ABSTRACT Quantum computing utilizes the underlying principles of quantum mechanics to perform computations with unmatched performance capabilities. Rather than using classical bits, it operates on qubits, which can exist in superposition and entangled states. This enables the solution of problems that are considered intractable for classical computers. However, since qubits are realized by physical systems such as the spins of electrons, they are highly sensitive to environmental disturbances and hardware imperfections. To achieve reliable scaling and practical application in the future, addressing these errors is of utmost importance. Different classes of errors exist, such as coherent and incoherent errors, caused by imperfections in quantum operations or the decoherence of quantum states. They are inherently different, as they arise from either a lack of precision or intrinsic randomness. Current literature struggles to provide a unified framework that models both types of errors simultaneously. In this paper, an approach based on possibility theory—a theory of imprecise probabilities—is presented to model quantum uncertainty. Possibility theory is particularly useful for systems affected by both epistemic and aleatoric uncertainty, that is, uncertainty due to limited knowledge and uncertainty due to inherent randomness, respectively. By exploring noisy quantum algorithms within a possibilistic framework, different statements about robustness can be derived without requiring prior assumptions about the underlying noise model. Moreover, a possibilistic model enables the derivation of sampling criteria for guaranteed statistical performance and provides insight into the number of measurements required—an important consideration, given that such resources are costly in practice.

In multi-agent systems, the interactions between autonomous agents within dynamic and uncertain environments are crucial for achieving their objectives. Current research leverages model checking techniques to verify these interactions, with social accessibility relations commonly used to formalize agent interactions. In multi-agent systems that incorporate generalized possibility measures, the quantification, computation, and model checking of trust properties present significant challenges. This paper introduces an indirect model checking algorithm designed to transform social trust under uncertainty into quantifiable properties for verification. A Generalized Possibilistic Trust Interpreted System (GPTIS) is proposed to model and characterize multi-agent systems with trust-related uncertainties. Subsequently, the trust operators are extended based on Generalized Possibilistic Computation Tree Logic (GPoCTL) to develop the Generalized Possibilistic Trust Computation Tree Logic (GPTCTL), which is employed to express the trust properties of the system. Then, a model checking algorithm that maps trust accessibility relations to trust actions is introduced, thereby transforming the model checking of GPTCTL on GPTIS into model checking of GPoCTL on Generalized Possibility Kripke Structures (GPKSs). The proposed algorithm is provided with a correctness proof and complexity analysis, followed by an example demonstrating its practical feasibility.

This paper investigates the asymptotic stabilisation problem of interval type-3 fuzzy systems under deception attacks, using a functional observer-based feedback control approach. A non-parallel distributed compensation controller, combined with functional feedback, is designed to counter the effects of deception attacks and improve the overall stability of the system by virtue of partially known system states. In addition, the inclusion of secondary membership functions enables interval type-3 fuzzy systems to effectively handle uncertainties and noisy data within the framework of possibility theory, highlighting their modelling advantages. By applying Lyapunov stability theory, sufficient conditions for guaranteeing asymptotic stability are established in the form of linear matrix inequalities (LMI). Furthermore, convex relaxation technique is incorporated into the LMI formulation to enhance the convergence rate and provide greater flexibility in the design of the controller. To demonstrate the effectiveness and reliability of the proposed method, two numerical examples are presented, including a real-time application involving a mass-spring-damper system, confirming the practical applicability of the control strategy.

ABSTRACT This study introduces the Type-NS Possibility Neutrosophic Hypersoft Set (Type-NS PNHSS), a novel framework that integrates possibility theory with neutrosophic hypersoft sets through neutrosophic possibility numbers to manage uncertain, indeterminate, and often inconsistent information across multiple attributes simultaneously in multi-criteria decision-making (MCDM). We establish the foundational theory of the Type-NS PNHSS, including its fundamental operations, measures, and aggregation operators. Building upon this theoretical framework, we propose a multi-criteria decision-making model tailored to address decision-making problems within the Type-NS PNHSS environment. Finally, a real-world case study, the selection of tobacco control strategies, is conducted to demonstrate the efficacy and advantages of the proposed theory and approach. The proposed model evaluates tobacco control strategies based on 08 policies, 05 attribute groups, and 20 sub-attributes. The results indicate that the ‘mass media communications’ strategy is the best choice, and this finding is also further supported by comparative analyses with other existing methods, confirming the model’s utility as a robust tool for advanced decision analysis.

