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Keywords = plithogenic set

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46 pages, 478 KB  
Article
Extensions of Multidirected Graphs: Fuzzy, Neutrosophic, Plithogenic, Rough, Soft, Hypergraph, and Superhypergraph Variants
by Takaaki Fujita
Int. J. Topol. 2025, 2(3), 11; https://doi.org/10.3390/ijt2030011 - 21 Jul 2025
Viewed by 458
Abstract
Graph theory models relationships by representing entities as vertices and their interactionsas edges. To handle directionality and multiple head–tail assignments, various extensions—directed, bidirected, and multidirected graphs—have been introduced, with the multidirected graph unifying the first two. In this work, we further enrich this [...] Read more.
Graph theory models relationships by representing entities as vertices and their interactionsas edges. To handle directionality and multiple head–tail assignments, various extensions—directed, bidirected, and multidirected graphs—have been introduced, with the multidirected graph unifying the first two. In this work, we further enrich this landscape by proposing the Multidirected hypergraph, which merges the flexibility of hypergraphs and superhypergraphs to describe higher-order and hierarchical connections. Building on this, we introduce five uncertainty-aware Multidirected frameworks—fuzzy, neutrosophic, plithogenic, rough, and soft multidirected graphs—by embedding classical uncertainty models into the Multidirected setting. We outline their formal definitions, examine key structural properties, and illustrate each with examples, thereby laying groundwork for future advances in uncertain graph analysis and decision-making. Full article
15 pages, 398 KB  
Article
The Development of a Hybrid Model for Dam Site Selection Using a Fuzzy Hypersoft Set and a Plithogenic Multipolar Fuzzy Hypersoft Set
by Sheikh Zain Majid, Muhammad Saeed, Umar Ishtiaq and Ioannis K. Argyros
Foundations 2024, 4(1), 32-46; https://doi.org/10.3390/foundations4010004 - 3 Jan 2024
Viewed by 1829
Abstract
Inrecent years, there has been a notable increase in utilising multiple criteria decision-making (MCDM) methods in practical problem solving. The advancement of enhanced decision models with greater capabilities, coupled with technologies like geographic information systems (GIS) and artificial intelligence (AI), has fueled the [...] Read more.
Inrecent years, there has been a notable increase in utilising multiple criteria decision-making (MCDM) methods in practical problem solving. The advancement of enhanced decision models with greater capabilities, coupled with technologies like geographic information systems (GIS) and artificial intelligence (AI), has fueled the application of MCDM techniques across various domains. To address the scarcity of irrigation water resources in Bortala, Northwest China, the selection of a dam site has been approached using a hybrid model integrating a multipolar Fuzzy set and a plithogenic Fuzzy hypersoft set along with a GIS. This study considered criteria such as a geological layer, slope, soil type, and land cover. Four potential and reasonably suitable dam locations were identified using a dam construction suitability map developed for Bortala. Ultimately, we showcased the benefits of the innovative method, emphasizing an open, transparent, and science-based approach to selecting optimal dam sites through local studies and group discussions. The results highlight the effectiveness of the hybrid approach involving a fuzzy hypersoft set and plithogenic multipolar fuzzy hypersoft set in addressing the challenges of dam site selection. Full article
(This article belongs to the Section Mathematical Sciences)
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14 pages, 265 KB  
Article
On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices
by Hamiyet Merkepçi
Symmetry 2023, 15(8), 1494; https://doi.org/10.3390/sym15081494 - 27 Jul 2023
Cited by 8 | Viewed by 1124
Abstract
Symbolic n-plithogenic sets are considered to be modern concepts that carry within their framework both an algebraic and logical structure. The concept of symbolic n-plithogenic algebraic rings is considered to be a novel generalization of classical algebraic rings with many symmetric properties. These [...] Read more.
Symbolic n-plithogenic sets are considered to be modern concepts that carry within their framework both an algebraic and logical structure. The concept of symbolic n-plithogenic algebraic rings is considered to be a novel generalization of classical algebraic rings with many symmetric properties. These structures can be written as linear combinations of many symmetric elements taken from other classical algebraic structures, where the square symbolic k-plithogenic real matrices are square matrices with real symbolic k-plithogenic entries. In this research, we will find easy-to-use algorithms for calculating the determinant of a symbolic 3-plithogenic/4-plithogenic matrix, and for finding its inverse based on its classical components, and even for diagonalizing matrices of these types. On the other hand, we will present a new algorithm for calculating the eigenvalues and eigenvectors associated with matrices of these types. Also, the exponent of symbolic 3-plithogenic and 4-plithogenic real matrices will be presented, with many examples to clarify the novelty of this work. Full article
(This article belongs to the Special Issue Symmetry in Algebra and Its Applications)
23 pages, 1694 KB  
Article
An Integrated Decision-Making Model Based on Plithogenic-Neutrosophic Rough Number for Sustainable Financing Enterprise Selection
by Peiwen Wang, Yan Lin and Zhiping Wang
Sustainability 2022, 14(19), 12473; https://doi.org/10.3390/su141912473 - 30 Sep 2022
Cited by 3 | Viewed by 1908
Abstract
Due to the continuous improvement of people’s awareness of sustainable development, sustainable financing enterprise selection (SFES) has gradually become a hotspot in the field of multi-criteria group decision-making (MCGDM). In the environment of increasing risk factors, how to accurately and objectively select the [...] Read more.
