Research on Fuzzy Logic and Mathematics with Applications II

Preface

The notion of a non-rigid fuzzy set was introduced by Lotfi A. Zadeh [1] in 1965. In order to analyze the imprecision, fuzzy sets are promising since they have no fixed extension, and also the laws of consistency and the excluded middle do not work. It is well known that in daily life and also in scientific thinking, we time and again encounter concepts which are ambulant, mobile, flexible, and dialectical. The problem of how to formalize such non-rigid concepts emerged. Tackling this problem gave rise to the concept of the fuzzy set, which adds to the classical two-valued logic an infinite-valued logic to take care of non-rigid objects and reflects the concepts (with non-fixed extension) of the objective reality, i.e., an infinite value of truth lying in the interval from 1 to 0. Zadeh is also the founder of fuzzy logic [2,3,4]. Since the advent of the notion of the fuzzy set, Zadeh and other researchers have used this important set and established a great deal of interesting research in fuzzy logic, fuzzy topology, fuzzy arithmetics, etc. This Special Issue deals with fuzzy logic and mathematics, with applications in decision making, data mining, graph theory, risk assessment, information theory, and other engineering applications.

In this present issue, there are 22 research articles: “Research on Fuzzy Logic and Mathematics with Applications II” of the MDPI Symmetry journal. In what follows, we will provide a brief account of their results and findings.

In Contribution 1, “Bipolar Spherical Fuzzy Soft Topology with Applications to Multi-Criteria Group Decision-Making in Building Risk Assessment”, Adem Yolcu presents a bipolar spherical fuzzy soft set as well as a bipolar spherical fuzzy soft topology. In this respect, the author introduces several new, useful, and important notions, such as a bipolar spherical fuzzy soft intersection, a bipolar spherical fuzzy soft null set, a spherical fuzzy soft absolute set, and other operations on bipolar spherical fuzzy soft sets, including the bipolar spherical fuzzy soft open set, the bipolar spherical fuzzy soft closes set, etc. Furthermore, the author sets forth a group decision-making algorithm based on the TOPSIS (Technique of Order Preference by Similarity to an Ideal Solution) approach to problem solving along with a numerical example to justify the applicability of the suggested approach.

In Contribution 2, “Some Properties of Cubic Fuzzy Graphs with an Applications”, the authors Xiaolong Shi, Maryam Akhoundi, Ali Asghar Talebi, and Seyed Hossein Sadati introduce the notion of the Wiener index in a cubic fuzzy graph as a cubic fuzzy number. They also offer some properties in this regard. They discuss a comparison between a connectivity index and the Wiener index, changes in the Wiener index by deleting a node or an edge, and determining the Wiener index in some specific cubic fuzzy graphs. Moreover, they utilize the concepts of the saturated cubic fuzzy cycle to determine the Wiener index. They provide an application of the Wiener index to investigate the properties of some monomer molecules.

In Contribution 3, “Prioritized Aggregation Operators for Intuitionistic Fuzzy Information Based on Aczel–Alsina T-Norm and T-Conorm and Their Applications in Group Decision-Making”, the authors Mehwish Sarfraz, Kifayat Ullah, Maria Akram, Dragan Pamucar, and Darko Božanić focus on proposing prioritized aggregation operators (AOs) for intuitionistic fuzzy (IF) information. More specifically, they propose IF-prioritized Aczel–Alsina averaging (IFPAAA) and IF-prioritized Aczel–Alsina geometric (IFPAAG) operators and present the fact that these AOs fulfill the basic features of aggregation. Moreover, they also study some results related to these AOs. The authors not only give an application used in an MADM (multi-attribute decision-making) problem but also provide a comparison of the proposed AOs with other well-known AOs to show the significance of the IFPAAA and IFPAAG operators.

