Research

21 pages, 318 KiB

Open AccessArticle

An Introduction to Single-Valued Neutrosophic Primal Theory

by Fahad Alsharari, Hanan Alohali, Yaser Saber and Florentin Smarandache

Symmetry 2024, 16(4), 402; https://doi.org/10.3390/sym16040402 - 29 Mar 2024

Viewed by 480

This article explores the interconnections among the single-valued neutrosophic grill, single-valued neutrosophic primal and their stratification, uncovering their fundamental characteristics and correlated findings. By introducing the notion of a single-valued neutrosophic primal, a broader framework including the fuzzy primal and intuitionistic fuzzy primal [...] Read more.

This article explores the interconnections among the single-valued neutrosophic grill, single-valued neutrosophic primal and their stratification, uncovering their fundamental characteristics and correlated findings. By introducing the notion of a single-valued neutrosophic primal, a broader framework including the fuzzy primal and intuitionistic fuzzy primal is established. Additionally, the concept of a single-valued neutrosophic open local function for a single-valued neutrosophic topological space is presented. We introduce an operator based on a single-valued neutrosophic primal, illustrating that the single-valued neutrosophic primal topology is finer than the single-valued neutrosophic topology. Lastly, the concept of single-valued neutrosophic open compatibility between the single-valued neutrosophic primal and single-valued neutrosophic topologies is introduced, along with the establishment of several equivalent conditions related to this notion. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

15 pages, 473 KiB

Open AccessArticle

Bipolar Fuzzy Supra Topology via (Q-) Neighborhood and Its Application in Data Mining Process

by Banu Pazar Varol and Hami Malkoç

Symmetry 2024, 16(2), 216; https://doi.org/10.3390/sym16020216 - 10 Feb 2024

Viewed by 614

Abstract

The aim of this study is to provide neighborhood structures in bipolar fuzzy supra topological space and to show the applicability of bipolar fuzzy supra topology to the medical diagnosis problem. Firstly, we give some properties related to bipolar fuzzy points and their [...] Read more.

The aim of this study is to provide neighborhood structures in bipolar fuzzy supra topological space and to show the applicability of bipolar fuzzy supra topology to the medical diagnosis problem. Firstly, we give some properties related to bipolar fuzzy points and their neighborhood structure in bipolar fuzzy supra topological spaces. Then, we consider another important structure, “quasi-coincident”, in the case of bipolar fuzzy points and bipolar fuzzy sets. Then, we introduce the corresponding neighborhood structure called “Q-neighborhood system” by using the quasi-coincident relations. Furthermore, we also investigate the characterization of bipolar fuzzy supra topological space in terms of quasi-neighborhoods. Finally, we present a new method to solve medical diagnosis problems by using the bipolar fuzzy score function. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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16 pages, 445 KiB

Open AccessArticle

A Novel Concept of Level Graph in Interval-Valued Fuzzy Graphs with Application

by Yongsheng Rao, Siran Lei, Ali Asghar Talebi and Masomeh Mojahedfar

Symmetry 2023, 15(12), 2106; https://doi.org/10.3390/sym15122106 - 23 Nov 2023

Viewed by 643

Abstract

Many problems of practical interest can be modeled and solved by using interval-valued fuzzy graph (IVFG) algorithms. An IVFG is a very useful and effective tool for studying various calculations, fields of intelligence, and computer science, such as networking, imaging, and other fields, [...] Read more.

Many problems of practical interest can be modeled and solved by using interval-valued fuzzy graph (IVFG) algorithms. An IVFG is a very useful and effective tool for studying various calculations, fields of intelligence, and computer science, such as networking, imaging, and other fields, such as biological sciences. In different applications, they present an appropriate construction means. There were limitations in the definition of fuzzy graphs (FGs), which prompted us to propose a new definition for IVFGs. Some interesting properties related to the new IVFGs are investigated, and enough conditions under which the level graph on IVFGs is equivalent are obtained. Therefore, in this study, we present the properties of a level graph (LG) of an IVFG, and four operations, the Cartesian product (CP), composition (CO), union, and join, are investigated on it. Today, in a treatment system, one of the issues that can be very valuable and important to the quality of service to patients is finding qualified and efficient people in each department, which is not an easy task. But the interval-valued fuzzy graph, as an important fuzzy graph, can help us by considering the ability of each person in the form of intervals of numbers and the effectiveness of each one on the other (according to the relationships between them) in order to find the most worthy people. So, an application of IVFG to find the most effective person in a hospital information system has been introduced. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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29 pages, 2460 KiB

