Possibility Theory Research Articles

MCDM Method for Managing the Water Resources Based on Possibility Theory under Bipolar Fuzzy Environment

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.

Estimation of Reservoir Storage Capacity Using the Gould-Dincer Formula with the Aid of Possibility Theory

This paper presents a method for estimating reservoir storage capacity using the Gould–Dincer normal formula (G-DN), enhanced by the possibility theory. The G-DN equation is valuable for regional studies of reservoir reliability, particularly under climate change scenarios, using regional statistics. However, because the G-DN formula deals with measured data, it introduces a degree of uncertainty and fuzziness that traditional probability theory struggles to address. Possibility theory, an extension of fuzzy set theory, offers a suitable framework for managing this uncertainty and fuzziness. In this study, the G-DN formula is adapted to incorporate fuzzy logic, and the possibilistic nature of reservoir capacity is translated into a probabilistic framework using α-cuts from the possibility theory. These α-cuts approximate probability confidence intervals with high confidence. Applying the proposed methodology, in the present crisp case with the storage capacity D = 0.75, the value of the capacity C was found to be 1271×106 m3, and that for D = 0.5 was 634.5×106 m3. On the other hand, in the fuzzy case using the possibility theory, the value of the capacity for D = 0.75 is the internal [315,5679]×106 m3 and for D = 0.5 the value is interval [158,2839]×106 m3, with a probability of ≥95% and a risk level of α = 5% for both cases. The proposed approach could be used as a robust tool in the toolkit of engineers working on irrigation, drainage, and water resource projects, supporting informed and effective engineering decisions.

The Efficiency Evaluation of DEA Model Incorporating Improved Possibility Theory

The data envelopment analysis (DEA) models have been widely recognized and applied in various fields. However, these models have limitations, such as their inability to globally rank DMUs, the efficiency values are definite numerical values, they are unable to reflect potential efficiency changes, and they fail to adequately reflect the degree of the decision maker’s preference. In order to address these shortcomings, this paper combines possibility theory with self-interest and non-self-interest principles to improve the DEA model to provide a more detailed reflection of the differences between DMUs. First, the self-interest and non-self-interest principles are employed to establish the DEA evaluation model, and the determined numerical efficiency is transformed into efficiency intervals. Second, an attitude function is added to the common possible-degree formula to reflect the decision maker’s preference, and a more reasonable method for solving the attitude function is presented. Finally, the improved possible-degree formula proposed in this paper is used to rank and compare the interval efficiencies. This improved method not only provides more comprehensive ranking information but also better captures the decision maker’s preferences. This model takes preference issues into account and has improved stability and accuracy compared with existing models. The application of the improved model in airlines shows that the model proposed in this paper effectively achieved a full ranking. From a developmental perspective, the efficiency levels of Chinese airlines were generally comparable. Joyair and One Two Three performed poorly, exhibiting significant gaps compared with other airlines.

Intuitionistic Fuzzy Sequential Three-Way Decision Model in Incomplete Information Systems

As an effective method for uncertain knowledge discovery and decision-making, the three-way decisions model has attracted extensive attention from scholars. However, in practice, the existing sequential three-way decision model often faces challenges due to factors such as missing data and unbalanced attribute granularity. To address these issues, we propose an intuitionistic fuzzy sequential three-way decision (IFSTWD) model, which introduces several significant contributions: (1) New intuitionistic fuzzy similarity relations. By integrating possibility theory, our model defines similarity and dissimilarity in incomplete information systems, establishing new intuitionistic fuzzy similarity relations and their cut relations. (2) Granulation method innovation. We propose a density neighborhood-based granulation method to partition decision attributes and introduce a novel criterion for evaluating attribute importance. (3) Enhanced decision process. By incorporating sequential three-way decision theory and developing a multi-level granularity structure, our model replaces the traditional equivalent relation in the decision-theoretic rough sets model, thus advancing the model’s applicability and effectiveness. The practical utility of our model is demonstrated through an example analysis of “Chinese + vocational skills” talent competency and validated through simulation experiments on the UCI dataset, showing superior performance compared to existing methods.

