Formal verification is an essential task to ensure the functional correctness of circuits. While several formal verification methods exist to ensure the functional correctness of circuits, they do not provide tight upper bounds for space and time complexities. Therefore, Polynomial Formal Verification (PFV) has been introduced to tackle this problem. In prior work, it has been shown that binary circuits with constant cutwidth can be verified in linear time using Answer Set Programming (ASP). Extending binary logic verification to Multi-Valued Logic (MVL) presents challenges due to the computational complexity of MVL gates and their encodings. In this paper, we propose Linear Formal Verification (LFV) of MVL circuits as a subclass of PFV. Additionally, we prove that MVL circuits with constant cutwidth can be verified in linear time and space. Finally, we evaluate circuits with constant cutwidth in terms of the upper bound of the cutwidth and verification time under different logic levels to confirm our theoretical findings.
The purpose of this work is to explore the connection between Tarski's notion of logical invariance under permutations and the universe of finitely supported sets, both in the classical Fraenkel-Mostowski axiomatic setting and in recent approaches involving invariant sets. We demonstrate that such finitely supported entities naturally qualify as logical notions in Tarski's sense, thereby illustrating the structural harmony between symmetry principles in logic and set theory.
This study presents an innovative approach to optimize delivery success in the online retail industry. The research's core is a machine learning (ML) model that predicts order delivery success, which is made explainable using SHAP (Shapley Additive exPlanations) values. The main novelty of the study is the transformation of SHAP values into Spherical Fuzzy Sets (SFS) and their integration with the TOPSIS method, creating a powerful decision-making mechanism. This mechanism optimizes monthly delivery plans through two scenarios: multi-package delivery, which increases efficiency, and immediate delivery, which enhances customer satisfaction. ML and SHAP serve as tools in this process, while SFS-TOPSIS integration is the main goal of decision-making. This hybrid approach strikes an optimal balance between prediction accuracy, model explainability, and decision-making flexibility. As a result, this study presents a novel methodology that enables the development of data-driven, understandable, and feasible delivery strategies in the online retail sector.
This study introduces the concepts of intuitionistic fuzzy prime ideal, prime intuitionistic fuzzy ideal, intuitionistic fuzzy 2-absorbing, 2absorbing intuitionistic fuzzy ideal, intuitionistic fuzzy primary ideal, and primary intuitionistic fuzzy ideal on a lattice. Then, intuitionistic fuzzy 2-absorbing primary ideals of a lattice are characterized. The transitions among these concepts and their relationships with the ideals of a lattice are discussed. Finally, these concepts are examined on a lattice formed by the Cartesian product of lattices.
A vague graph (VG) is one of the versatile application tools in the field of mathematics, which allows the user to easily describe the vague relation between any objects. VGs are beneficial to give more precision and flexibility to the system as compared to the classical model (i.e.,) crisp theory. The topological index (TI) of graph has a wide range of applications in theoretical chemistry, network design, computer science, etc. In chemical graph theory, the wiener index (also wiener number) introduced by Harry Wiener, is a topological index of a molecular, defined as the sum of the lengths of the shortest paths between all pairs of nodes in the chemical graph. Many topological indices exist only in the crisp but it's new to the VG-environment. The main aim of this research work is to define the topological indices in VGs. Here, indices described in VGs index (MWI), Schultz index (SI), and Gutman index (GI) with illustrations. Various examples are given for each of these topological indices and the necessary condition for the equality of connectivity index (CI) , WI is introduced. We have shown that if two graphs are isomorphic, then their WI are equal. Finally, we give an application of the WI, which is used as a simple screening model based on risk factors in patients to find the most effective factor in cancer.
Despite significant resource allocation, mobile applications lacking effective design are phased out before gaining widespread adoption. To ensure the sustainability of mobile applications, a comprehensive analysis of customer expectations is imperative. This research aims to investigate user preferences regarding the features of mobile applications, drawing data from a survey conducted with 525 participants and incorporating 33 essential features for a mobile shopping application. The study employs the KANO model, Timko classification, and fuzzy Kano model to achieve two main objectives. Firstly, it seeks to compare results obtained from these classification methods, assessing the impact of mobile application features on user satisfaction and perceived quality. Secondly, the study analyzes classification outcomes for participant groups categorized by demographic factors such as gender, age, and marital status. The study's findings revealed that the identified 33 features are categorized into four groups, and no statistically significant differences were observed among any of these groups.