Due to the continuous improvement of people’s awareness of sustainable development, sustainable financing enterprise selection (SFES) has gradually become a hotspot in the field of multi-criteria group decision-making (MCGDM). In the environment of increasing risk factors, how to accurately and objectively select the optimal enterprise for financing is still pending. Thus, this paper proposes an integrated plithogenic-neutrosophic rough number (P-NRN) information aggregation decision model. The model is adapted to group decision-making by taking advantages of plithogenic set operations in handling uncertainty and vagueness and the merit of NRN in eliminating imprecision and subjectivity of decision-makers (DM) in evaluating information boundaries. Then, this paper develops an MCGDM framework based on the weight determination techniques and complex proportional assessment (COPRAS). Moreover, by extending the similarity measure theory and the maximizing deviation method, the weights of DMs and risk criteria are derived, respectively. After obtaining the results of P-NRN information aggregation and weight evaluation, we apply COPRAS to conduct alternative ranking and select the optimal one. The proposed model is successfully implemented in a real case of financing enterprise selection, and comparisons with five representative tools from three decision-making phases are performed to verify the superiority of the model in dealing with uncertainty and subjectivity. Full article
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23 pages, 1080 KB  
Article
A Novel MCDM Method Based on Plithogenic Hypersoft Sets under Fuzzy Neutrosophic Environment
by Muhammad Rayees Ahmad, Muhammad Saeed, Usman Afzal and Miin-Shen Yang
Symmetry 2020, 12(11), 1855; https://doi.org/10.3390/sym12111855 - 10 Nov 2020
Cited by 28 | Viewed by 3435
Abstract
In this paper, we advance the study of plithogenic hypersoft set (PHSS). We present four classifications of PHSS that are based on the number of attributes chosen for application and the nature of alternatives or that of attribute value degree of appurtenance. These [...] Read more.
In this paper, we advance the study of plithogenic hypersoft set (PHSS). We present four classifications of PHSS that are based on the number of attributes chosen for application and the nature of alternatives or that of attribute value degree of appurtenance. These four PHSS classifications cover most of the fuzzy and neutrosophic cases that can have neutrosophic applications in symmetry. We also make explanations with an illustrative example for demonstrating these four classifications. We then propose a novel multi-criteria decision making (MCDM) method that is based on PHSS, as an extension of the technique for order preference by similarity to an ideal solution (TOPSIS). A number of real MCDM problems are complicated with uncertainty that require each selection criteria or attribute to be further subdivided into attribute values and all alternatives to be evaluated separately against each attribute value. The proposed PHSS-based TOPSIS can be used in order to solve these real MCDM problems that are precisely modeled by the concept of PHSS, in which each attribute value has a neutrosophic degree of appurtenance corresponding to each alternative under consideration, in the light of some given criteria. For a real application, a parking spot choice problem is solved by the proposed PHSS-based TOPSIS under fuzzy neutrosophic environment and it is validated by considering two different sets of alternatives along with a comparison with fuzzy TOPSIS in each case. The results are highly encouraging and a MATLAB code of the algorithm of PHSS-based TOPSIS is also complied in order to extend the scope of the work to analyze time series and in developing algorithms for graph theory, machine learning, pattern recognition, and artificial intelligence. Full article
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17 pages, 1059 KB  
Article
Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making
by Shio Gai Quek, Ganeshsree Selvachandran, Florentin Smarandache, J. Vimala, Son Hoang Le, Quang-Thinh Bui and Vassilis C. Gerogiannis
Mathematics 2020, 8(6), 965; https://doi.org/10.3390/math8060965 - 12 Jun 2020
Cited by 23 | Viewed by 4642
Abstract
Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the [...] Read more.
Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic sets have been introduced. The requirements for any function to be an entropy measure of plithogenic sets are outlined in the axiomatic definition of the plithogenic entropy using the axiomatic requirements of neutrosophic entropy. Several new formulae for the entropy measure of plithogenic sets are also introduced. The newly introduced entropy measures are then applied to a multi-attribute decision making problem related to the selection of locations. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
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