In Contribution 4, “Novel Complex Pythagorean Fuzzy Sets under Aczel–Alsina Operators and Their Application in Multi-Attribute Decision Making”, Huanhuan Jin, Abrar Hussain, Kifayat Ullah, and Aqib Javed offer a detailed explanation of the notion of the Aczel–Alsina t-norm and t-conorm under the system of complex Pythagorean fuzzy sets. They obtain some basic operational laws of the Aczel–Alsina t-norm and t-conorm. They discuss some aggregation operators of complex Pythagorean fuzzy sets, and in order to solve an MADM ( multi-attribute decision making) technique, the authors construct an example. Further, through a comparison between the results of the AOs and the new ones, they show the preferences of the proposed AOs established in this article.

In Contribution 5, “Confidence Levels-Based Cubic Fermatean Fuzzy Aggregation Operators and Their Application to MCDM Problems”, the authors Harish Garg, Muhammad Rahim, Fazli Amin, Saeid Jafari, and Ibrahim M. Hezam focus largely on the utilization of cubic Fermatean fuzzy set features to resolve two kinds of problems: knowledge of rating domains and the performance of rating objects (called confidence levels). The authors introduce information aggregation operators with confidence degrees to cope with the ambiguous information of the aggregated arguments. They propose two AOs, i.e. the confidence cubic Fermatean fuzzy weighted averaging operator and the confidence cubic Fermatean fuzzy weighted geometric operator, using them as a framework to create an MCDM (multi-criteria decision-making) process supported by an example showing how effective and applicable it is.

In Contribution 6, “A Novel GDMD-PROMETHEE Algorithm Based on the Maximizing Deviation Method and Social Media Data Mining for Large Group Decision Making”, Juxiang Wang, Si Li, and Xiangyu Zhou propose not only a new generalized probabilistic hybrid distance measure method based on Hamming distance but also an extended GDMD-PROMETHEE large-scale multi-attribute group decision-making method. The latter is based on the former. These are proposed due to the complexity of emergency-handling decision making and the asymmetry of user evaluation information. They calculate the objective weight of decision makers and also the comprehensive weights of the attributes. They provide a realization of the distance measures and information fusion of probabilistic linguistic term sets under a cumulative prospect theory and the ranking results of the emergency-handling plans based on the extended GDMD-PROMETHEE algorithm. In this respect, they provide and discuss a case study of the explosion-accident-handling decision making of Shanghai “6.18” Petrochemical to show the advantages of their algorithm with respect to the traditional ones.

In Contribution 7, “Fermatean Fuzzy CODAS Approach with Topology and Its Application to Sustainable Supplier Selection”, Hafiz Muhammad Athar Farid, Mohamed Bouye, Muhammad Riaz, and Nimra Jamil establish the new notion of Fermatean fuzzy topology based on the class of Fermatean fuzzy sets. It is worth mentioning that a Fermatean fuzzy set (FFS) is a reliable method for representing uncertainty in “multi-criteria decision-making” (MCDM). The authors introduced and studied several new and important notions in the context of FFT. Moreover, they proposed a technique based on a Fermatean fuzzy “combinative distance-based assessment” to deal with multiple challenges in sustainable supply chain management. Among others, they develop an application to show the benefit of the suggested supplier selection approach.

In Contribution 8, “Multiple-Attribute Decision Making Based on Intuitionistic Hesitant Fuzzy Connection Set Environment”, Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Hamza Ghazanfar Toor, Faraz Akram, Saeid Jafari, Md. Zia Uddin, and Mohammad Mehedi Hassan propose the suitability of combining the intuitionistic hesitant fuzzy set (IHFS) and set pair analysis (SPA) theories in multi-attribute decision making (MADM) and present a hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). They also pinpoint the benefits of their proposed work and provide a graphical interpretation to show the consistency and efficiency of their approach.