Open AccessArticle

Fuzzy Logic and Its Application in the Assessment of Information Security Risk of Industrial Internet of Things

by Seyit Kerimkhulle, Zhulduz Dildebayeva, Akylbek Tokhmetov, Akzhibek Amirova, Jamalbek Tussupov, Ulzhan Makhazhanova, Alibek Adalbek, Roman Taberkhan, Alma Zakirova and Alua Salykbayeva

Symmetry 2023, 15(10), 1958; https://doi.org/10.3390/sym15101958 - 23 Oct 2023

Cited by 1 | Viewed by 1383

Abstract

This article addresses the issue of information security in the Industrial Internet of Things (IIoT) environment. Information security risk assessment in the IIoT is complicated by several factors: the complexity and heterogeneity of the system, the dynamic nature of the system, the distributed [...] Read more.

This article addresses the issue of information security in the Industrial Internet of Things (IIoT) environment. Information security risk assessment in the IIoT is complicated by several factors: the complexity and heterogeneity of the system, the dynamic nature of the system, the distributed network infrastructure, the lack of standards and guidelines, and the increased consequences of security breaches. Given these factors, information security risk assessment in the IIoT requires a comprehensive approach adapted to the peculiarities and requirements of a particular system and industry. It is necessary to use specialized risk assessment methods and to take into account the context and peculiarities of the system. The method of information security risk assessment in the IIoT, based on the mathematical apparatus of fuzzy set theory, is proposed. This paper analyzes information security threats for IIoT systems, from which the most significant criteria are selected. The rules, based on which decisions are made, are formulated in the form of logical formulas containing input parameters. Three fuzzy inference systems are used: one to estimate the probability of threat realization, another to estimate the probable damage, and a final one to estimate the information security risk for the IIoT system. Based on the proposed method, examples of calculating the information security risk assessment in the IIoT environment are provided. The proposed scientific approach can serve as a foundation for creating expert decision support systems for designing IIoT systems. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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14 pages, 335 KiB

Open AccessArticle

Baire Category Soft Sets and Their Symmetric Local Properties

by Zanyar A. Ameen and Mesfer H. Alqahtani

Symmetry 2023, 15(10), 1810; https://doi.org/10.3390/sym15101810 - 22 Sep 2023

Cited by 8 | Viewed by 713

Abstract

In this paper, we study soft sets of the first and second Baire categories. The soft sets of the first Baire category are examined to be small soft sets from the point of view of soft topology, while the soft sets of the [...] Read more.

In this paper, we study soft sets of the first and second Baire categories. The soft sets of the first Baire category are examined to be small soft sets from the point of view of soft topology, while the soft sets of the second Baire category are examined to be large. The family of soft sets of the first Baire category in a soft topological space forms a soft

σ

-ideal. This contributes to the development of the theory of soft ideal topology. The main properties of these classes of soft sets are discussed. The concepts of soft points where soft sets are of the first or second Baire category are introduced. These types of soft points are subclasses of non-cluster and cluster soft sets. Then, various results on the first and second Baire category soft points are obtained. Among others, the set of all soft points at which a soft set is of the second Baire category is soft regular closed. Moreover, we show that there is symmetry between a soft set that is of the first Baire category and a soft set in which each of its soft points is of the first Baire category. This is equivalent to saying that the union of any collection of soft open sets of the first Baire category is again a soft set of the first Baire category. The last assertion can be regarded as a generalized version of one of the fundamental theorems in topology known as the Banach Category Theorem. Furthermore, it is shown that any soft set can be represented as a disjoint soft union of two soft sets, one of the first Baire category and the other not of the first Baire category at each of its soft points. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

24 pages, 700 KiB

Open AccessArticle

Multi-Attribute Group Decision Making Based on Spherical Fuzzy Zagreb Energy

by Gang Fang, Uzma Ahmad, Sobia Ikhlaq and Leila Asgharsharghi

Symmetry 2023, 15(8), 1536; https://doi.org/10.3390/sym15081536 - 03 Aug 2023

Cited by 1 | Viewed by 1066

Abstract

Based on picture fuzzy sets (PFSs), we use a mathematical model to tackle such types of problems when a person has opinions like yes, no, abstain, and refusal. The spherical fuzzy model is more flexible and practical than the picture fuzzy model, as [...] Read more.