Innovative player evaluation: Dual-possibility Pythagorean fuzzy hypersoft sets for accurate international football rankings

This study introduces an advanced approach for ranking international football players, addressing the inherent uncertainties in performance evaluations. By integrating dual possibility theory and Pythagorean fuzzy sets, the model accommodates varying degrees of ambiguity and imprecision in player attributes. Additionally, the use of hypersoft set theory enriches the analysis by capturing the multifaceted nature of player evaluations. The proposed aggregation operators refine the synthesis of diverse information sources, leading to a comprehensive and nuanced assessment. This research significantly enhances player evaluation methodologies, providing a more adaptable framework for a fair assessment of international football talent. A practical example illustrates the application of dual-possibility Pythagorean fuzzy hypersoft sets (DP-PFHSS). A numerical technique is proposed for solving multi-criteria decision-making (MCDM) challenges with known dual possibility information using the proposed aggregation operators. This decision-making algorithm effectively determines a football player's worth, contributing to the overall ranking and evaluation process. The approach aids in scouting and recruitment by facilitating talent identification and informed player signings. Graphical analysis, comparing existing and proposed methods using average and geometric operators, demonstrates the superiority of the proposed approach in the players evaluation, indicating that F1 is in the top ranking.

Translanguaging and early childhood literacy: Themes and possibilities for theory, pedagogy, and policy

Translanguaging and early childhood literacy: Themes and possibilities for theory, pedagogy, and policy

A novel fuzzy GRA-based possibility theory soft computing process for selection pest control methods

The study presents the effective approach that combines the ideal with non-ideal points, GRA, and possibility theory to handle uncertain information in selecting pest control methods within an MCDM problem. The proposed approach for selecting pest control methods can incorporate uncertainty information expressed by fuzzy numbers, possibilistic mean, and possibilistic variance. Decision-maker can comprehend the gaps between alternative solutions and the aspired outcomes, and it allows for the consideration of decision-making risks under a fuzzy environment. The study establishes an evaluation framework for selecting pest control methods by using the empirical study, and one obtains an appropriate pest control method for managing Tessaratoma papillosa in Taiwanese crops. Through the practical example, the proposed approach can be demonstrated the feasibility and efficiency.

A Possibilistic Formulation of Autonomous Search for Targets.

Autonomous search is an ongoing cycle of sensing, statistical estimation, and motion control with the objective to find and localise targets in a designated search area. Traditionally, the theoretical framework for autonomous search combines sequential Bayesian estimation with information theoretic motion control. This paper formulates autonomous search in the framework of possibility theory. Although the possibilistic formulation is slightly more involved than the traditional method, it provides a means for quantitative modelling and reasoning in the presence of epistemic uncertainty. This feature is demonstrated in the paper in the context of partially known probability of detection, expressed as an interval value. The paper presents an elegant Bayes-like solution to sequential estimation, with the reward function for motion control defined to take into account the epistemic uncertainty. The advantages of the proposed search algorithm are demonstrated by numerical simulations.

The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions

The possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use its ellipsoidal uncertainty set in a minimax optimization problem to model this uncertainty. We also show that this minimax optimization problem reduces to a strictly convex minimization problem. Thus, unlike the possibilistic MV model, we get diversified optimal portfolios uniquely with our approach. After laying down the theoretical points of our approach, we illustrate it with a real-world example in the literature by using a software package for convex optimization. To the best of our knowledge, this is the first paper that considers uncertain possibility distributions in the possibilistic MV model.

A Bibliometric Analysis of Possibilistic Portfolio Selection Models

Possibility theory is one of the most used uncertainty theories in decision-making. This study aims to examine possibilistic portfolio selection models. In this context, we perform their bibliometric analysis with the Web of Science (WOS) data, using the Bibliometrix, without limiting the timespan. We get many results by analyzing the data of 303 documents, of which timespan is from 1995 to 2023. We see that W. G. Zhang is the most influential author in this field. The paper introducing the possibilistic mean-variance (MV) model is the most influential document in this field. The paper introducing Markowitz’s MV model is the most influential reference. China is the most productive country in this field, whereas The South China University of Technology is the most productive institution in this field. Fuzzy Sets and Systems is the most influential journal in this field. Variance originated from Markowitz’s MV model is the most critical keyword plus in this field. It has also maintained its trend topic position for a long time. To the best of our knowledge, this is the first paper making a bibliometric analysis of possibilistic portfolio selection models.