The system generates a sorted list of other options for compatible materials and manufacturing techniques. This approach has advantages over current systems that are either deficient in decision modules or are not coupled with databases. Decisions on materials and manufacturing techniques must be determined before design for manufacture can begin. The prototype material and manufacturing process selection system known as MAMPS, which integrates a relational database and a formal multi-attribute decision model, is introduced in this paper. The decision model allows the designer's preferences in connection to the deciding elements to be represented. The needs of the product profile and the alternatives stored in the database are rated for compatibility with each choice criterion using possibility theory. The vector of compatibility ratings is used to calculate a single compatibility rating for the alternative. The possibility theory is used to produce choice criteria. It rates how well the alternatives stack up against the needs of the product profile. The vector of compatibility ratings is used to calculate a single compatibility rating for the alternative. A prioritized list of compatible material and manufacturing process alternatives is generated by the system. This approach has advantages over existing systems that either don't have a decisionmodule or aren't linked to a database. The choice of manufacturing processes has a significant impact on product quality, cost-effectiveness, and sustainability, which makes it an important research topic. Researchers can improve production processes, increase efficiency, decrease waste, and develop cutting-edge techniques by researching various process options, which helps to advance the manufacturing industries around the world. Evaluation of various factors, including cost, quality requirements, production volume, material properties, and equipment capabilities, is necessary when choosing a manufacturing process methodology. Finding the best strategy that maximises efficiency, complies with requirements, and supports business goals requires careful analysis and consideration. Taken as Alternative parameters for Process, Sand casting, Gravity die casting, Investment casting, Pressure die casting, Additive manufacturing. Taken as Evaluation parameter for Productivity, Accuracy, Complexity, Flexibility, Material utilization, Quality, Operation cost. The first ranking training is obtained with the lowest quality of compensation.

Conditioning is an essential operation in knowledge representation and uncertainty modeling. It enables a priori beliefs to be adjusted in response to new information considered to be fully certain. This work focuses on the computation of Fagin and Halpern (FH-)conditioning in the context where uncertain information is represented by weighted or possibilistic logic belief bases. Weighted belief bases are extensions of classical logic belief bases where a weight or degree of belief is associated with each propositional logic formula. This paper proposes a characterization of the syntactic computation of the revision of weighted belief bases in the light of new information, which is in full agreement with the semantics of the FH-conditioning of possibility distributions. We show that the size of the revised belief base is linear with respect to the size of the initial base and that the computational complexity amounts to performing O ( log 2 ( n ) ) calls to the propositional logic satisfiability tests, where n is the number of different degrees of certainty used in the initial belief base. The last section of this paper examines both semantically and syntactically FH-conditioning under uncertain information, within the framework of possibility theory. • Reviews possibilistic logic and the use of weighted belief bases to represent uncertainty. • Introduces FH-conditioning within the framework of possibility theory. • Proposes a syntactic computation of FH-conditioning using three transformation steps. • Extends FH-conditioning to the case of uncertain observations. • Discusses complexity and interpretation of FH-conditioning as belief revision or update.

A strictly Bayesian model consists of a set of possible data distributions and a prior distribution over that set. If there are other models available, how well they predicted the data may be compared using Bayes factors. If not, a model may be checked using a Bayesian p-value such as a prior predictive p-value or a posterior predictive p-value. However, recent criticisms of ordinary p-values apply with equal force against Bayesian p-values. Many of those criticisms are overcome by e-values, martingales interpreted as the amount of evidence discrediting a null hypothesis, measured as a payoff for betting against it. This article proposes the use of e-values to check Bayesian models by testing their prior predictive distributions as null hypotheses. Two generally applicable methods for checking strictly Bayesian models are provided. The first method calibrates Bayesian p-values by transforming them into Bayesian e-values. The second method uses Bayes factors or their approximations as Bayesian e-values. A robust Bayesian model, a set of strictly Bayesian models, may be checked using various functions that use the e-values of those strictly Bayesian models. Other functions measure how much the data support a Bayesian model. Relations to possibility theory are discussed.

Abstract This paper elaborates on the symmetric Sugeno integral introduced by Michel Grabisch, and an asymmetric generalization of it devoted to handling bipolar qualitative information. We extend to this framework the representation results for Sugeno integrals in terms of if–then selection and elimination rules. We also study various preferences orderings induced by bipolar integrals, and relate them to a former approach to handing bipolar qualitative preference information in the setting of possibility theory. We finally propose a counterpart of Grabisch’s symmetric Sugeno integral in a qualitative bipolar scale where consecutive levels are assumed to be equidistant.

ABSTRACT The possibilistic view of information and uncertainty, rooted in fuzzy set theory and possibility theory, is distinct from the probabilistic view adopted by economics-based accounting research. Fuzzy set and possibility theories provide a versatile framework for modeling situations where uncertainty arises from vague boundaries of natural language. We discuss two potential applications to accounting research: (1) comparing information structures with linguistic imprecision and (2) measuring the uncertainty and relative information arising from linguistic imprecision in financial disclosures. Data Availability: Data are available from sources identified in the paper. JEL Classifications: D81; G14; M41.