Based on picture fuzzy sets (PFSs), we use a mathematical model to tackle such types of problems when a person has opinions like yes, no, abstain, and refusal. The spherical fuzzy model is more flexible and practical than the picture fuzzy model, as it enhances the space of uncertainty. It broadens the space of vague information evaluated by decision makers since graphs are the pictorial representation of information. Graphs are a tool to represent a network. To handle some real-world problems, spherical fuzzy graphs can be used more effectively as compared to picture fuzzy graphs (PFGs). In this article, we expand the notion of fuzzy Zagreb indices of the fuzzy graph to the spherical fuzzy Zagreb indices of the spherical fuzzy graph (SFG). The spherical fuzzy Zagreb matrix of SFG and Zagreb energy of SFG are defined with examples. Additionally, we develop several lower and upper bounds of the spherical Zagreb energy of SFG. In addition, we present an application of SFG by computing its Zagreb energy in the decision-making problem of choosing the best location for business purposes. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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10 pages, 298 KiB

Open AccessArticle

Fuzzy Soft Sets and Decision Making in Ideal Nutrition

by Abdelfattah A. El-Atik, Radwan Abu-Gdairi, Arafa A. Nasef, Saeid Jafari and Mohammed Badr

Symmetry 2023, 15(8), 1523; https://doi.org/10.3390/sym15081523 - 02 Aug 2023

Cited by 3 | Viewed by 1015

Abstract

Issues in daily life, where making the best decisions is crucial, are frequently encountered. But, in the majority of these situations, the best course of action is uncertain. We must take into account a number of parameters in order to find the best [...] Read more.

Issues in daily life, where making the best decisions is crucial, are frequently encountered. But, in the majority of these situations, the best course of action is uncertain. We must take into account a number of parameters in order to find the best possible solution to these difficulties. The best mathematical instrument for this is fuzzy soft set

F S S

theory in decision making. Nutrition is the process of supplying cells and organisms with the nutrients they need to grow and thrive and to sustain life. A healthy diet has the potential to prevent or mitigate numerous prevalent health issues. The purpose of this paper is to select a burning problem for the nutrition of students and successfully apply the

F S S

theory in decision making. We aim to prove that the approach to decision-making problems with imprecise data via

F S S

s is more accurate than other types of approaches, and we present a new approach to the

F S S

model and its applications in decision-making problems. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

27 pages, 436 KiB

Open AccessArticle

Choquet Integral-Based Aczel–Alsina Aggregation Operators for Interval-Valued Intuitionistic Fuzzy Information and Their Application to Human Activity Recognition

by Harish Garg, Tehreem, Gia Nhu Nguyen, Tmader Alballa and Hamiden Abd El-Wahed Khalifa

Symmetry 2023, 15(7), 1438; https://doi.org/10.3390/sym15071438 - 18 Jul 2023

Cited by 1 | Viewed by 1503

Abstract

Human activity recognition (HAR) is the process of interpreting human activities with the help of electronic devices such as computer and machine version technology. Humans can be explained or clarified as gestures, behavior, and activities that are recorded by sensors. In this manuscript, [...] Read more.

Human activity recognition (HAR) is the process of interpreting human activities with the help of electronic devices such as computer and machine version technology. Humans can be explained or clarified as gestures, behavior, and activities that are recorded by sensors. In this manuscript, we concentrate on studying the problem of HAR; for this, we use the proposed theory of Aczel and Alsina, such as Aczel–Alsina (AA) norms, and the derived theory of Choquet, such as the Choquet integral in the presence of Atanassov interval-valued intuitionistic fuzzy (AIVIF) set theory for evaluating the novel concept of AIVIF Choquet integral AA averaging (AIVIFC-IAAA), AIVIF Choquet integral AA ordered averaging (AIVIFC-IAAOA), AIVIF Choquet integral AA hybrid averaging (AIVIFC-IAAHA), AIVIF Choquet integral AA geometric (AIVIFC-IAAG), AIVIF Choquet integral AA ordered geometric (AIVIFC-IAAOG), and AIVIF Choquet integral AA hybrid geometric (AIVIFC-IAAHG) operators. Many essential characteristics of the presented techniques are shown, and we also identify their properties with some results. Additionally, we take advantage of the above techniques to produce a technique to evaluate the HAR multiattribute decision-making complications. We derive a functional model for HAR problems to justify the evaluated approaches and to demonstrate their supremacy and practicality. Finally, we conduct a comparison between the proposed and prevailing techniques for the legitimacy of the invented methodologies. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

