Imprecise Information Research Articles

Collaborative Decision Model for Allocating Intensive Care Units Beds with Scarce Resources in Health Systems: A Portfolio Based Approach under Expected Utility Theory and Bayesian Decision Analysis

The COVID-19 pandemic has brought health systems to the brink of collapse in several regions around the world, as the demand for health care has outstripped the capacity of their services, especially regarding intensive care. In this context, health system managers have faced a difficult question: who should be admitted to an intensive care unit (ICU), and who should not? This paper addresses this decision problem using Expected Utility Theory and Bayesian decision analysis. In order to estimate the chances of survival for patients, a structured protocol has been proposed conjointly with physicians, based on the Sequential Organ Failure Assessment (SOFA) score. A portfolio selection approach is proposed to support tackling the ICU allocation problem. A simulation study shows that the proposed approach is more advantageous than other approaches already presented in the literature, with respect to the number of lives saved. The patients’ probabilities of survival inside and outside the ICU are important parameters of the model. However, assessing such probabilities can be a difficult task for health professionals. In order to give due treatment to the imprecise information regarding these probabilities, a Monte Carlo simulation is used to estimate the probabilities of recommending a patient be admitted to the ICU is the most appropriate decision, given the conditions presented. The methodology was implemented in an Information and Decision System called SIDTriagem, which is available online for free. With regards to managerial implications, SIDTriagem has a great potential to help in the response to public health emergencies systems as it facilitates rational decision-making regarding allocating ICU beds when resources are scarce.

Solving a multi-objective chance constrained hierarchical optimization problem under intuitionistic fuzzy environment with its application

Various optimization approaches have been developed and used for generating optimal solutions for different industry related optimization problems. The semantic representation of imprecise coefficients and various types of uncertainties arising in real life optimization problems are still a challenging task and require attention of academicians as well as professionals. Decision makers (DMs) often face problems in presenting the linguistically expressed constraints. The impreciseness of information also plays a key role in modelling and thus in decision making. The impreciseness of coefficients is usually handled by using various elements of fuzzy set theory. The uncertainty associated with constraints in optimization problem is handled by using stochastic programming approaches. These coefficients are usually revealed by a logical DM, who takes into account the scope of hesitation along with the imprecise nature of data. Such coefficients can be very well represented by using Intuitionistic fuzzy numbers. In this work, an approach for solving multi-objective bi-level chance constrained optimization problem in an intuitionistic fuzzy environment has been presented. The technological coefficients and the coefficients of objective functions are represented by Triangular Intuitionistic fuzzy numbers whereas normal random variables are used to represent the coefficient of resources. The concept of component wise optimization is used for the reduction of intuitionistic fuzzy objective into their equivalent deterministic form. The concept of alpha-beta cut, chance constrained programming and interval programming are then used to convert the problem into a deterministic multi-objective bi-level linear programming problem. The resultant deterministic optimization problem is then solved by using TOPSIS method. The production planning problem of a firm has been modelled and solved by using the proposed approach.

Including imprecisely georeferenced specimens improves accuracy of species distribution models and estimates of niche breadth

AbstractAimMuseum and herbarium specimen records are frequently used to assess the conservation status of species and their responses to climate change. Typically, occurrences with imprecise geolocality information are discarded because they cannot be matched confidently to environmental conditions and are thus expected to increase uncertainty in downstream analyses. However, using only precisely georeferenced records risks undersampling of the environmental and geographical distributions of species. We present two related methods to allow the use of imprecisely georeferenced occurrences in biogeographical analysis.InnovationOur two procedures assign imprecise records to the (1) locations or (2) climates that are closest to the geographical or environmental centroid of the precise records of a species. For virtual species, including imprecise records alongside precise records improved the accuracy of ecological niche models projected to the present and the future, especially for species with c. 20 or fewer precise occurrences. Using only precise records underestimated loss of suitable habitat and overestimated the amount of suitable habitat in both the present and the future. Including imprecise records also improves estimates of niche breadth and extent of occurrence. An analysis of 44 species of North American Asclepias (Apocynaceae) yielded similar results.Main conclusionsExisting studies examining the effects of spatial imprecision typically compare outcomes based on precise records against the same records with spatial error added to them. However, in real‐world cases, analysts possess a mix of precise and imprecise records and must decide whether to retain or discard the latter. Discarding imprecise records can undersample the geographical and environmental distributions of species and lead to mis‐estimation of responses to past and future climate change. Our method, for which we provide a software implementation in the enmSdmX package for R, is simple to use and can help leverage the large number of specimen records that are typically deemed “unusable” because of spatial imprecision in their geolocation.

