Decision Making
Ali Dolati; Elham Mokhtari; Ali Dastbaravarde
Volume 21, Issue 6 , November and December 2024, Pages 1-13
Abstract
The assumption of conditional symmetry, which implies that the distribution of one random variable given another random variable has a symmetric form, plays a crucial role in various probability and statistics problems. This study examines copula properties related ...
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The assumption of conditional symmetry, which implies that the distribution of one random variable given another random variable has a symmetric form, plays a crucial role in various probability and statistics problems. This study examines copula properties related to the conditional symmetry/asymmetry of two random variables. We investigate the possibility of ordering copulas based on their level of conditional asymmetry, similar to the concordance ordering for dependence. To quantify the degree of conditional asymmetry of a copula, we introduce measures that are monotonic for the proposed ordering. The characteristics of the proposed order and measures are elaborated upon. Several examples are included to demonstrate the results.
Fuzzy Scheduling
N G PRAVEENA; SELVARAJ K; Kalai Selvi T; Srigitha S Nath; Prabakaran D
Volume 21, Issue 6 , November and December 2024, Pages 15-31
Abstract
Vehicular ad-hoc networks (VANET) represent an improved iteration of Wireless Sensor Networks (WSN) with mobile sensory nodes situated within vehicles. The Vehicular Adhoc Networks hold a crucial position within smart city applications as inter-vehicle communication is deemed indispensable for maintaining ...
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Vehicular ad-hoc networks (VANET) represent an improved iteration of Wireless Sensor Networks (WSN) with mobile sensory nodes situated within vehicles. The Vehicular Adhoc Networks hold a crucial position within smart city applications as inter-vehicle communication is deemed indispensable for maintaining the technological efficiency of the city. Despite the benefits provided by VANET, it encounters numerous challenges and drawbacks within the context of smart city applications. One such challenge pertains to the security and privacy principles of VANET. Privacy and security emerge as principal concerns associated with VANET, prompting multiple researchers to propose security solutions over the past decade. The present research endeavor focuses on elevating the quality of service (QoS) by offering an enhanced level of security for data communication. This security enhancement is achieved through the use of blockchain technology and the integration of Elliptical Curve Cryptography with secure hash functions to safeguard data communication from node to Mobile Control Unit (MCU). Furthermore, the proposed research work presents an efficient routing mechanism for data between mobile nodes and the Control Unit by employing neuro fuzzy logic to identify the optimal path from the source node to the Mobile Control Unit (MCU). The proposed work is compared with existing cryptographic methodologies as well as state-of-the-art routing path optimization algorithms, namely Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Memetic Algorithm (MA), and Honey Bee Optimization (HBO), in order to establish its superiority in terms of computational time, throughput, packet delivery ratio, and accuracy.
Fuzzy Math
Funda Karacal; Kübra Karacair; Ümit Ertuğrul
Volume 21, Issue 6 , November and December 2024, Pages 33-54
Abstract
In recent years, implication operators have been studied intensively from many perspectives. These include the study of construction methods of implication operators. Additionally, it has been investigated whether some aggregation operators such as t-norm in interval-valued L-fuzzy set theory are representable. ...
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In recent years, implication operators have been studied intensively from many perspectives. These include the study of construction methods of implication operators. Additionally, it has been investigated whether some aggregation operators such as t-norm in interval-valued L-fuzzy set theory are representable. In this paper, we present some construction methods to obtain interval-valued implications, which are i-representable or not depending on the lattice and fuzzy logic operators, via some fuzzy logic operators, order preserving and/or order reversing functions. Moreover, many illustrative examples are included.
Fuzzy Math
Guojun Wu; Wei Yao
Volume 21, Issue 6 , November and December 2024, Pages 55-68
Abstract
With a commutative integral quantale $L$ as the truth value table, this study focuses on the characterizations of the sobriety of stratified $L$-convex spaces, as introduced by Liu and Yue in 2024. It is shown that a stratified sober $L$-convex space $Y$ is a sobrification of a stratified $L$-convex ...
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With a commutative integral quantale $L$ as the truth value table, this study focuses on the characterizations of the sobriety of stratified $L$-convex spaces, as introduced by Liu and Yue in 2024. It is shown that a stratified sober $L$-convex space $Y$ is a sobrification of a stratified $L$-convex space $X$ if and only if there exists a quasihomeomorphism from $X$ to $Y$; a stratified $L$-convex space is sober if and only if it is a strictly injective object in the category of stratified $S_0$ $L$-convex spaces.