23 pages, 993 KiB

Open AccessArticle

by Arpan Singh Rajput, Shailja Shukla and Samajh Singh Thakur

Symmetry 2023, 15(7), 1385; https://doi.org/10.3390/sym15071385 - 08 Jul 2023

Viewed by 832

Abstract

A fuzzy set is a powerful tool to handle uncertainty and ambiguity, and generally, the notions of symmetry and similarity are also exhibited in the fuzzy set theory. The class of (m, n)-rung orthopair fuzzy sets through two universes are more flexible and [...] Read more.

A fuzzy set is a powerful tool to handle uncertainty and ambiguity, and generally, the notions of symmetry and similarity are also exhibited in the fuzzy set theory. The class of (m, n)-rung orthopair fuzzy sets through two universes are more flexible and efficient than the q-rung orthopair fuzzy sets when discussing the symmetry and similarity between multiple objects. This research article comprehensively investigates ten similarity measures that employ cosine and cotangent functions for comparing (m, n)-rung orthopair fuzzy sets, which are a superclass of q-rung orthopair fuzzy sets. Moreover, the proposed weighted similarity measures are applied to real-world problems in building material analysis. A comparative analysis is conducted between the proposed measures and the existing cosine and cotangent measures of q-rung orthopair fuzzy sets, showing that the proposed measures are more efficient than existing ones. Additionally, a numerical example demonstrates the practical and scientific applications of these similarity measures in classifying plant leaf diseases. The sensitivity analysis shows that the existing measures cannot be applied to (m, n)-fuzzy data for distinct values of m and n. The results are supported by graphical interpretations, further illustrating the efficacy of the proposed measures. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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16 pages, 303 KiB

Open AccessArticle

Application of the Double Fuzzy Sawi Transform for Solving a Telegraph Equation

by Atanaska Tencheva Georgieva and Albena Pavlova

Symmetry 2023, 15(4), 854; https://doi.org/10.3390/sym15040854 - 03 Apr 2023

Cited by 1 | Viewed by 824

Abstract

The main purpose of this study is to introduce a new double fuzzy transform called the double fuzzy Sawi transform. A proof of some basic properties of the single fuzzy Sawi transform and the double fuzzy Sawi transform are provided. These new results [...] Read more.

The main purpose of this study is to introduce a new double fuzzy transform called the double fuzzy Sawi transform. A proof of some basic properties of the single fuzzy Sawi transform and the double fuzzy Sawi transform are provided. These new results are implemented to obtain the exact solution of a non-homogeneous linear fuzzy telegraph equation under a generalized Hukuhara partial differentiability. In addition, by using the symmetric triangular fuzzy numbers, numerical examples are given to demonstrate the validity and superiority of the double fuzzy Sawi transform in solving the fuzzy linear telegraph equation. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

18 pages, 1527 KiB

Open AccessArticle

Multiple-Attribute Decision Making Based on Intuitionistic Hesitant Fuzzy Connection Set Environment

by Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Hamza Ghazanfar Toor, Faraz Akram, Saeid Jafari, Md. Zia Uddin and Mohammad Mehedi Hassan

Symmetry 2023, 15(3), 778; https://doi.org/10.3390/sym15030778 - 22 Mar 2023

Cited by 15 | Viewed by 1913

Abstract

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and [...] Read more.

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and handle situations more proficiently. Another related theory is the theory of set pair analysis (SPA), which considers both certainties and uncertainties as a cohesive system and represents them from three aspects: identity, discrepancy, and contrary. In this article, we explore the suitability of combining the IHFS and SPA theories in multi-attribute decision making (MADM) and present the hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). To facilitate the design of a novel MADM algorithm, we first develop several averaging and geometric aggregation operators on IHCS. Finally, we highlight the benefits of our proposed work, including a comparative examination of the recommended models with a few current models to demonstrate the practicality of an ideal decision in practice. Additionally, we provide a graphical interpretation of the devised attempt to exhibit the consistency and efficiency of our approach. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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26 pages, 404 KiB