Vaccine selection for COVID-19 by AHP and novel VIKOR hybrid approach with interval type-2 fuzzy sets

Decisions in the health industry have a significant impact on human lives. With the COVID-19 pandemic, a global war is being waged. Vaccination is a critical component in this fight. The governments are attempting to offer their citizens the best vaccine for the public based on limitations. However, due to the unique characterizations of countries and the people who live in the country, the definition of “the ideal vaccination” is indefinite. Fuzzy set theory has been an ideal tool to cope with problems involving imprecise information such as the meaning of “ideal” in this case. In this study Interval Type-2 Fuzzy Sets (IT2FSs) will be used to describe uncertainty. This IT2FS structure will be the framework of the AHP (Analytic Hierarchy Process), to determine the criteria weights, and the VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje), to generate a set of optimal choices. The main objective of this study is to sustain the necessary effect of uncertainty of fuzzy sets via the Interval Type-2 Fuzzy (IT2F) metric to the VIKOR method and thus propose an extended VIKOR. The presented new approach will be applied to the problem of vaccine selection for COVID-19. Hence, for the first time in the literature, an application with a multilevel hierarchy will be used in IT2FAHP-VIKOR. Also, obtained optimal solution set with this hybrid framework will be compared with fuzzy AHP-VIKOR and the rankings evaluated with the IT2FTOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) and sensitivity analysis will be performed.

Concept lattice simplification with fuzzy linguistic information based on three-way clustering

Numerous linguistically valued facts from the actual world have been modeled using the fuzzy linguistic approach. Concept lattice theory has the potential to be used in information processing in imprecise language environments as a methodology for data analysis and knowledge representation. The concept lattice with linguistic values can manage fuzzy linguistic data which are either comparable or incomparable. However, the acquired conceptual knowledge is difficult to understand due to the substantial amount of linguistic concept knowledge in the concept lattice with imprecise linguistic information. This work proposes a linguistic-valued layered concept lattice simplification method based on three-way clustering to reduce the scale of the linguistic-valued layered concept lattice. In order to create the linguistically valued layered concept lattice, a reconstruction function is first used to produce an attribute selection model in fuzzy linguistic formal contexts. Second, the intent similarity and extent similarity are employed to achieve the concept similarity measure in linguistic-valued layered concept lattices, taking into account the relationship among various layers of fuzzy linguistic values. To get the initial concept hard clustering results, the linguistic-valued layered concepts are then clustered using k-modes clustering. In addition, we explore the classification of boundary linguistic-valued layered concepts and achieve the three-way clustering findings of linguistic-valued layered concepts to deal with the ambiguity of linguistic expressions. Finally, experimental findings on real-world datasets show how effective the proposed method is for simplifying linguistic-valued layered concept lattices.

Implementation of fuzzy multi: Criteria decision making for recommendation student selection

Multi Criteria Decision Making (MCDM) uses different techniques to find a best alternative from multi-alternative and multi-criteria conditions. TOPSIS is an important practical technique for ranking and selection of different alternatives by distance measures. Fuzzy set theories are also employed due to the presence of vagueness and imprecision of information. This paper brings out the application of Multi Criteria Decision Making (MCDM) method known as technique for order preference by similarity to ideal solution (TOPSIS) using pentagonal intuitionistic fuzzy numbers. Therefore the objective of this paper is to select a best student on the basis of the student’s performance using ranking techniques for pentagonal intuitionistic fuzzy numbers can be converted into crisp value with the help of this value using TOPSIS method we get the best student of college. An example has been worked out to illustrate the application of TOPSIS for a multi-criteria decision making scenario.