Approximate Reasoning
Ya-Ming Wang; Dongxue Jiang; Yexing Dan
Volume 21, Issue 6 , November and December 2024, Pages 69-82
Abstract
More recently, Hua conducted an investigation into the properties and constructions of idempotent semi-t-operators on bounded lattices. In her paper, there were two corollaries (without proof) showing the nonexistence of idempotent semi-t-operators on the bounded lattice which contains one of the eight ...
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More recently, Hua conducted an investigation into the properties and constructions of idempotent semi-t-operators on bounded lattices. In her paper, there were two corollaries (without proof) showing the nonexistence of idempotent semi-t-operators on the bounded lattice which contains one of the eight sublattices mentioned in those corollaries. Unfortunately, it has been discovered that the conclusions drawn from those two corollaries are not entirely correct. This work aims to not only identify the errors in those corollaries through three counterexamples but also supplement all findings pertaining to the existence of idempotent semi-t-operators on any bounded lattice.
Fuzzy Math
Dojin Kim; Hyeonseo Kim; Lee-Chae Jang
Volume 21, Issue 6 , November and December 2024, Pages 83-99
Abstract
Recently, D. Zhang et al. introduced the generalized Choquet integral, extending pseudo-integrals and Choquet-like integrals while exploring their foundational properties. Building on this framework, we introduce the concept of generalized Choquet integrals for triangular fuzzy number (TFN)-valued functions, ...
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Recently, D. Zhang et al. introduced the generalized Choquet integral, extending pseudo-integrals and Choquet-like integrals while exploring their foundational properties. Building on this framework, we introduce the concept of generalized Choquet integrals for triangular fuzzy number (TFN)-valued functions, referred to as TGC-integrals. This work investigates the key properties of TGC-integrals, including monotone non-decreasing convergence theorems and inequalities such as the Fatou type, Jensen type, Minkowski type, and H\"older type inequalities, specifically tailored for TFN-valued functions. Furthermore, we provide illustrative examples that demonstrate practical applications of TGC-integrals, such as TFN-valued Choquet expected utility and pseudo-functional analysis. These results establish a robust theoretical foundation for analyzing TFN-valued functions and highlight their potential for addressing uncertainty and ambiguity in real-world problems.
Engineering
Ali Mirzaei; Alireza Nazemi
Volume 21, Issue 6 , November and December 2024, Pages 101-126
Abstract
In this paper, an intelligent approach based on Radial Basis Function Neural Networks (RBFNNs) is used forsynchronization problem between two chaotic systems.In this scheme, parallel systems have been firstapplied by converting thesynchronization problem between two chaotic systems to synchronization ...
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In this paper, an intelligent approach based on Radial Basis Function Neural Networks (RBFNNs) is used forsynchronization problem between two chaotic systems.In this scheme, parallel systems have been firstapplied by converting thesynchronization problem between two chaotic systems to synchronization problembetween their parallel systems.By employing an active control strategy, an Infinite Horizon Optimal Control Problem (IHOCP) is constructed related to theobtained paralleled dynamical models.Using a suitable transformation, the IHOCP is then transformed into an equivalent finite-horizon one.According to Pontryagin Maximum Principle (PMP),the necessary optimality conditions for the finite horizon problemare examined in the form of two-point boundary value problems (TPBVPs).A fuzzy neural network approachthat utilizes Radial Basis Functions (RBFs) as its activation functions for one of the hidden layers is established toapproximate the solution of the TPBVP. By relying on the ability of RBFNN as function approximator,the trial solutions of variables are substituted in the TPBVP. Theobtainedalgebraic nonlinear equations system is then reduced into an error function minimization problem.A learningscheme via center points of RBFsas training dataset and based onthe Levenberg-Marquardt algorithm is employed as the optimizerto derive the adjustable parameters of trial solutions.Some various chaotic systems are synchronized based onnumerical simulations to guarantee the capability of theproposed plan.
Computer Science
Anton A. Esin
Volume 21, Issue 6 , November and December 2024, Pages 127-145
Abstract
This paper develops a mathematical framework to ensure the functionality and efficiency of digital electronics built on multi-valued logic (MVL). We investigate the properties of precomplete classes and closure for families of MVL functions, focusing on the existence and structure of R-closed sets in ...