Open AccessArticle

Fermatean Fuzzy CODAS Approach with Topology and Its Application to Sustainable Supplier Selection

by Hafiz Muhammad Athar Farid, Mohamed Bouye, Muhammad Riaz and Nimra Jamil

Symmetry 2023, 15(2), 433; https://doi.org/10.3390/sym15020433 - 06 Feb 2023

Cited by 6 | Viewed by 1524

Abstract

A Fermatean fuzzy set (FFS) is a reliable method for representing uncertainty in “multi-criteria decision-making” (MCDM). This research seeks to examine the topological properties of FFSs and to establish the notion of “Fermatean fuzzy topology” (FFT). An FFT is the generalisation of existing [...] Read more.

A Fermatean fuzzy set (FFS) is a reliable method for representing uncertainty in “multi-criteria decision-making” (MCDM). This research seeks to examine the topological properties of FFSs and to establish the notion of “Fermatean fuzzy topology” (FFT). An FFT is the generalisation of existing fuzzy topologies. Several aspects of FFT are examined and various novel concepts are proposed, which include Fermatean fuzzy

α

-continuity between FFTSs and Fermatean fuzzy connectedness. To deal multiple challenges in sustainable supply chain management, a Fermatean fuzzy “combinative distance-based assessment” (CODAS) method was developed. The proposed FF CODAS technique involves various key features for MCDM. Firstly, a known reputation vector or equal expert weights is determined based on the reputation, experience and qualifications of the experts. Secondly, the Fermatean fuzzy direct rating approach is used to establish the relative relevance of criteria based on the expert group’s evaluation preferences. Thirdly, the Fermatean fuzzy CODAS approach is used to construct alternative orderings based on their assessment scores. Finally, an application is developed to show the benefit of the suggested supplier selection approach. Additionally, the symmetry of an optimal decision in application is carried out by a comparison analysis of the suggested models with some existing models. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

25 pages, 3275 KiB

Open AccessArticle

A Novel GDMD-PROMETHEE Algorithm Based on the Maximizing Deviation Method and Social Media Data Mining for Large Group Decision Making

by Juxiang Wang, Si Li and Xiangyu Zhou

Symmetry 2023, 15(2), 387; https://doi.org/10.3390/sym15020387 - 01 Feb 2023

Cited by 6 | Viewed by 1540

Abstract

Multi-attribute group decision making is widely used in the real world, and many scholars have done a lot of research on it. The public’s focus on emergencies can provide an important reference for emergency handling decision making in the social media big data [...] Read more.

Multi-attribute group decision making is widely used in the real world, and many scholars have done a lot of research on it. The public’s focus on emergencies can provide an important reference for emergency handling decision making in the social media big data environment. Due to the complexity of emergency handling decision making, the asymmetry of user evaluation information is easy to cause the loss of important information. It is very important to mine valuable information for decision making through online reviews. Then, a generalized extended hybrid distance measure method between the probabilistic linguistic term sets is proposed. Based on this, an extended GDMD-PROMETHEE large-scale multi-attribute group decision-making method is proposed as well, which can be used to decision making under symmetric information and asymmetric information. Firstly, web crawler technology is used to explore the topics of public concern of emergency handling on social media platforms, and use

k

-means cluster analysis to classify the crawling variables, then the attributes and subjective weights of emergency handling plans are obtained by TF-IDF and Word2vec technology. Secondly, in order to better retain the linguistic evaluation information from decision-makers, a new generalized probabilistic hybrid distance measure method based on Hamming distance is proposed. Considering the difference of decision makers’ evaluation, the objective weight of decision makers is calculated by combining the maximum deviation method with the new extended hybrid Euclidean distance. On this basis, the comprehensive weights of the attributes are calculated by combining subjective and objective factors. Meanwhile, this paper realizes the distance measures and information fusion of probabilistic linguistic term sets under cumulative prospect theory, and the ranking results of the emergency handling plans based on the extended GDMD-PROMETHEE algorithm are given. Finally, the feasibility and effectiveness of the extended GDMD-PROMETHEE algorithm are verified by the case study of the explosion accident handling decision making of Shanghai “6.18” Petrochemical, and the comparative analyses between the several traditional algorithms demonstrate the extended GDMD-PROMETHEE algorithm is more scientific and superior in this paper. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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26 pages, 777 KiB

Open AccessArticle

Confidence Levels-Based Cubic Fermatean Fuzzy Aggregation Operators and Their Application to MCDM Problems

by Harish Garg, Muhammad Rahim, Fazli Amin, Saeid Jafari and Ibrahim M. Hezam

Symmetry 2023, 15(2), 260; https://doi.org/10.3390/sym15020260 - 17 Jan 2023

Cited by 7 | Viewed by 1120

Abstract

Assessment specialists (experts) are sometimes expected to provide two types of information: knowledge of rating domains and the performance of rating objects (called confidence levels). Unfortunately, the results of previous information aggregation studies cannot be properly used to combine the two categories of [...] Read more.