An Improved Rank Order Centroid Method (IROC) for Criteria Weight Estimation: An Application in the Engine/Vehicle Selection Problem

The focus of this paper is on the criteria weight approximation in Multiple Criteria Decision Making (MCDM). An approximate weighting method produces the weights that are surrogates for the exact values that cannot be elicited directly from the DM. In this field, a very famous model is Rank Order Centroid (ROC). The paper shows that there is a drawback to the ROC method that could be resolved. The paper gives an idea to develop a revised version of the ROC method called Improved ROC (IROC). The behaviour of the IROC method is investigated using a set of simulation experiments. The IROC method could be employed in situations of time pressure, imprecise information, etc. The paper also proposes a methodology including the application of the IROC method in a group decision making mode, to estimate the weights of the criteria in a tree-shaped structure. The proposed methodology is useful for academics/managers/decision makers who want to deal with MCDM problem. A study case is examined to show applicability of the proposed methodology in a real-world situation. This case is engine/vehicle selection problem, that is one of the fundamental challenges of road transport sector of any country.

Approximations by Ideal Minimal Structure with Chemical Application

The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information. It can be characterized by two crisp sets, named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset. This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space via ideal . The novel approach (indicated by ) modifies the approximation space to diminish the boundary region and enhance the measure of accuracy. The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques. Via illustrated examples, several remarkable results using these notions are obtained and some of their properties are established. Several sorts of near open (resp. closed) sets based on are studied. Furthermore, the connections between these assorted kinds of near-open sets in are deduced. The advantages and disadvantages of the proposed approach compared to previous ones are examined. An algorithm using MATLAB and a framework for decision-making problems are verified. Finally, the chemical application for the classification of amino acids (AAs) is treated to highlight the significance of applying the suggested approximation.

Ranking and Evaluation Risks of Human Error Factors in Uncertain and Imprecision Information

Reasons for Human Error, the term risk is used to describe the many potential causes of human mistakes. Capabilities, organizational culture, job complexity, and environmental variables are just a few of the many aspects that fall under this category. Accidents, improvements in safety, and gains in productivity may all benefit from a better understanding of and approach to minimizing human error. This paper highlights the necessity for comprehensive methods and actions to limit the effect of human error by providing an overview of the primary human error components and their implications for risk management. Due to various criteria, the concept of multi-criteria decision-making (MCDM) is used to deal with various criteria. This paper used the MCDM tools to rank and evaluate the risks of human error factors. The DEMATEL method is a MCDM tool is used to compute the weights of these factors and rank the risks. The DEMATEL method is integrated with the neutrosophic set to deal with uncertain information. This paper used the single-valued neutrosophic set with three values (truth, indeterminacy, and falsity) values. The twenty risks are identified in this paper and ranked.

A Grey Simulation-Based Fuzzy Hierarchical Approach for Diagnosing Healthcare Service Quality

This study aims to assess and rank the service quality of the healthcare system utilizing a Fuzzy Analytical Hierarchical Process (Fuzzy AHP) and Grey Relational Analysis (Fuzzy GRA) technique. In this study, the six primary characteristics of healthcare service quality, comprising Tangibles (A), Healthcare Staff (B), Responsiveness (C), Relationships (D), Support Service (E), and Accessibility (F), are examined through a case study of 20 private and public hospitals in Hanoi, Vietnam. The weighting results of Fuzzy AHP technique indicated that Responsiveness (C) has the highest ranking, followed by Relationships (D) and Healthcare Staff (B). Meanwhile, Tangibility has finally comprised the next priority for increasing satisfaction with the service quality in the healthcare industry. Additionally, the highest service quality rankings are top 5 private hospitals via the Fuzzy GRA approach. Notably, this proposed approach may be applied to a complex decision-making process, which often makes sense with subjective data or imprecise information.

Soft Carathéodory extension theorem and soft outer measure

Molodsov defined the concept of a soft set, which is widely used when drawing conclusionsif we have unclear, incomplete and imprecise information. Soft set theory became an interest of many researchers who defined new concepts such as soft measure, soft ?-algebra, soft premeasure, soft outer measure, soft content, etc. In this paper, it was shown that with a certain extension, we can construct a soft measure on the obtained soft ?-algebra starting from a soft premeasure on a soft semiring.

Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set with Their Application to Solve MCDM Problem

Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval-valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.