Fraud detection and financial analysis are two different and critical techniques within the realm of finance and business. Fraud detection is the procedure of using information analysis to simplify fraud activities and financial analysis is aprocedure that assesses the financial health and performance of a business. The major influence of this manuscript is to evaluate the Dombi operational laws under the presence of the Neutrosophic fuzzy rough (NFR) information and simplify it with the help of suitable examples. Furthermore, we initiate the theory of NFR Dombi weighted averaging (NFRDWA) operator, NFR Dombi ordered weighted averaging (NFRDOWA) operator, NFR Dombi hybrid averaging (NFRDHA) operator, NFR Dombi weighted geometric (NFRDWG) operator, NFR Dombi ordered weighted geometric (NFRDOWG) operator, NFR Dombi hybrid geometric (NFRDHG) operator, and also derive their valuable properties. Additionally, we derive the technique of multi-attribute decision-making (MADM) problems for evaluating the problem of fraud detection and financial analysis under the consideration oft he derived operators t o enhance the worth of the initiated techniques. Finally, we compare the ranking results of the proposed techniques and existing techniques to show the supremacy and validity of the initiated information.
Improvement of the environment can be achieved by taking limited resources under control by giving importance to sustainable development. Especially since the policies of the European Union countries on sustainable development shape the global economy, it is important to measure the sustainable development performance of the EU countries. This study aims to propose an effective methodology for assessing the sustainable environmental transformation performance of EU countries. The outline of the proposed hybrid algorithm is based on Fermatean fuzzy sets with weighted aggregated sum product assessment (WASPAS) and MEREC. The Fermatean MEREC approach objectively determines criterion weights, while Fermatean WASPAS generates robust country rankings. Our analysis identifies "Energy productivity" as the most significant criterion among the evaluated sustainability indicators. The application of the FFS-MEREC-WASPAS framework reveals Sweden and Denmark as the top performers in environmental sustainability, demonstrating the method's effectiveness in cross-national sustainability assessment.
In this paper, we introduce a notion of K-nonvanishing map on a field K, and we obtain polynomially defined d-algebras which are not BC Kalgebras, as well as some conditions for these to be strong d-algebras. Moreover, we investigate some relations between polynomially defined d-algebras with left-zero semigroups and beta-algebras.
Pythagorean fuzzy soft set (PFSS), an extension of intuitionistic fuzzy soft set (IFSS), proves instrumental in managing ambiguity within numerous real-life scenarios. When applied to graph theory, these sets introduce a range of novel concepts, such as Pythagorean fuzzy soft graphs (PFSGs), complete Pythagorean fuzzy soft graphs, strong Pythagorean fuzzy soft graphs (Str-PFSGs), and the self-complement of Pythagorean fuzzy soft graphs (Self-Comp PFSGs). Our exploration involves detailing diverse construction methods and delving into their associated properties to gain a comprehensive understanding of their applicability and significance. Finally, some operations related to the above concepts are stated and proved.
An MV-semimodule is a left semimodule over an MV-semiring. We prove the homomorphism theorems of MV-semimodules, discuss the relations between simple MV-semimodules and maximal MV-subsemimodules, and the relations between superfluous MVsubsemimodules and essential MV-subsemimodules. Especially, we introduce and characterize the socles and the radicals of MVsemimodules.
In this paper, we give two proofs of a theorem of Bose and Dowling on non necessarily regular graphs satisfying the two other conditions of strong regularity. This theorem states that a simple graph for which there exist two non-negative entegers )and & micro; such that any two adjacent vertices have exactly ) common neighbors and any two nonadjacent vertices have exactly & micro; common neighbors, is regular except for some cases that can be considered as trivial.
Fuzzy numbers are very helpful in resolving issues in the real world which contain the cryptic or obscure data, as they deal with uncertainty. Ranking of fuzzy numbers plays a vital role in solving multi criteria decision making (MCDM) problems to decide the better choice with the enigmatic data. The present paper deals with a new total ranking method to discriminate generalised trapezoidal fuzzy numbers which generalizes the usual ordering of crisp real numbers. Further, illustrative examples are given to describe the method and a comparative study is carried out to validate the proposed method.
