Journal of Fuzzy Extension and Applications
Volume:5 Issue: 1, Winter 2024

This exploration addresses some aspects of Zoroastrianism, examining how the ancient Persian belief system aligns with the dynamic and indeterminate principles of  Fuzzy, Neutrosophic, and MultiAlist systems. Zoroastrianism, rooted in the eternal struggle between good and evil, light and darkness, exhibits parallels with Neutrosophy's acknowledgment of indeterminacy, incompleteness, and the dynamic interplay of opposites. The prophet Zarathustra's vision of a neutrosophic God challenges conventional notions of divine attributes, emphasizing a dynamic and evolving universe. Before investigating these vague areas, the concept of unclear conceptual borders is explored, emphasizing the indeterminacy and imprecision inherent in defining opposites or partially opposite concepts. The law of included infinitely-many-middles suggests that between opposites, there exist infinitely many nuances or middle values. Sorites' paradoxes challenge traditional logic by exposing the difficulties in defining vague boundaries. Neutrosophic Interpretation suggests introducing a buffer zone between opposites, resulting in Neutrosophic Sorites Paradoxes. Moreover, this exploration highlights the need for a more flexible and nuanced understanding of conceptual boundaries, acknowledging the dynamic and indeterminate nature of many philosophical and logical constructs. Finally, we delve into the application of neutrosophy to various cultural and philosophical concepts. The legendary figure of Gilgamesh, described as two-thirds god and one-third human, is examined through both traditional and neutrosophic perspectives. Additionally, Hindu concepts of Dharma, Adharma, and Karma are reexamined within the context of neutrosophy. The logic of the Diamond Sutra in Mahayana Buddhism, characterized by paradoxical language and a focus on emptiness, aligns with neutrosophic principles in challenging fixed notions and embracing the interconnected and indeterminate aspects of reality. Despite diverse cultural origins, these examples share a common thread in questioning absolutes and embracing the dynamic nature of existence.

This study investigates integrating and optimizing an intelligent rural management system leveraging advanced technologies, including the Internet of Things (IoT), blockchain, and social networks. Initially, it identifies and scrutinizes prevailing issues in rural development processes, emphasizing the role of rural cultural dissemination, with a specific focus on the impact of social networks. Subsequently, by incorporating fuzzy set theory and adopting an enhanced blockchain consensus algorithm—the Byzantine Fault Tolerance (BFT) algorithm— a comprehensive rural management system is established, combining fuzzy sets and blockchain. Lastly, an intelligent traffic management system is developed to address logistics and distribution challenges in rural revitalization, facilitating efficient interurban delivery. The system automatically invokes the Matlab dynamic link library and employs a hybrid genetic algorithm to plan delivery routes. This study presents key findings on implementing an intelligent rural management system incorporating fuzzy sets, blockchain, and IoT technology. The system notably enhances transparency and traceability in agricultural production and supply chain processes, optimizes logistics and distribution efficiency, and reduces operational costs through intelligent management techniques. Additionally, the integrated application significantly bolsters consumer trust in the quality and safety of agricultural products, leading to heightened overall user satisfaction.

In this study, we attempted to demonstrate the interval-valued fuzzy code by extending the concept of an interval-valued fuzzy set. Further, we discussed the operations of the interval-valued fuzzy code. The interval-valued fuzzy soft code is introduced, and various related properties are investigated in this paper. Finally, we show that the operations of interval-valued fuzzy soft code are discussed. Through this paper, we use the set of integers modulo 2, that is = {0, 1}.

Unmanned Aerial Vehicles (UAVs) bring both potential and difficulties for emergency applications, including packet loss and changes in network topology. UAVs are also quickly taking up a sizable portion of the airspace, allowing Flying Ad-hoc NETworks (FANETs) to conduct effective ad hoc missions. Therefore, building routing protocols for FANETs is difficult due to flight restrictions and changing topology. To solve these problems, a bio-inspired route selection technique is proposed for FANET. A combined trustworthy and bioinspired-based transmission strategy is developed as a result of the growing need for dynamic and adaptable communications in FANETs. The fitness theory is used to assess direct trust and evaluate credibility and activity to estimate indirect trust. In particular, assessing UAV behavior is still a crucial problem in this field. It recommends fuzzy logic, one of the most widely utilized techniques for trusted route computing, for this purpose. Fuzzy logic can manage complicated settings by classifying nodes based on various criteria. This method combines geocaching and unicasting, anticipating the location of intermediate UAVs using 3-D estimates. This method guarantees resilience, dependability, and an extended path lifetime, improving FANET performance noticeably. Two primary features of FANETs that shorten the route lifetime must be accommodated in routing. First, the collaborative nature necessitates communication and coordination between the flying nodes, which uses a lot of energy. Second, the flying nodes' highly dynamic mobility pattern in 3D space may cause link disconnection because of their potential dispersion. Using ant colony optimization, it employs trusted leader drone selection within the cluster and safe routing among leaders. a fuzzy‐based UAV behavior analytics is presented for trust management in FANETs. Compared to existing protocols, the simulated results demonstrate improvements in delay routing overhead in FANET.