A Review of Neutrosophic Linear Programming Problems Under Uncertain Environments

This review article focuses on the integration of Neutrosophic Set Theory and Extended Fuzzy Set Theory in the context of Linear Programming (LP) problems. Neutrosophic set theory deals with uncertain, imprecise, and indeterminate information, while Extended Fuzzy Set Theory extends the classical fuzzy set theory to handle more complex and nuanced membership degrees. The combination of these two frameworks provides a powerful toolset for modeling and solving LP problems in environments where uncertainty and ambiguity are prevalent. This review aims to analyze and summarize the existing literature on Neutrosophic Linear Programming problems in extended fuzzy environments, exploring the theoretical foundations and practical applications. The review article seeks to contribute to the understanding of these integrated approaches and their potential for addressing decision-making problems under complex and uncertain conditions.

Distance measures of picture fuzzy sets and interval-valued picture fuzzy sets with their applications

<abstract><p>Picture fuzzy sets (PFSs) are a versatile generalization of fuzzy sets and intuitionistic fuzzy sets (IFSs), providing a robust framework for modeling imprecise, uncertain, and inconsistent information across various fields. As an advanced extension of PFSs, interval-valued picture fuzzy sets (IvPFSs) offer superior capabilities for handling incomplete and indeterminate information in various practical applications. Distance measures have always been an important topic in fuzzy sets and their variants. Some existing distance measures for PFSs have shown limitations and may yield counterintuitive results under certain conditions. Furthermore, there are currently few studies on distance measures for IvPFSs. To solve these problems, in this paper we devised a series of novel distance measures between PFSs and IvPFSs inspired by the Hellinger distance. Specifically, all the distance measures were divided into two parts: One considered the positive membership degree, neutral membership degree and negative membership degree, and the other added the refusal membership degree. Moreover, the proposed distance measures met some important properties, including boundedness, non-degeneracy, symmetry, and consistency, but also showed superiority compared to the existing measures, as confirmed through numerical comparisons. Finally, the proposed distance measures were validated in pattern recognition and medical diagnosis applications, indicating that the proposed distance measures can deliver credible, reasonable results, particularly in similar cases.</p></abstract>

Neutrosophic-based Machine Learning Techniques in the Context of Supply Chain Management: A Survey

Supply Chain Management (SCM) plays a critical role in the success of any business organization. Individuals involved in business activities often have to make decisions regarding different aspects of the supply chain, including planning, procurement, production, inventory management, transportation, distribution, and customer relationship management. The combination of neutrosophic logic and machine learning has gained significant attention in the field of SCM as a means to tackle uncertainties and improve decision-making. This paper highlights the potential benefits and applications of integrating neutrosophic reasoning and machine learning in SCM. Neutrosophic reasoning provides a framework for handling imprecise and uncertain information, while machine learning techniques offer powerful tools for data analysis, pattern recognition, and predictive modeling. By leveraging machine learning algorithms within the context of neutrosophic logic, SCM practitioners can enhance demand forecasting accuracy, optimize inventory management, improve transportation and routing decisions, and strengthen supply chain collaboration. The integration of neutrosophic logic and machine learning enables the handling of complex supply chain data, accommodates dynamic and uncertain environments, and supports proactive decision-making. Furthermore, the combination of these approaches can contribute to improved supply chain resilience, sustainability, and customer satisfaction. This paper applied the neutrosophic AHP method as a feature section to select the highest importance criteria as an input to machine learning. Then we applied two machine learning models named random forest and decision. The results show the random forest has the highest accuracy followed by a decision tree.

A few little steps beyond Knuth’s Boolean Logic Table with Neutrosophic Logic: A Paradigm Shift in Uncertain Computation

The present article delves into the extension of Knuth’s fundamental Boolean logic table to accommodate the complexities of indeterminate truth values through the integration of neutrosophic logic (Smarandache Christianto, 2008). Neutrosophic logic, rooted in Florentin Smarandache’s groundbreaking work on Neutrosophic Logic (cf. Smarandache, 2005, and his other works), introduces an additional truth value, ‘indeterminate,’ enabling a more comprehensive framework to analyze uncertainties inherent in computational systems. By bridging the gap between traditional boolean operations and the indeterminacy present in various real-world scenarios, this extension redefines logic tables, introducing neutrosophic operators that capture nuances beyond the binary realm. Through a thorough exploration of neutrosophic logic's principles and its implications in computational paradigms, this study proposes a novel approach to logic design that accommodates uncertain, imprecise, and incomplete information. This paradigm shift in logic tables not only broadens the spectrum of computing methodologies but also holds promise in fields such as decision-making systems and data analytics. This article amalgamates insights from over twelve key references encompassing seminal works in boolean logic, neutrosophic logic, and their applications in diverse scientific and computational domains, aiming to pave the way for a more robust and adaptable logic framework in computation.