ABSTRACT Soames attributes to Kripke the theory of epistemic possibility that uses metaphysical impossibilities in explaining necessary a posteriori truths. I attribute to Kripke a theory from epistemic counterparthood. I develop an epistemic accessibility based on Kripke’s appeal to Lewis’ counterpart theory that is reflexive, non-transitive, and non-symmetric. I also propose an epistemic counterpart function and a description function.

The article presents a new method for evaluating investment projects in uncertain conditions, assuming that uncertainty may have two origins: aleatory (related to randomness) and epistemic (due to incomplete knowledge). Epistemic uncertainty is rarely considered in investment analysis, which can result in undervaluing the future opportunities and risks. Our contribution is built around a correlated random–fuzzy Geometric Brownian Motion, a hybrid Monte Carlo engine that propagates mixed uncertainty into a probability box, combined with three p-box-to-CDF transformations (pignistic, ambiguity-based and credibility-based) to reflect decision-maker attitudes. Our approach utilizes the Datar–Mathews method (DM method) to gather relevant information regarding the potential value of a real option. By combining probabilistic and possibilistic approaches, the proposed valuation model incorporates hybrid Monte Carlo simulation and a random–fuzzy Geometric Brownian Motion, considering the interdependence between parameters. The result of the hybrid simulation is a pair of upper and lower cumulative probability distributions, known as a p-box, which represents the uncertainty range of the Net Present Value (NPV). We propose three transformations of the p-box into a subjective probability distribution, which allow decision makers to incorporate their subjective beliefs and risk preferences when performing real option valuation. Thus, our approach allows the combination of objective available information about valuation of investment with the decision maker’s attitude in front of partial ignorance. To demonstrate the effectiveness of our approach in practical scenarios, we provide a numerical illustration that clearly showcases how our approach delivers a more precise valuation of real options.

This paper investigates the application of fuzzy possibility theory for assessing the safety of portal steel frames, addressing the limitations of traditional methods such as Load and Resistance Factor Design (LRFD) and Al- lowable Stress Design (ASD) in handling uncertainties and subjective judgments in structural systems. Portal steel frames, widely used in industrial buildings, are susceptible to various uncertainties in loads, material prop- erties, and geometric dimensions. Unlike probability theory, fuzzy possibility theory offers a robust framework for quantifying the possibility of safety or failure under imprecise or incomplete information, making it ideal for capturing real-world variability. The study establishes a practical procedure for structural fuzzy possibil- ity analysis. It further introduces a new fuzzy possibility degree model that accounts for the importance of information at different membership levels, enhancing the assessment of structural safety compared to exist- ing models. Numerical results demonstrate that the proposed model, operating within an extended possibility measure interval of (−1, 2), provides more refined and reasonable outcomes than traditional models confined to (0, 1), effectively distinguishing between absolute safety, absolute failure, and intermediate cases. Through a case study of a portal steel frame subjected to dead loads, live loads, wind loads, and foundation settlement, the paper evaluates safety and failure possibilities using deterministic and different fuzzy methods. Findings highlight the superiority of the proposed fuzzy possibilistic model in capturing complex uncertainties, though its non-traditional results require careful interpretation. Validating the model against empirical data, explor- ing sensitivity analyses, and developing normalization methods to bridge traditional and extended possibility frameworks, offer valuable insights for enhancing structural safety assessments in civil engineering.

Now a days, the Closed-loop Supply Chain Networks Problem (CLSCNP) is a most popular optimization problem. We examine closed-loop supply chains that are multi-capacitated and multi-time period, involving producers, distributors, and recyclers in an unpredictable setting. Examining the retail costs of new products and rewards given to customers for returning their used goods is the main objective. In this study, possibility theory is used to enable Saving Matrix Approach (SMA) to find the best answers in uncertain situations. The primary goal of the study is to reduce the overall cost of closed-loop supply chain network by determining the total number of facilities that will be opened and by maximizing the cost of all forward and reverse flow between the various CLSC network levels. Lastly, sample data is used to analyze theoretical results. To demonstrate the benefits of the suggested strategy, the outcomes.

