Imprecise Information Research Articles

A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells

The objective of this paper is to present new interactive averaging aggregation operators by assigning associate probabilities for T-spherical fuzzy sets (T-SFSs). T-SFS is a generalization of several existing theories such as intuitionistic fuzzy sets and picture fuzzy sets to handle imprecise information. Under such an environment, we developed a series of averaging interactive aggregation operators under the features that each element is represented with T-spherical fuzzy numbers. Various properties of the proposed operators are also investigated. Further, to rank the different T-SFSs, we exhibit the new score functions and state their some properties. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. To save non-renewable resources and to the protect environment, the use of renewable resources is important. Solar energy is one of the best renewable energy resources and is also environment-friendly and thus the selection of solar cells is typically a multi-attribute decision-making problem. Therefore, the applicability of the developed algorithm is demonstrated with a numerical example in the selection of the solar cells and comparison of their performance with the several existing approaches.

Multi-objective non-linear four-valued refined neutrosophic optimization

The neutrosophic sets are the prevailing frameworks that not only generalize the concept of fuzzy sets, but also analyse the connectivity of neutralities with different ideational spectra. In this article, we define a special type of neutrosophic set, named four-valued refined neutrosophic set (FVRNO), based on which various set-theoretic operators and properties of four-valued refined neutrosophic sets are studied. Often in many optimization problems of the real world, only the partial information about the values of parameters is available. In such situations, where impreciseness is involved in the information, classical techniques do not exhibit an appropriate optimal solution. A new concept to handle imprecise information is introduced and computational algorithm is formulated in four-valued refined neutrosophic environment. The new concept of optimization problem is an extension of intuitionistic fuzzy optimization as well as single-valued neutrosophic optimization. In this extended concept, indeterminacy is further refined as uncertain (U) and contradiction $$(C= T\wedge F)$$ . Some examples to illustrate FVRNO are given and a comparative study of optimal solution between intuitionistic fuzzy optimization, single-valued neutrosophic optimization, multi-objective optimization using genetic algorithm, multi-objective goal attainment and four-valued refined neutrosophic optimization techniques were carried out and that concludes better optimal approximation is attained with new proposed optimization technique.

Robust decision making and Epoch–Era analysis: A comparison of two robustness frameworks for decision-making under uncertainty

Several model-based frameworks have been introduced in support of robust decision-making. While they agree on a need to cope with uncertainty for robust inferences, the frameworks differ in the way that they treat uncertainty and obtain decision insights. In this article, we compare and contrast two such frameworks: Robust Decision Making and Epoch–Era Analysis. We critically analyse the two frameworks in terms of their aims and expected decision insights, the way they cope with uncertainty, and the extent to which they use model-based and participatory analysis. Our conceptual comparison sheds light on the strengths and limitations of the two frameworks in different contexts. We then apply both frameworks to an illustrative case to analyse their benefits and caveats in practice. We conclude that the superiority of each framework is not unconditional, and depends on the context and the problem at hand. While Robust Decision Making is a more effective framework under contested and imprecise information about the future, Epoch–Era Analysis can work better when stakeholder knowledge about the future allows a deliberative specification of future scenarios. The evaluation of both frameworks’ strengths and limitations can contribute to future methodological developments in the literature on decision-making under uncertainty.

Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making

The power Bonferroni mean (PBM) operator can relieve the influence of unreasonable aggregation values and also capture the interrelationship among the input arguments, which is an important generalization of power average operator and Bonferroni mean operator, and Pythagorean fuzzy set is an effective mathematical method to handle imprecise and uncertain information. In this paper, we extend PBM operator to integrate Pythagorean fuzzy numbers (PFNs) based on the interaction operational laws of PFNs, and propose Pythagorean fuzzy interaction PBM operator and weighted Pythagorean fuzzy interaction PBM operator. These new Pythagorean fuzzy interaction PBM operators can capture the interactions between the membership and nonmembership function of PFNs and retain the main merits of the PBM operator. Then, we analyze some desirable properties and particular cases of the presented operators. Further, a new multiple attribute decision making method based on the proposed method has been presented. Finally, a numerical example concerning the evaluation of online payment service providers is provided to illustrate the validity and merits of the new method by comparing it with the existing methods.

A Study on Hypergraph Representations of Complex Fuzzy Information

The paradigm shift prompted by Zadeh’s fuzzy sets in 1965 did not end with the fuzzy model and logic. Extensions in various lines have produced e.g., intuitionistic fuzzy sets in 1983, complex fuzzy sets in 2002, or hesitant fuzzy sets in 2010. The researcher can avail himself of graphs of various types in order to represent concepts like networks with imprecise information, whether it is fuzzy, intuitionistic, or has more general characteristics. When the relationships in the network are symmetrical, and each member can be linked with groups of members, the natural concept for a representation is a hypergraph. In this paper we develop novel generalized hypergraphs in a wide fuzzy context, namely, complex intuitionistic fuzzy hypergraphs, complex Pythagorean fuzzy hypergraphs, and complex q-rung orthopair fuzzy hypergraphs. Further, we consider the transversals and minimal transversals of complex q-rung orthopair fuzzy hypergraphs. We present some algorithms to construct the minimal transversals and certain related concepts. As an application, we describe a collaboration network model through a complex q-rung orthopair fuzzy hypergraph. We use it to find the author having the most outstanding collaboration skills using score and choice values.