Assessment specialists (experts) are sometimes expected to provide two types of information: knowledge of rating domains and the performance of rating objects (called confidence levels). Unfortunately, the results of previous information aggregation studies cannot be properly used to combine the two categories of data covered above. Additionally, a significant range of symmetric/asymmetric events and structures are frequently included in the implementation process or practical use of fuzzy systems. The primary goal of the current study was to use cubic Fermatean fuzzy set features to address such situations. To deal with the ambiguous information of the aggregated arguments, we defined information aggregation operators with confidence degrees. Two of the aggregation operators we initially proposed were the confidence cubic Fermatean fuzzy weighted averaging (CCFFWA) operator and the confidence cubic Fermatean fuzzy weighted geometric (CCFFWG) operator. They were used as a framework to create an MCDM process, which was supported by an example to show how effective and applicable it is. The comparison of computed results was carried out with the help of existing approaches. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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37 pages, 4672 KiB

Open AccessArticle

Novel Complex Pythagorean Fuzzy Sets under Aczel–Alsina Operators and Their Application in Multi-Attribute Decision Making

by Huanhuan Jin, Abrar Hussain, Kifayat Ullah and Aqib Javed

Symmetry 2023, 15(1), 68; https://doi.org/10.3390/sym15010068 - 26 Dec 2022

Cited by 14 | Viewed by 1304

Abstract

Aggregation operators (AOs) are utilized to overcome the influence of uncertain and vague information in different fuzzy environments. A multi-attribute decision-making (MADM) technique plays a vital role in several fields of different environments such as networking analysis, risk assessment, cognitive science, recommender systems, [...] Read more.

Aggregation operators (AOs) are utilized to overcome the influence of uncertain and vague information in different fuzzy environments. A multi-attribute decision-making (MADM) technique plays a vital role in several fields of different environments such as networking analysis, risk assessment, cognitive science, recommender systems, signal processing, and many more domains in ambiguous circumstances. In this article, we elaborated the notion of Aczel–Alsina t-norm (TNM) and t-conorm (TCNM) under the system of complex Pythagorean fuzzy (CPyF) sets (CPyFSs). Some basic operational laws of Aczel–Alsina TNM and TCNM are established including Aczel–Alsina sum, product, scalar multiplication, and power operations based on CPyFSs. We established several AOs of CPyFSs such as CPyF Aczel–Alsina weighted average (CPyFAAWA), and CPyF Aczel–Alsina weighted geometric (CPyFAAWG) operators. The proposed CPyFAAWA and CPyFAAWG operators are symmetric in nature and satisfy the properties of idempotency, monotonicity, boundedness and commutativity. To solve an MADM technique, we established an illustrative example to select a suitable candidate for a vacant post in a multinational company. To see the advantages of our proposed AOs, we compared the results of existing AOs with the results of newly established AOs. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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21 pages, 1244 KiB

Open AccessArticle

Prioritized Aggregation Operators for Intuitionistic Fuzzy Information Based on Aczel–Alsina T-Norm and T-Conorm and Their Applications in Group Decision-Making

by Mehwish Sarfraz, Kifayat Ullah, Maria Akram, Dragan Pamucar and Darko Božanić

Symmetry 2022, 14(12), 2655; https://doi.org/10.3390/sym14122655 - 15 Dec 2022

Cited by 10 | Viewed by 5440

Abstract

In multi-attribute group decision-making (MAGDM) problems, prioritization is sometimes important. Several techniques and methods have been introduced in fuzzy systems to use prioritization. The main purpose of this paper is to propose prioritized aggregation operators (AOs) for intuitionistic fuzzy (IF) information. These AOs [...] Read more.

