Search Results (17)

This paper proposes a theoretical framework for studying rough intuitionistic fuzzy filters within the structure of BE-algebras. Building on rough set theory and intuitionistic fuzzy set theory, we introduce rough intuitionistic fuzzy filters via lower and upper approximation operators induced by congruence relations. To further generalize the framework, we define set-valued homomorphisms on BE-algebras and use them to formulate $\Gamma$-rough intuitionistic fuzzy filters. Several structural properties and characterization results are established, including stability under approximation operators, relationships with classical intuitionistic fuzzy filters, and preservation under homomorphic mappings. The proposed approach provides an algebraic mechanism for modeling uncertainty, hesitation, and imprecision in implication-based systems, with potential relevance to uncertainty-aware reasoning in artificial intelligence, decision-support systems, and medical diagnosis. Full article

Additive manufacturing is driving a significant change in industry, extending beyond prototyping to the inclusion of printed parts in final designs. Stereolithography (SLA) is a polymerization technique valued for producing highly detailed parts with smooth surface finishes. This study presents a hybrid intelligent framework for modeling and optimizing the SLA 3D printer process’s parameters for Acrylonitrile Butadiene Styrene (ABS) photopolymer parts. The nonlinear relationships between the process’s parameters (Orientation, Lifting Speed, Lifting Distance, Exposure Time) and multiple performance characteristics (ultimate tensile strength, yield strength, modulus of elasticity, Shore D hardness, and surface roughness), which represent complex relationships, were investigated. A Taguchi design of the experiment with an L18 orthogonal array was employed as an efficient experimental design. A novel hybrid fuzzy logic–Particle Swarm Optimization (PSO) algorithm, ARGOS (Adaptive Rule Generation with Optimized Structure), was developed to automatically generate high-accuracy Mamdani-type fuzzy inference systems (FISs) from experimental data. The algorithm starts by customizing Modified Learn From Example (MLFE) to create an initial FIS. Subsequently, the generated FIS is tuned using PSO to develop and enhance predictive accuracy. The ARGOS models provided excellent performances, achieving correlation coefficients (R²) exceeding 0.9999 for all five output responses. Once the FISs were tuned, a multi-objective optimization was carried out based on the weighted sum method. This step helped to identify a well-balanced set of parameters that optimizes the key qualities of the printed parts, ensuring that the results are not just mathematically ideal, but also genuinely helpful for real-world manufacturing. The results showed that the proposed hybrid approach is a robust and highly accurate method for the modeling and multi-objective optimization of the SLA 3D process. Full article

The multi-choice rough bi-level multi-objective nonlinear programming problem (MR-BLMNPP) has noticeably risen in various real applications. In the current model, the objective functions have a multi-choice parameter, and the constraints are represented as a rough set. In the first phase, Newton divided differences (NDDs) are utilized to formulate a polynomial of the objective functions. Then, based on the rough set theory, the model is converted into an Upper Approximation Model (UAM) and Lower Approximation Model (LAM). In the second phase, two Technique of Order Preferences by Similarity to Ideal Solution (TOPSIS)-based models are presented to solve the MR-BLMNPP. A TOPSIS-based fuzzy max–min and fuzzy goal programming (FGP) model are applied to tackle the conflict between the modified bi-objective distance functions. An algorithm for solving MR-BLNPP is also presented. The applicability and efficiency of the two TOPSIS-based models suggested in this study are presented through an algorithm and a numerical illustration. Finally, the study presents a bi-level production planning model (BL-PPM) as an illustrative application. Full article

This paper presents the novel concept of rough intuitionistic fuzzy ideals within the realm of BCK-algebras and investigates their fundamental properties. Furthermore, we introduce a set-valued homomorphism over a BCK-algebra, laying the foundation for the establishment of T-rough intuitionistic fuzzy ideals. The characterization of these innovative ideals is accomplished by employing the $(\alpha ,\beta )$-cut of intuitionistic fuzzy sets in the context of BCK-algebras. Full article

In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy $\beta$-neighborhoods (IHF $\beta$-neighborhoods) and intuitionistic hesitant fuzzy complementary $\beta$-neighborhoods (IHFC $\beta$-neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF $\beta$-neighborhoods and IHFC $\beta$-neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated. Full article

The relationship between Rough Set (RS) and algebraic systems has been long studied by mathematicians. RS is a growing research area that encourages studies into both real-world applications and the theory itself. In RS, a universe subset is characterized by a pair of ordinary sets called lower and upper approximations. In this study, we look attentively at the use of rough sets when the universe set has a ring structure. The main contribution of the paper is to concentrate on the study of rough fuzzy ideals concerning the gamma ring and to describe some properties of its lower and upper approximations. This paper deals with the connection between Rough Fuzzy Sets (RFS) and ring theory. The goal of this paper is to present the notion of Left Operator Rings (LOR) and Right Operator Rings (ROR) in the gamma ring structure. We introduce some basic concepts of rough fuzzy left and right operator rings. Furthermore, we investigate some characterizations of left and right operator rings and prove some theorems based on these results. Full article