Fuzzy Finite Elements Solution Describing Recession Flow in Unconfined Aquifers

In this work, a novel fuzzy FEM (Finite Elements Method) numerical solution describing the recession flow in unconfined aquifers is proposed. In general, recession flow and drainage problems can be described by the nonlinear Boussinesq equation, while the introduced hydraulic parameters (Conductivity K and Porosity S) present significant uncertainties for various reasons (e.g., spatial distribution, human errors, etc.). Considering the general lack of in situ measurements for these parameters as well as the certain spatial variability that they present in field scales, a fuzzy approach was adopted to include the problem uncertainties and cover the disadvantage of ground truth missing data. The overall problem is encountered with a new approximate fuzzy FEM numerical solution, leading to a system of crisp boundary value problems. To prove the validity and efficiency of the new fuzzy FEM, a comparative analysis between the proposed approach and other well-known and tested approximations was carried out. According to the results, the proposed FEM numerical solution agrees with Karadinumerical method for the crisp case and is in close agreement with the original analytical solution proposed by Boussinesq in 1904 with the absolute reduced error to be 4.6‰. Additionally, the possibility theory is applied, enabling the engineers and designers of irrigation, drainage, and water resources projects to gain knowledge of hydraulic properties (e.g., water level, outflow volume) and make the right decisions for rational and productive engineering studies.

Factorizing formal contexts from closures of necessity operators

Factorizing datasets is an interesting process in a multitude of approaches, but many times it is not possible or efficient the computation of a factorization of the dataset. A method to obtain independent subcontexts of a formal context with Boolean data was proposed in Dubois and Prade based on the operators used in possibility theory. In this paper, we will analyze this method and study different properties related to the pairs of sets from which a factorization of a formal context arises. We also inspect how the properties given in the classical case can be extended to the fuzzy framework, which is essential to obtain a mechanism that allows the computation of independent subcontexts of a fuzzy context.

Fuzzy Estimators of Drain spacing in Subsoil Drainage using Fuzzy Logic and Possibility Theories

In the permanent flow of subsoil drainage, a lot of equations are used, most of them based on the Dupuit assumption. All related mathematical models present uncertainties and fuzziness, which create problems in the design of drainage networks. Fuzzy Logic deals with this problem and allows the management of uncertain information. This paper presents the solution of the Hooghout equation based on Fuzzy Logic and Possibility theories, using the Reduced Transformation Method for the related numerical calculations. This results in a fuzzy estimator for the drain spacing, whose α-cuts, provide, according to Possibility Theory, the confidence intervals of the drain spacing with a certain strong probability. Results on subsoil drainage in the case of soils with parallel drains located at any position from the impermeable bottom are presented. The possibility theory application enables the engineers and designers of irrigation, drainage, and water resources projects to gain knowledge of hydraulic properties (e.g., water level, outflow volume) and make the right decision for rational and productive engineering studies.

The End of the Theory of Expectation Possibility in Criminal Law

The expectation possibility theory of criminal law is one of the important theories in the field of criminal responsibility, which focuses on whether the perpetrator has the possibility of avoiding the illegal act when committing the crime. This paper attempts to find the fate of the theory in China's criminal law through the discussion of the historical development of the theory of expected possibility, its relationship with China's criminal liability, its introduction analysis, and the analysis of the reasons for exemption from liability beyond the law.

Some notes on possibilistic randomisation with t-norm based joint distributions in strategic-form games

This article continues the investigation started in [18] on the role of possibilistic mixed strategies in strategic-form games. In this earlier work we assumed, as standard in possibility theory, that joint possibility distributions were computed by combining possibilistic mixed strategies with the minimum t-norm. In this paper, we investigate the consequences of defining joint possibility distributions by using any continuous t-norm, with players' expected utilities based on the Choquet integral. We characterise under which conditions a pair of possibilistic mixed strategies is an equilibrium, generalising the results first presented in [18], and also show that the set of equilibria in possibilistic mixed strategies depends on the set of idempotent elements of a t-norm and not just on the chosen t-norm.