In multi-attribute group decision-making (MAGDM) problems, prioritization is sometimes important. Several techniques and methods have been introduced in fuzzy systems to use prioritization. The main purpose of this paper is to propose prioritized aggregation operators (AOs) for intuitionistic fuzzy (IF) information. These AOs are symmetric in nature and are based on the novel Aczel–Alsina t-norm and t-conorm. Herein, we propose IF-prioritized Aczel–Alsina averaging (IFPAAA) and IF-prioritized Aczel–Alsina geometric (IFPAAG) operators. It is shown that these AOs satisfy the basic features of aggregation. Some additional results for these AOs are also investigated. These proposed operators can capture the prioritization phenomenon among the aggregated arguments, and the weights for prioritization are obtained from expert information. Finally, the proposed AOs are used in an MAGDM problem where a doctor is selected for a hospital. A comparison of the proposed prioritized AOs is also established with other well-known AOs to show the significance of the IFPAAA and IFPAAG operators. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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19 pages, 404 KiB

Open AccessArticle

Some Properties of Cubic Fuzzy Graphs with an Application

by Xiaolong Shi, Maryam Akhoundi, Ali Asghar Talebi and Seyed Hossein Sadati

Symmetry 2022, 14(12), 2623; https://doi.org/10.3390/sym14122623 - 11 Dec 2022

Cited by 9 | Viewed by 1362

Abstract

The advent of fuzzy sets, and consequently fuzzy graphs, has solved many problems in ambiguous and uncertain contexts. It is interesting and necessary to study the Wiener index in a cubic fuzzy graph that employs both fuzzy membership and interval-valued fuzzy membership at [...] Read more.

The advent of fuzzy sets, and consequently fuzzy graphs, has solved many problems in ambiguous and uncertain contexts. It is interesting and necessary to study the Wiener index in a cubic fuzzy graph that employs both fuzzy membership and interval-valued fuzzy membership at the same time. In this paper, the Wiener index in a cubic fuzzy graph is introduced as a cubic fuzzy number and some related results are described. The comparison between connectivity index and Wiener index, changes in Wiener index through deleting a node or an edge, and determining the Wiener index in some specific cubic fuzzy graphs have been the other topics studied in this research. In addition, the Wiener index is determined by mentioning concepts of the saturated cubic fuzzy cycle. In this review, the Wiener index is shown as a combination of classical and interval numbers. The results indicate that when some vertices are removed, the Wiener index may change. However, this change will not be exclusively related to both values. Finally, an application of the Wiener index is presented in the study of the properties of some monomer molecules. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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22 pages, 461 KiB

Open AccessArticle

Bipolar Spherical Fuzzy Soft Topology with Applications to Multi-Criteria Group Decision-Making in Buildings Risk Assessment

by Adem Yolcu

Symmetry 2022, 14(11), 2362; https://doi.org/10.3390/sym14112362 - 09 Nov 2022

Cited by 2 | Viewed by 1229

Abstract

A generalized soft set model that is more accurate, useful, and realistic is the bipolar spherical fuzzy soft set (BSFSs). It is a more developed variant of current fuzzy soft set models that may be applied to characterize erroneous data in practical applications. [...] Read more.

A generalized soft set model that is more accurate, useful, and realistic is the bipolar spherical fuzzy soft set (BSFSs). It is a more developed variant of current fuzzy soft set models that may be applied to characterize erroneous data in practical applications. Bipolar spherical fuzzy soft sets and bipolar spherical fuzzy soft topology are novel ideas that are intended to be introduced in this work. Bipolar spherical fuzzy soft intersection, bipolar spherical fuzzy soft null set, spherical fuzzy soft absolute set, and other operations on bipolar spherical fuzzy soft sets are some of the fundamental ideas defined in this work. The bipolar spherical fuzzy soft open set, the bipolar spherical fuzzy soft close set, the bipolar spherical fuzzy soft closure, and the spherical fuzzy soft interior are also defined. Additionally, the characteristics of this specified set are covered and described using pertinent instances. The innovative notion of BSFSs makes it easier to describe the symmetry of two or more objects. Moreover, a group decision-making algorithm based on the TOPSIS (Technique of Order Preference by Similarity to an Ideal Solution) approach to problem-solving is described. We analyze the symmetry of the optimal decision and ranking of feasible alternatives. A numerical example is used to show how the suggested approach may be used. The extensive benefits of the proposed work over the existing techniques have been listed. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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