In Contribution 9, “Application of the Double Fuzzy Sawi Transform for Solving a Telegraph Equation”, Atanaska Tencheva Georgieva and Albena Pavlova offered a new double fuzzy transform called the double fuzzy Sawi transform and presented some basic properties of both the single fuzzy Sawi transform and the double fuzzy Sawi transform. They also obtained the exact solution of a non-homogeneous linear fuzzy telegraph equation under a generalized Hukuhara partial differentiability. They exhibited with examples, utilizing the symmetric triangular fuzzy numbers, the validity and superiority of the double fuzzy Sawi transform in solving the fuzzy linear telegraph equation.

In Contribution 10, “Cosine Similarity Measures of (m, n)-Rung Orthopair Fuzzy Sets and Their Applications in Plant Leaf Disease Classification”, Arpan Singh Rajput, Shailja Shukla, and Samajh Singh Thakur study ten similarity measures that employ cosine and cotangent functions for comparing (m, n)-rung orthopair fuzzy sets. They used the proposed weighted similarity measures for real-world problems in building-material analysis. Further, they performed a comparative analysis between the proposed measures, demonstrating the efficiency of them with respect to the existing ones.

In Contribution 11, “Choquet Integral-Based Aczel–Alsina Aggregation Operators for Interval-Valued Intuitionistic Fuzzy Information and Their Application to Human Activity Recognition”, Harish Garg, Tehreem, Gia Nhu Nguyen, Tmader Alballa, and Hamiden Abd El-Wahed Khalifa investigate the problem of human activity recognition (HAR). In this respect, they use the proposed theory of Aczel and Alsina—the Aczel–Alsina norms—and the derived theory of Choquet. They demonstrate not only some characteristics and features of the presented techniques but also utilizing these techniques to evaluate the HAR multiattribute decision-making complications. By applying a functional model for HAR problems, they demonstrate a two-folded goal: to justify the evaluated approaches and also their efficiency.

In Contribution 12, “Fuzzy Soft Sets and Decision Making in Ideal Nutrition”, Abdelfattah A. El-Atik, Radwan Abu-Gdairi, Arafa A. Nasef, Saeid Jafari, and Mohammed Badr apply the fuzzy set theory with respect to the selection of a burning problem for the nutrition of students in decision making. They show the supremacy and effectiveness of their approach compared with other approaches.

In Contribution 13, “Multi-Attribute Group Decision Making Based on Spherical Fuzzy Zagreb Energy”, Gang Fang, Uzma Ahmad, Sobia Ikhlaq, and Leila Asgharsharghi expand the notion of fuzzy Zagreb indices of the fuzzy graph to the spherical fuzzy Zagreb indices of the spherical fuzzy graph (SFG) to better handle some real-world problems. By using examples, they define the spherical fuzzy Zagreb matrix of SFG and Zagreb energy of SFG. They develop several lower and upper bounds of the spherical Zagreb energy of SFG and offer an application of SFG by computing the Zagreb energy in a decision-making problem.

In Contribution 14, “Baire Category Soft Sets and Their Symmetric Local Properties”, Zanyar A. Ameen and Mesfer H. Alqahtani focus on the study of soft sets of the first and second Baire categories. They establish the main properties of soft sets. They introduce some types of soft points, where soft sets are of the first or second category. They present several interesting, useful, and important results.

In Contribution 15, “Fuzzy Logic and Its Application in the Assessment of Information Security Risk of Industrial Internet of Things”, Seyit Kerimkhulle, Zhulduz Dildebayeva, Akylbek Tokhmetov, Akzhibek Amirova, Jamalbek Tussupov, Ulzhan Makhazhanova, Alibek Adalbek, Roman Taberkhan, Alma Zakirova, and Alua Salykbayeva concentrate on the issue of information security in the Industrial Internet of Things (IIoT) environment. They perform an information security risk assessment in the IIoT. Indeed, the authors analyze the information security threats for IIoT systems and set forth a proposed method. They provide examples of calculating the information security risk assessment in the IIoT environment based on this method and state that their proposed approach can be used as a foundation for creating expert decision support systems for designing IIoT systems.

