setting, while a fuzzy multiset is a vital mathematical tool in the expression and processing of multi-valued fuzzy information with different and/or same fuzzy values. If neutrosophic numbers are introduced into fuzzy sequences in a fuzzy multiset, the introduced neutrosophic number sequences can be constructed as the neutrosophic number multiset or indeterminate fuzzy multiset. Motivated… More >
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ARTICLE
Neutrosophic N-Structures Applied to Sheffer Stroke BL-Algebras
Tugce Katican, Tahsin Oner, Akbar Rezaei, Florentin Smarandache
Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 355-372, 2021, DOI:10.32604/cmes.2021.016996
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract In this paper, we introduce a neutrosophic
N-subalgebra, a (ultra) neutrosophic
N-filter, level sets of these neutrosophic
N-structures and their properties on a Sheffer stroke BL-algebra. By defining a quasi-subalgebra of a Sheffer stroke BL-algebra, it is proved that the level set of neutrosophic
N-subalgebras on the algebraic structure is its quasi-subalgebra and vice versa. Then we show that the family of all neutrosophic
N-subalgebras of a Sheffer stroke BL-algebra forms a complete distributive lattice. After that a (ultra) neutrosophic
N-filter of a Sheffer stroke BL-algebra is described, we demonstrate that every neutrosophic
N-filter of a Sheffer stroke BL-algebra is…
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ARTICLE
The New Neutrosophic Double and Triple Exponentially Weighted Moving Average Control Charts
Ambreen Shafqat, Muhammad Aslam, Muhammad Saleem, Zameer Abbas
Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 373-391, 2021, DOI:10.32604/cmes.2021.016772
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract The concept of neutrosophic statistics is applied to propose two monitoring schemes which are an improvement of the neutrosophic exponentially weighted moving average (NEWMA) chart. In this study, two control charts are designed under the uncertain environment or neutrosophic statistical interval system, when all observations are undermined, imprecise or fuzzy. These are termed neutrosophic double and triple exponentially weighted moving average (NDEWMA and NTEWMA) control charts. For the proficiency of the proposed chart, Monte Carlo simulations are used to calculate the run-length characteristics (such as average run length (ARL), standard deviation of the run length (SDRL), percentiles (P
25, P
50, P
75))…
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ARTICLE
P-Indeterminate Vector Similarity Measures of Orthopair Neutrosophic Number Sets and Their Decision-Making Method with Indeterminate Degrees
Mailing Zhao, Jun Ye
Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 1219-1230, 2021, DOI:10.32604/cmes.2021.016871
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract In the complexity and indeterminacy of decision making (DM) environments, orthopair neutrosophic number set (ONNS) presented by Ye et al. can be described by the truth and falsity indeterminacy degrees. Then, ONNS demonstrates its advantages in the indeterminate information expression, aggregations, and DM problems with some indeterminate ranges. However, the existing research lacks some similarity measures between ONNSs. They are indispensable mathematical tools and play a crucial role in DM, pattern recognition, and clustering analysis. Thus, it is necessary to propose some similarity measures between ONNSs to supplement the gap. To solve the issue, this study firstly proposes the p-indeterminate…
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Open Access
ARTICLE
Decision Making Algorithmic Approaches Based on Parameterization of Neutrosophic Set under Hypersoft Set Environment with Fuzzy, Intuitionistic Fuzzy and Neutrosophic Settings
Atiqe Ur Rahman, Muhammad Saeed, Sultan S. Alodhaibi, Hamiden Abd El-Wahed Khalifa
Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 743-777, 2021, DOI:10.32604/cmes.2021.016736
（This article belongs to this Special Issue:
Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Abstract Hypersoft set is an extension of soft set as it further partitions each attribute into its corresponding attribute-valued set. This structure is more flexible and useful as it addresses the limitation of soft set for dealing with the scenarios having disjoint attribute-valued sets corresponding to distinct attributes. The main purpose of this study is to make the existing literature regarding neutrosophic parameterized soft set in line with the need of multi-attribute approximate function. Firstly, we conceptualize the neutrosophic parameterized hypersoft sets under the settings of fuzzy set, intuitionistic fuzzy set and neutrosophic set along with some of their elementary properties…
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