With the increasing operating mileage and ownership of high-speed electric multiple units (EMU), a reasonable operation and maintenance strategy is the key to ensure their safe and reliable operation. As a key component of recombined EMU, creating a reasonable and effective risk assessment method for the fully automatic coupler draft gear (FACDG) is the first task. Therefore, based on fuzzy rough number theory, combined with the analytic hierarchy process (AHP), entropy weight method (EWM), technique for order performance by similarity to ideal solution (TOPSIS) and grey relational analysis (GRA), a risk priority indicator of comprehensive nearness degree is developed. Furthermore, a novel multi-criteria decision making (MCDM) failure modes, effects and criticality analysis (FMECA) assessment method is proposed. The effectiveness and rationality of the risk assessment method proposed are verified by the analysis of data and failure modes of a certain FACDG at fourth-level engineering maintenance. Full article

Due to the increase in the impact of different manufacturing processes on the environment, green manufacturing processes are the prime focus of many current pieces of research. In the current article, a green machining process for stainless steel and SS304 and AISI1045 steel has been optimized using newly developed Fuzzy Measurement Alternatives and Ranking according to the COmpromise Solution (F-MARCOS) method in the form of two case studies. In the first case study, nose radius, cutting speed, depth of cut, and feed rate are selected as the process parameters whereas surface roughness, consumption of electrical energy, and power factor are the outputs. In the second case study width of cut, depth of cut, feed rate, and cutting speed were the process parameters and material removal rate (MRR), active energy consumption (ACE), and surface roughness (Ra) are the response variables. The MARCOS method ranks the alternatives based on the ideal and anti-ideal solutions for the different criteria. The inclusion of fuzzy logic adds worth to the model by using a linguistic scale to make the method more practical and flexible. Based on the detailed analysis, it ranked the best alternative in case study one which results in a power factor of 0.862, 26.68 kJ of electrical energy consumption, and surface roughness of 0.36 $\mathsf{\mu }\mathrm{m}$. In the second case study, the best alternative selected by this method gave an MRR of 2400 ${\mathrm{mm}}^3/\min$ and Ra of 2.29 $\mathsf{\mu }\mathrm{m}$ and utilizes 53.988 kJ ACE. Full article

One of the most common tools for achieving optimization and adequate production process management is linear programming (LP) in various forms. However, there are specific cases of the application of linear programming when production optimization implies several potential solutions instead of one. Exactly such a problem is solved in this paper, which integrates linear programming and a Multi-Criteria Decision-Making (MCDM) model. First, linear programming was applied to optimize production and several potential solutions lying on the line segment AB were obtained. A list of criteria was created and evaluated using the Improved Fuzzy Stepwise Weight Assessment Ratio Analysis (IMF SWARA). To obtain the final solution, a novel Rough compromise ranking of alternatives from distance to ideal solution (R-CRADIS) method was developed and verified through comparative analysis. The results show that the integration of linear programming and a Fuzzy-Rough MCDM model can be an exceptional solution for solving specific optimization problems. Full article

Fuzzy sets are a major simplification and wing of classical sets. The extended concept of set theory is rough set (RS) theory. It is a formalistic theory based upon a foundational study of the logical features of the fundamental system. The RS theory provides a new mathematical method for insufficient understanding. It enables the creation of sets of verdict rules from data in a presentable manner. An RS boundary area can be created using the algebraic operators union and intersection, which is known as an approximation. In terms of data uncertainty, fuzzy set theory and RS theory are both applicable. In general, as a uniting theme that unites diverse areas of modern arithmetic, symmetry is immensely important and helpful. The goal of this article is to present the notion of rough fuzzy ideals (RFI) in the gamma ring structure. We introduce the basic concept of RFI, and the theorems are proven for their characteristic function. After that, we explain the operations on RFI, and related theorems are given. Additionally, we prove some theorems on rough fuzzy prime ideals. Furthermore, using the concept of rough gamma endomorphism, we propose some theorems on the morphism properties of RFI in the gamma ring. Full article

The nature of universe problems is ambiguous due to the presence of asymmetric data in almost all disciplines, including engineering, mathematics, medical sciences, physics, computer science, operations research, artificial intelligence, and management sciences, and they involve various types of uncertainties when dealing with them on various occasions. To deal with the challenges of uncertainty and asymmetric information, different theories have been developed, including probability, fuzzy sets, rough sets, soft ideals, etc. The strategies of hybrid ideals, hybrid nil radicals, hybrid semiprime ideals, and hybrid products of rings are introduced in this paper and hybrid structures are used to examine the structural properties of rings. Full article