In this paper, we characterize hyper commutative basic algebras in which 0 or 1 is a scalar element. And then we give the conditions on which a hyper commutative basic algebra to be a commutative basic algebra. We also investigate the hyper substructure of hyper commutative basic algebras.
Classical break-even analysis (BEA) is applied by considering linear or non-linear revenue and total cost functions. However, the experts' estimations for these functions are vague and imprecise rather than exact. If the experts have insufficient data, the application of the classical BEA approach will not yield accurate results. Under these conditions, experts prefer to make predictions for parameters by using linguistic expressions. Due to the capability of fuzzy set theory to model such predictions, fuzzy BEA will be developed in this paper using one of the fuzzy sets' extensions in the literature. Picture fuzzy sets, which are one of the most recent extensions of ordinary fuzzy sets, are employed in the development of BEA under fuzziness incorporating experts' thoughts on the positive, neutral, and negative membership degrees of an estimation. Picture fuzzy singular and triple non-linear total cost and revenue functions are considered in the BEA model. The developed picture fuzzy BEA is applied to an excavator rent or buy decision problem.
Yang and Dunn [28] recently introduced implicational (dual) residuated partial gaggle logics. Here we extend those logics to semilinear ones. More precisely, this paper first defines the class of implicational (dual) residuated prelinear gaggle logics and shows that these logics are semilinear in an algebraic context, that is, they are semilinear in the sense that on linearly ordered matrices they are complete. We next introduce a relational semantics, called Routley-Meyer-style semantics, for finitary those logics and provide completeness for them using the semantics. We finally generalize the term "semilinear" to a notion applicable in both algebraic and set-theoretic contexts and show that finitary those logics are semilinear in this sense.
Morsi etal. [23] initiated the concept of tied adjointness algebra (TAA) and gave the idea of many valued rough sets (MVRSs) based on two independently chosen complete lattices and a t-norm. In the present study, we extend this concept by proposing constructive approaches of one and two pairs of (Phi,psi)-fuzzy rough approximation ((Phi,psi)-FRA) operators based on TAA, where (Phi,
This article explores a novel application of fuzzy logic in the context of addressing contemporary challenges and enhancing digital marketing strategies within the culinary tourism industry. As the industry grapples with evolving consumer preferences, technological advancements, and global economic shifts, a fuzzy logic approach offers a nuanced and adaptive framework. Fuzzy logic enables a more flexible and context-aware decision-making process, particularly relevant in the dynamic landscape of culinary tourism where diverse factors influence consumer choices. The article delves into the integration of fuzzy logic to optimize digital marketing efforts, taking into account variables such as cultural nuances, flavor preferences, and regional culinary trends. By embracing fuzzy logic, stakeholders in the culinary tourism sector can tailor marketing strategies with a heightened sensitivity to the inherent uncertainties and complexities of the industry. The study discusses practical implementations of fuzzy logic in digital marketing campaigns, emphasizing its ability to refine targeting, personalize content, and enhance user engagement. Furthermore, the article explores case studies and examples showcasing the efficacy of fuzzy logic in adapting marketing approaches to changing consumer behaviors. Ultimately, this research contributes valuable insights to the intersection of fuzzy logic and digital marketing, offering a promising avenue for elevating the effectiveness of promotional efforts in the dynamic realm of culinary tourism.
This study focuses on developing a new extension of Analytic Hierarchy Process (AHP) by using Intuitionistic Fuzzy Sets with Ordered Pairs (IFSOP). By leveraging the functionality of two-way questions, positive and negative, the membership degrees are determined, and fuzzy sets are constructed based on expert responses. The research contributes to the field by introducing a hierarchical prioritization using the recently introduced analytic hierarchy process based on Intuitionistic Fuzzy Sets with Ordered Pairs (IFSOP-AHP).
This paper proposes a fuzzy-based user equity scheduler (FUES) to prioritize traffic according to a plan through a dynamic fuzzy inference system. The fuzzy logic engine uses fuzzy rule reasoning to define packet priorities. The priority is proportional to traffic types that are more likely to miss their Quality of Service (QoS) requirements and have poor channel conditions. Simulations are used to compare and analyze our proposed scheduler FUES with six other scheduling methods based on fairness and performance metrics. Overall, the proposed scheduler exhibits superior fairness and performance compared to other methods, although there may be specific scenarios where other methods do not excel. This suggests that proposed scheduler 'FUES' provides a more balanced scheduling approach.