A New Modified Logistic Distribution: Properties and Applications in Uncertainty Data Modeling

The logistic distribution is widely used to model various types of applied data. The modified logistic distribution under neutrosophic statistics is introduced in this work. The neutrosophic logistic distribution (NLD) and its engineering applications are mainly emphasized. An appealing characteristic of the suggested NLD is that it is useful to many widely utilized survival assessment metrics, including the reliability function, hazard function, and survival function. Applications of some mathematical and statistical properties of the suggested model are discussed. Numerical investigations on simulated data are used to validate the theoretical findings experimentally. From an application point of view, it is inferred that the proposed distribution fits data with imprecise, hazy, and fuzzy information better than the usual model. In addition, the maximum likelihood (ML) technique for the proposed model is discussed under the neutrosophic inference framework. Eventually, some illustrative examples related to system reliability are provided to clarify further the implementation of the neutrosophic probabilistic model in real-world problems.

Application of a fuzzy controller in adaptive e-learning content used to evaluate student activity

This article presents an e-learning system that supports the adaptation of course content to the student's way of learning. The adaptability of an e-learning course is a challenging task that requires appropriate tools and a well-thought-out architecture. The solution presented in this article is based on the concept of information imprecision and fuzzy control. The proposed fuzzy controller, based on an expert rule base calculates the student's activity in the course in order to determine the questions in tests at the end of successive parts of the course. The solution proposed was implemented in an e-learning Applications of Fuzzy Sets course, which was part of an Artificial Intelligence class. The proposed system successfully adapts the course content to the student's learning style. The article highlights the potential of fuzzy controllers in adaptive e-learning systems. The use of fuzzy controllers makes it possible to take into account the imprecision of information, enabling better handling of uncertainty and variability in the student's learning style.

A bi-level optimization model for the asset-liability management of insurance companies

<p style='text-indent:20px;'>Different from traditional asset-liability management where only investment allocation is considered, this paper introduces policy product allocation into asset-liability management of insurance companies. In order to balance product allocation and investment allocation, a bi-level optimization model is employed. Since the decision-making environment of the two allocation processes is full of indeterminacy, the imprecise information of the model is measured by uncertain variables in order to deal with the lack of enough historical data. To solve this bi-level Optimization problem containing uncertain variables, an uncertain bilevel programming model is used. Furthermore, we simulate a scenario to compare the bi-level optimization approach with other approaches by virtue of hybrid intelligent algorithms.</p>

Sustainable practices to reduce environmental impact of industry using interaction aggregation operators under interval-valued Pythagorean fuzzy hypersoft set

<abstract><p>Optimization techniques can be used to find the optimal combination of inputs and parameters and help identify the most efficient solution. Aggregation operators (AOs) play a prominent role in discernment between two circulations of prospect and pull out anxieties from that insight. The most fundamental objective of this research is to extend the interaction AOs to the interval-valued Pythagorean fuzzy hypersoft set (IVPFHSS), the comprehensive system of the interval-valued Pythagorean fuzzy soft set (IVPFSS). The IVPFHSS adroitly contracts with defective and ambagious facts compared to the prevalent Pythagorean fuzzy soft set and interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS). It is the dominant technique for enlarging imprecise information in decision-making (DM). The most important intention of this exploration is to intend interactional operational laws for IVPFHSNs. We extend the AOs to interaction AOs under IVPFHSS setting such as interval-valued Pythagorean fuzzy hypersoft interactive weighted average (IVPFHSIWA) and interval-valued Pythagorean fuzzy hypersoft interactive weighted geometric (IVPFHSIWG) operators. Also, we study the significant properties of the proposed operators, such as Idempotency, Boundedness, and Homogeneity. Still, the prevalent multi-criteria group decision-making (MCGDM) approaches consistently carry irreconcilable consequences. Meanwhile, our proposed MCGDM model is deliberate to accommodate these shortcomings. By utilizing a developed mathematical model and optimization technique, Industry 5.0 can achieve digital green innovation, enabling the development of sustainable processes that significantly decrease environmental impact. The impacts show that the intentional model is more operative and consistent in conducting inaccurate data based on IVPFHSS.</p></abstract>