The bipolar fuzzy (BF) set is an extension of the fuzzy set used to solve the uncertainty of having two poles, positive and negative. The rough set is a useful mathematical technique to handle vagueness and impreciseness. The major objective of this paper is to analyze the notion of approximation of BF ideals of semirings by combining the theories of the rough and BF sets. Then, the idea of rough approximation of BF subsemirings (ideals, bi-ideals and interior ideals) of semirings is developed. In addition, semirings are characterized by upper and lower rough approximations using BF ideals. Further, it is seen that congruence relations (CRs) and complete congruence relations (CCRs) play fundamental roles for rough approximations of bipolar fuzzy ideals. Therefore, their associated properties are investigated by means of CRs and CCRs. Full article

Titanium and its alloys exhibit numerous uses in aerospace, automobile, biomedical and marine industries because of their enhanced mechanical properties. However, the machinability of titanium alloys can be cumbersome due to their lower density, high hardness, low thermal conductivity, and low elastic modulus. The wire electrical discharge machining (WEDM) process is an effective choice for machining titanium and its alloys due to its unique machining characteristics. The present work proposes multi-objective optimization of WEDM on Ti6Al4V alloy using a fuzzy integrated multi-criteria decision-making (MCDM) approach. The use of MCDM has become an active area of research due to its proven ability to solve complex problems. The novelty of the present work is to use integrated fuzzy analytic hierarchy process (AHP) and fuzzy technique for order preference by similarity to ideal situation (TOPSIS) to optimize the WEDM process. The experiments were systematically conducted adapting the face-centered central composite design approach of response surface methodology. Three independent factors—pulse-on time (T_on), pulse-off time (T_off), and current—were chosen, each having three levels to monitor the process response in terms of cutting speed (V_C), material removal rate (MRR), and surface roughness (SR). To assess the relevance and significance of the models, an analysis of variance was carried out. The optimal process parameters after integrating fuzzy AHP coupled with fuzzy TOPSIS approach found were T_on = 40 µs, T_off = 15 µs, and current = 2A. Full article

The task to understand systemic functioning and predict the behavior of today’s sociotechnical systems is a major challenge facing researchers due to the nonlinearity, dynamicity, and uncertainty of such systems. Many variables can only be evaluated in terms of qualitative terms due to their vague nature and uncertainty. In the first stage of our project, we proposed the application of the Functional Resonance Analysis Method (FRAM), a recently emerging technique, to evaluate aircraft deicing operations from a systemic perspective. In the second stage, we proposed the integration of fuzzy logic into FRAM to construct a predictive assessment model capable of providing quantified outcomes to present more intersubjective and comprehensible results. The integration process of fuzzy logic was thorough and required significant effort due to the high number of input variables and the consequent large number of rules. In this paper, we aim to further improve the proposed prototype in the second stage by integrating rough sets as a data-mining tool to generate and reduce the size of the rule base and classify outcomes. Rough sets provide a mathematical framework suitable for deriving rules and decisions from uncertain and incomplete data. The mixed rough sets/fuzzy logic model was applied again here to the context of aircraft deicing operations, keeping the same settings as in the second stage to better compare both results. The obtained results were identical to the results of the second stage despite the significant reduction in size of the rule base. However, the presented model here is a simulated one constructed with ideal data sets accounting for all possible combinations of input variables, which resulted in maximum accuracy. The same should be further optimized and examined using real-world data to validate the results. Full article

Titanium alloys are widely used in various applications including biomedicine, aerospace, marine, energy, and chemical industries because of their superior characteristics such as high hot strength and hardness, low density, and superior fracture toughness and corrosion resistance. However, there are different challenges when machining titanium alloys because of the high heat generated during cutting processes which adversely affects the product quality and process performance in general. Thus, optimization of the machining conditions while machining such alloys is necessary. In this work, an experimental investigation into the influence of different cutting parameters (i.e., depth of cut, cutting length, feed rate, and cutting speed) on surface roughness (Rz), flank wear (VB), power consumption as well as the material removal rate (MRR) during high-speed turning of Ti-6Al-4V alloy is presented and discussed. In addition, a backpropagation neural network (BPNN) along with the technique for order of preference by similarity to ideal solution (TOPSIS)-fuzzy integrated approach was employed to model and optimize the overall cutting performance. It should be stated that the predicted values for all machining outputs demonstrated excellent agreement with the experimental values at the selected optimal solution. In addition, the selected optimal solution did not provide the best performance for each measured output, but it achieved a balance among all studied responses. Full article