Mathematical Modeling of Possibility Markov Chains by Possibility Theory

Mathematical Modeling of Possibility Markov Chains by Possibility Theory

A multi-attribute decision making context for supply chain management using possibility single-valued neutrosophic soft settings

Argued decisions, risk estimation, empirical study, forecasts, apprehension supervision, and productive exposition depend on the degree of possibility. It enables us to assess the degree to which specific results are acceptable and to make more informed decisions by drawing on the information at our disposal and logic. Although some scholars have previously examined hybrid structures resembling fuzzy soft sets with possibility degree settings serving as fuzzy membership grades, the current study introduces an innovative structure that permits more adaptable and comprehensive settings: single-valued neutrosophic grades, to serve as possibility degrees. Thus, this study aims to introduce a new mathematical structure, i.e., possibility single-valued neutrosophic soft set (psv-NSOS), which combines three important theories (i.e., possibility theory, single-valued neutrosophic theory, and soft set theory). The basic notions, and set-theoretic operations, i.e., union and intersection, of psv-NSOS are investigated and manipulated with matrix representations. Considering evaluating suppliers for a real estate construction project as a multi-attribute decision-making issue, an algorithm that utilizes the matrix manipulations of proposed set-theoretic operations is presented. The suggested algorithm?s robustness is confirmed by comparison to evaluate its dependability and adaptability for modeling uncertainties related to the supplier selection problem.

Modelo de análise aplicado ao estado da arte da epistemologia da administração

Abstract The article proposes a systematization of the epistemological paradigms already identified by research that studied the literature on administration epistemology. Such systematization is carried out through an analytical review, in which an analysis model, the result of a theoretical consortium between Ramos and Piaget, is the guiding thread. The different paradigms are analyzed according to their degree of reflexivity against the backdrop of the philosophical foundations of general epistemology. In the field of administration epistemology, it was observed that from the pioneering to the current works, the different authors defend a reflective decentring capable of generating a movement that takes the theory of organizations from the construct that Ramos calls the theory of necessity to the field of theory of possibility and beyond. Thus, the use of Platonic/Aristotelian/Cartesian archetypes by Kantian and post-Kantian archetypes was overcome. The analysis model is applied a second time to the abstracts of the last 30 theses of a graduate program in administration, defended from July 2019 to November 2022. Ten abstracts from each of the three lines of research were analyzed. In this second application, the model was adjusted with the inclusion of other theoretical and methodological aspects, now containing nine reflexivity indicators. It was demonstrated that, due to the different degrees of reflexivity, each line of research has its own characteristics in adopting theories and methods.

Leibniz despre principiul continuității

The idea that man is a living mirror of the universe, or, as a spirit, a living mirror of the divinity, is closely related to the theme of continuity. We will approach this issue less from the perspective of the theory of knowledge, but rather from a metaphysical perspective. The solution of the labyrinth of the composition of the continuum constitutes Ariadne’s thread through the labyrinth of Leibnizian thought, with the help of which we will be able to reach the end of many problems raised by the latter’s texts. Just like Ariadne’s thread, the solution of the labyrinth has two ends: one is located in the principle of continuity, the other in the theory of possibility, or, to put it differently, starting from the problematic theory of continuity we will reach the bright area of possibility.

Time-dependent reliability of structures under consideration of fuzzy uncertainty

Time-dependent reliability (TDR) is the possibility that a structure or system under consideration can perform the intended function under specified service conditions over a given time instant under fuzzy uncertainty. This paper is mainly concerned to identify fuzzy variables, generate the membership function of the input variables and output quantities, analyze timedependent performance level, estimate the possibility safety index, and evaluate the TDR of the structures. To evaluate TDR by a possibilistic approach, the fuzzy uncertainty that is characterized by membership function is considered. The type of uncertainty defines the method of reliability analysis, i.e., aleatory uncertainty possesses a probabilistic approach, whereas epistemic uncertainty leads to a possibilistic approach. The TDR analysis of the structures subjected to sustained load and corrosion based on probability theory is well developed. On the contrary, the TDR of structures subjected to combined effects sustained load, corrosion, creep, and shrinkage based on possibility theory lack research. Thus, this paper is significant to evaluate the TDR of structures subjected to the aforementioned effects based on possibility theory. However, it requires a rigorous procedure, a single-loop optimization method (SLOM) is employed to evaluate the TDR of structures involving epistemic uncertainty. To enhance the validation of the proposed approach, several examples are thoroughly carried out.