In Contribution 16, “A Novel Concept of Level Graph in Interval-Valued Fuzzy Graphs with Application”, Yongsheng Rao, Siran Lei, Ali Asghar Talebi, and Masomeh Mojahedfar study the level graph of an interval-valued fuzzy graph (IVFG), since many practical problems can be modeled and solved using the IVFG. In this regard, they investigate four operations: the Cartesian product, composition, union, and join. Moreover, they offer an application of the IVFG in order to spot the most effective person in a hospital information system.

In Contribution 17, “Bipolar Fuzzy Supra Topology via (Q-) Neighborhood and Its Application in Data Mining Process”, Banu Pazar Varol and Hami Malkoç investigate the neighborhood structures in bipolar fuzzy supra-topological space and exhibit the usefulness and applicability of bipolar fuzzy supra-topology to the medical diagnosis problem. They introduce some new and useful notions, and the obtained results are interesting. Moreover, the characterization of bipolar fuzzy supra-topological space in terms of quasi-neighborhoods is also given.

In Contribution 18, “An Introduction to Single-Valued Neutrosophic Primal Theory”, Fahad Alsharari, Hanan Alohali, Yaser Saber, and Florentin Smarandachenn investigate the interconnection among the single-valued neutrosophic grill, single-valued neutrosophic primal, and their stratification. By introducing the notion of a single-valued neutrosophic primal, they create a broader framework than the fuzzy primal and intuitionistic fuzzy primal. They also offer, among others, a new notion of the single-valued neutrosophic primal topology and obtain several interesting and important results.

In Contribution 19, “A Novel Neutrosophic Likert Scale Analysis of Perceptions of Organizational Distributive Justice via a Score Function: A Complete Statistical Study and Symmetry Evidence Using Real-Life Survey Data”, Seher Bodur, Selçuk Topal, Hacı Gürkan, and Seyyed Ahmad Edalatpanah introduce a new area of research in social science and use ten questions measuring distributive justice on classical Likert and neutrosophic Likert scales consisting of two subdimensions—distributive and procedural justice. The provided a comparison between the neutrosophic scale and the traditional Likert scale. They also discuss the symmetric and non-symmetric properties of statistical analysis in addition to general symmetric and non-symmetry properties. The authors believe that the new notion of neutrosophic Likert scale and the survay approach have som advantages what concerns collecting detailed and sensitive information on many topics, such as economics, health and etc.

In Contribution 20, “On Neutrosophic Fuzzy Metric Space and Its Topological Properties”, Samriddhi Ghosh, Sonam, Ramakant Bhardwaj, and Satyendra Narayan introduce and study a generalized metric space called neutrosophic fuzzy metric space. They obtained several new and important properties and establish counterparts of well-known theorems, such as the Uniform Convergence Theorem and the Baire Category Theorem, in the context of the neutrosophic fuzzy metric space.

In Contribution 21, “A New Fuzzy Bayesian Inference Approach for Risk Assessments”, Jintao Xu, Yang Sui, Tao Yu, Rui Ding, Tao Dai, and Mengyan Zheng propose a new fuzzy Bayesian network (BN) inference approach for risk assessments since they realized that BN cannot deal with the uncertain, fuzzy, random, and conflicting information from experts’ knowledge in the process of conducting a risk assessment. They obtain some BN inference results, which they analyze by utilizing the proposed algorithm, and two common BN inference algorithms, which the authors establish in the paper. Moreover, they validate the effectiveness of the proposed approach.

In Contribution 22, “Research on Heave Compensation System Based on Switched Reluctance Motor”, Juan Chen, Lai Jiang, and Xiaoping Zhang offer a composite control strategy based on a switched-reluctance motor (SRM)-driven active heave compensation device to live up to the requirements of the marine work platform for real-time control, time-varying speed, and the time-varying torque control of the motor-driven active heave compensation device. They use a model prediction trajectory algorithm to predict the compensation displacement obtained using the dynamic model and consider some other necessary matters. Moreover, they verify the system feasibility by setting different wave parameters.