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This paper develops a mathematical framework to ensure the functionality and efficiency of digital electronics built on multi-valued logic (MVL). We investigate the properties of precomplete classes and closure for families of MVL functions, focusing on the existence and structure of R-closed sets in \(P_k\) for \(k \geq 4\). Our work provides a systematic analysis of logical bases and their representations through structured diagrams, with a particular focus on Boolean and MVL functions. We rigorously classify \(R_2\)-complete families in \(P_3\)-spaces and propose extensions for the minimal linear superposition operator. Furthermore, we highlight how MVL significantly enhances information density in memory storage systems, providing pivotal benefits for cutting-edge computational systems. These results bridge theoretical advancements and practical implementations in computer science and logic.
Engineering
Morteza Mirzaee; Reza Kazemi
Volume 21, Issue 6 , November and December 2024, Pages 147-171
Abstract
Upper-limb exoskeleton robots have a significant impact on rehabilitation, assistive technology, and human augmentation, as they can restore or enhance human physical abilities. This paper presents a novel control approach, called Adaptive Fractional Integral Terminal Sliding Mode (AFITSM), which combines ...
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Upper-limb exoskeleton robots have a significant impact on rehabilitation, assistive technology, and human augmentation, as they can restore or enhance human physical abilities. This paper presents a novel control approach, called Adaptive Fractional Integral Terminal Sliding Mode (AFITSM), which combines an exponential reaching law with a unique interval type-2 Fuzzy Inference System (FIS). This controller is designed to achieve zero-force control of a 5-degree-of-freedom upper-limb exoskeleton robot, even in the presence of bounded uncertainties. The controller's integral terminal sliding surface ensures that the system converges in a finite time, allowing the exoskeleton to reach its desired state quickly, which is critical in time-sensitive applications. The exponential switching control term reduces chattering and tracking errors, while the AFITSM controller's adaptability, enabled by the interval type-2 FIS, allows it to adjust its parameters in real-time to handle uncertainties and external disturbances. Numerical simulations demonstrate the effectiveness and superiority of the proposed control method over traditional control approaches.
Fuzzy modelling
mehrzad mirzasadeghi; Hossein nezam abadi-pour
Volume 21, Issue 6 , November and December 2024, Pages 173-193
Abstract
Solar energy as a renewable energy, is widely used by many solar power plants to generate electricity. As production in this sector grows, conducting business in this area becomes increasingly important. Solar energy trading is facilitated through power purchase agreements (PPA), which outline the key ...
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Solar energy as a renewable energy, is widely used by many solar power plants to generate electricity. As production in this sector grows, conducting business in this area becomes increasingly important. Solar energy trading is facilitated through power purchase agreements (PPA), which outline the key elements for building a solar power plant and managing related transactions. However, the current trading system has several drawbacks. These challenges include the absence of transaction tracking and payment mechanisms, limited user access to transaction data, and low transparency, trust, and consistency in solar energy pricing. A new technology that has recently emerged and can be utilized for trading is blockchain technology. It is a continuously growing list of recordable items, called blocks that are linked together using encryption. By leveraging blockchain for solar energy trading, many existing challenges can be addressed. Essentially, blockchain functions as a decentralized shared ledger, enabling members to collaborate for specific purposes without depending on a central authority. One of the notable features of some blockchain networks, including Ethereum, is the ability to create smart contracts. A smart contract is a set of computer codes that automatically execute on a blockchain platform under predefined conditions, without the central authority need. Blockchain, through the use of smart contracts, can offer a secure, transparent, peer-to-peer, distributed, decentralized, verifiable, reliable, and traceable platform for solar energy transactions. Additionally, by defining national cryptocurrencies within this localized context, it is possible to prevent the outflow of currency from the country during international transactions. To address the issue of solar energy pricing, which depends on the inflation rate factor and the dollar rate factor, the use of a fuzzy system can be effective. Fuzzy logic is a computational approach used to model uncertainties and complexities in real-world systems. In the context of PPA, a fuzzy system can serve as an effective tool for pricing electricity generated by solar power plants. As a result, designing a platform with blockchain features for solar energy trading, implementing PPA contracts on the blockchain, and using a fuzzy system for solar energy pricing are extensive areas of focus for this research.