Stock portfolio problems are one of the most relevant real-world problems. In this study, we discuss the portfolio's risk amount, rate of risk-return, and expected return rate under a Fermatean fuzzy environment. A linear programming problem is used to formulate a Fermatean fuzzy portfolio. The Fermatean fuzzy portfolio is converted to a deterministic form using the score function. Lingo software is used to solve these deterministic portfolio problems. The main feature of this model is that investors can select a risk coefficient to enhance predicted returns and customize their strategies according to their circumstances. An example is offered that illustrates the effectiveness and dependability of the proposed approach.

Integers play a basic role in the structures of asymmetric crypto-algorithms. Many famous public key crypto-schemes use the basics of number theory to share keys and decrypt and encrypt messages and multimedia. As a novel trend in the world of cryptography, non-classical integer systems, such as neutrosophic or plithogenic integers, are used for encryption and decryption. The objective of this paper is to provide the basic foundations of 2-cyclic refined number theory and linear Diophantine equations in two variables by building suitable algebraic isomorphism between the 2-cyclic refined integer ring and a subring of the direct product of Z with itself three times. Also, this work presents two novel crypto schemes for the encryption and decryption of data and information based on the algebraic properties of 2-cyclic refined integers, where improved versions of the El-Gamal crypto-scheme and RSA algorithm will be established through the view of the algebra and number theory of 2-cyclic refined integers. On the other hand, we illustrate some examples and tables to show the validity and complexity of the novel algorithms.

The notion of Fuzzy Graphs (FGs) and Intuitionistic Fuzzy Graphs (IFGs) is generalized in the Picture Fuzzy Graph (PFG), which is a more common platform for expressing the degree of positive, negative, and neutral membership functions. Picture Fuzzy Soft Graphs (PFSGs) are powerful mathematical tools for modeling real-world vagueness. The concept of vulnerability parameters of PFSG is provided in this research work by introducing the novel cardinality, domination number, integrity, and Domination Integrity (ÐÏ) of PFSG. Furthermore, a decision-making method for the PFSG has been presented using ÐÏ to suggest an algorithm for determining the ideal location for establishing a city diagnosis center

Chronic nephritic sickness is another name for Chronic Kidney Disease (CKD). Numerous complications, such as elevated blood levels, anemia, weak bones, and nerve damage, constitute a problem. It is usually possible to prevent chronic uropathy from getting worse by early identification and treatment. To circumvent these problems, current research has presented the Fruit Fly Optimization Algorithm (FFOA) and effective Multi-Kernel Support Vector Machine (MKSVM) for illness classification. Finding the best features from a collection is usually done using FFOA. MKSVM categorizes medical data using chosen dataset criteria. The accuracy of the classifier will be impacted by any range of variations in data obtained for this study. MKSVM continues to yield more incorrectly classified findings. To resolve those problems, a preprocessing step based on min-max normalization is used to normalize the input CKD data values scale. Then, significant features will be selected using Improved FFOA (IFFOA). The selected features will be clustered using Weighted Fuzzy C Means clustering (WFCM) to predict the class label of the data sample and reduce the misclassification results. Finally, as normal or abnormal, CKD  classification will be performed using the Enhanced Adaptive Neuro Fuzzy Inference System (EANFIS). The suggested strategy efficacy is demonstrated by findings in fields of recall, accuracy, precision, and f-measure.

This paper aims to create a strong background of many algebraic structures dealing with Weak Fuzzy Complex (WFC) elements. So, we build a special transformation function that has an important role in working with variables from a Real number set instead of a WFC set. We study its algebraic properties and models. Also, we define the WFC function, its canonical formula, and its main establishments. Therefore, we show some famous functions and relations formulas in WFC variables. On the other hand, differentiability, integrability, and continuity of WFC functions in one variable will be presented in terms of theorems, and many related examples will be illustrated to clarify the validity of our work.

The investigation of mathematics underlines accuracy, precision, and flawlessness, yet in numerous genuine circumstances, individuals face equivocalness, ambiguity, imprecision, and so forth. Intuitionistic fuzzy set theory, rough set theory, and soft set theory are three noble techniques in mathematics that are utilised for decision-making in vague and uncertain information systems. Intuitionistic fuzzy algebra-based math plays a huge part in the current era of mathematical research, and it deals with the algebraic concepts and models of intuitionistic fuzzy sets. The investigation of different ordered algebraic structures, like lattice-ordered groups, Riesz spaces, etc., is of great importance in algebra. The theory of lattice-ordered G-modules is very useful in the study of lattice-ordered groups and similar algebraic structures. In this article, the theories of intuitionistic fuzzy sets and lattice-ordered G-modules are synchronised in a reasonable way to develop a novel concept in mathematics, i.e., intuitionistic fuzzy lattice-ordered G-modules, which would pave the way for new researchers in intuitionistic fuzzy mathematics to explore much more in this field.