This paper delves into a multidimensional exploration of uncertainty through various theoretical lenses, including Probability Theory, Possibility Theory, Plausibility Theory, Belief Theory, Fuzzy Logic, Evidence Theory, and Vague Theory. Each framework offers a distinct perspective: Probability Theory deals with randomness, Possibility and Plausibility address feasibility and belief, Belief Theory integrates multiple sources of information, and Fuzzy Logic captures imprecision through degrees of truth. Vague Theory extends the discourse further by modeling information that is not only imprecise but also ill-defined or linguistically ambiguous. Evidence Theory serves as an overarching framework that synthesizes these perspectives. These theories are not mutually exclusive; instead, they complement each other and are often used in combination to model complex uncertainty in real-world applications. Integrating Vague Theory enhances our ability to reason under deep uncertainty, particularly in contexts involving subjective judgment and natural language. Together, these frameworks foster resilient, flexible, and nuanced decision-making under ambiguity.

In this paper, a novel approximate triangular fuzzy finite element method (FEM) is proposed to solve the one-dimensional second-order unsteady nonlinear fuzzy partial differential Boussinesq equation. The physical problem concerns the case of the drought flow of a horizontal unconfined aquifer with a limited breath B and special boundary conditions: (a) at x = 0, the water level is equal to zero, and (b) at x = B, the flow rate is equal to zero due to the presence of an impermeable wall. The initial water table is assumed to be curvilinear, following the form of an inverse incomplete beta function. To account for uncertainties in the system, the hydraulic parameters—hydraulic conductivity (K) and porosity (S)—are treated as fuzzy variables, considering sources of imprecision such as measurement errors and human-induced uncertainties. The performance of the proposed fuzzy FEM scheme is compared with the previously developed orthogonal fuzzy FEM solution as well as with an analytical solution. The results are in close agreement with those of the other methods, with the mean error of the analytical solution found to be equal to 1.19·10−6. Furthermore, the possibility theory is applied and fuzzy estimators constructed, leading to strong probabilistic interpretations. These findings provide valuable insights into the hydraulic properties of unconfined aquifers, aiding engineers and water resource managers in making informed and efficient decisions for sustainable hydrological and environmental planning.

Generalized possibilistic theories: entanglement, steering and Bell non-locality

Combining machine learning models and rule engines in clinical decision systems: Exploring optimal aggregation methods for vaccine hesitancy prediction.

Numerous design optimization methodologies and reliability analysis techniques have been developed to address aleatory and epistemic uncertainties in engineering system design. Aleatory uncertainty is modeled by statistical distributions, while epistemic uncertainty becomes an alternative in cases where data is sparse and cannot be fully captured statistically. Possibility and evidence theories are computationally efficient and robust for quantifying epistemic uncertainty in reliability analysis and design optimization. This paper provides a comprehensive analysis of existing methodologies, challenges, and opportunities in managing uncertainty in engineering systems. Additionally, the concepts and practical applications of possibility and evidence theories are reviewed. Potential future research directions are outlined ultimately. This paper provides the sector with a clear understanding of possibility theory and evidence theory and their developments.

ABSTRACTThis contribution introduces a novel camera‐based localization method for omnidirectional mobile robots using fisheye lenses to capture images of landmarks to estimate robot position and orientation. In this work, the landmarks are red poles that are indistinguishable from one another. Ambiguity is purposefully allowed for ease of installation. In order to face challenges like landmark detection ambiguity and noisy camera feeds, the proposed localization method employs possibility theory for robust state estimation, embracing the inherent uncertainties. This approach diverges from traditional precise localizations by considering a robust range of possible robot positions, presenting the opportunity of enhancing safety in applications such as collision avoidance. Early integration into a possibilistic filter algorithm shows promise for improving dynamic state estimation, marking an advancement in applying possibility theory to real‐world scenarios.

Background: Uncertainty is a common factor in every real-life decision-making problem. Possibility theory is one uncertainty theory in Fuzzy sets (FS). The possibility-based decision-making under a fuzzy environment is a significant multi-criteria decision-making (MCDM) method. Methods: A bipolar FS is an extension of a fuzzy set. With the bipolarity concept, we can handle both positive and negative thoughts. In this study, we have provided a possibility mean of a bipolar fuzzy number. We have developed a ranking method for bipolar fuzzy numbers using this pos-sibility concept. A novel possibility MCDM method is suggested for solving the water resources management (WRM) in the Nagpur area, Maharashtra State, India. Results: The MCDM technique is an effective tool for solving WRM problems in an area. Many uncertainties and bipolarities occur together in Nagpur water resources. WRM technique with fuzzy is one approach that can be used to solve the area's water problem. We have used the pro-posed MCDM to address the water-related issues of this district. With this proposed MCDM method, numerically, we employed water resource problems under a bipolar fuzzy environ-ment. Conclusion: The Nagpur area is covered by Basaltic rock and faces water shortage. The district is experiencing severe water shortages. Groundwater, surface water, and rainfall are three water resources considered as alternatives. According to the proposed MCDM technique in Nagpur district, Groundwater is the best water source from three flanks: quality of water, affordability, and availability.