Worker retirement responses to pension incentives: Do they respond to pension wealth?

Pension enhancements generate pension wealth spikes at the eligibility milestones. I analyze two major enhancements that generated different gains in pension wealth for eligible workers. The responsiveness of retirement behavior to these enhancements depends on how well workers understand their pension incentives. To test the retirement response to pension wealth, I use administrative data from Missouri teachers and leverage variation in enhancement impacts on teacher pension wealth owing to differences in teachers’ entering ages. I find that retirements respond strongly to pension enhancements, but the strength of the response does not align with their pecuniary value. My findings contribute to a growing body of research showing that workers have imperfect knowledge of their pension benefits and they use imprecise information to make retirement timing decisions.

Novel Exponential divergence measure of complex intuitionistic fuzzy sets with an application to decision-making process

As a generalization of the intuitionistic fuzzy sets (IFSs), complex IFSs (CIFSs) is a powerful and worthy tool to realize the imprecise information by using complex-valued membership degrees with an extra term, named as phase term. Divergence measure is a valuable tool to determine the degree of discrimination between the two sets. Driven by these fundamental characteristics, it is fascinating to manifest some divergence measures to the CIFSs. In this paper, we explain a method to solve the multi-criteria decision-making (MCDM) problem under CIFS environment. For it, firstly, the divergence measures are introduced between two CIFSs and examined their several properties and relations. Secondly, a novel algorithm is given based on the proposed measures to solve the problems in which weights corresponding to criteria are resolved using maximizing deviation method. Thirdly, a reasonable example is provided to verify the developed approach and to exhibit its practicality and utility with a comparative analysis to show its more manageable and adaptable nature.

A decision making model based on fuzzy inference to predict the impact of SCOR® indicators on customer perceived value

Customer perceived value (CPV) is critical for supply chain management, due to its link with satisfaction and market share. In addition, value perception is a consequence of several factors including operational performance. Hence, analyzing the cause and effect relationship between CPV and supply chain performance can help decision makers to identify attributes of performance that need improvement efforts so as to enhance CPV. However, modeling this relationship is very dependent of cognitive judgments associated with incomplete or imprecise information. To overcome this, fuzzy inference has been largely used in supply chain management. However, no study was found that applies this soft computing technique with natural language processing to investigate the impact of supply chain performance on CPV. Therefore, this article proposes a decision making model based on fuzzy inference to help predicting the impact on CPV of the performance indicators of the SCOR® (Supply Chain Operations Reference) model. The SCOR® level 1 indicators were applied as a mean to assess CPV in a multidimensional way, to enable benchmarking with other supply chains and to facilitate the communication with stakeholders. It is an axiomatic prescriptive model-based research that includes an illustrative application based on the distribution of beverages to final customers. Analysis of the response surfaces of both Fuzzy Inference Systems allowed identification of the attributes of performance that most impact CPV, therefore providing the possibility of anticipation and prioritization. The model is adaptable to various supply chain configurations. Also, it provides the possibility of internalizing CPV as a driver for supply chain continuous improvement initiatives.

Outsourcing modelling using a novel interval-valued fuzzy quantitative strategic planning matrix (QSPM) and multiple criteria decision-making (MCDMs)

Outsourcing drives companies to focus on: their capabilities, advantages of external resources, and decreasing overall operational costs. Selecting appropriate alliances, which are aligned with the company's strategies, establishes a situation through which the firms can enhance their technical capabilities and achieve new technologies. However, two critical issues in outsourcing modeling should be addressed: how to find strategic indicators for building successful alliances, and how to select these partners. Besides, as the imprecise and vague information (due to a lack of data) existing in the outsourcing models cannot be neglected, the application of fuzzy interval sets could efficiently address the complexity of these problems.To deal with these issues, this paper proposes a two-step interval-based framework for the problem. At the beginning, and for the first time, the novel integration of an interval valued fuzzy (IVF) version of strength-weakness-opportunity-threats (SWOT) technique and the quantitative strategic planning matrix (QSPM) with Gap analysis is designed to find the most effective strategies for the alliance evaluation, and to weight them. In the next step, four interval-valued version of multiple criteria decision-making methods (IVF-MCDMs) are implemented to evaluate the strategic partners.Finally, the results are aggregated with the help of the utility interval approach, and a sensitivity analysis is implemented to assess the robustness of the proposed methodology. To illustrate the efficiency of the proposed approach, a real partner selection problem at a holding car manufacturing factory in Iran is presented.

Predição Leitora e Consciência Textual: um estudo com alunos do Ensino Fundamental

Based on psycholinguistic studies, this article deals with reading comprehension skills focusing prediction and the textual consciousness level imbricated in this strategy. To demonstrate this theory, a research has been carried on with 55 sixth grade-students whose ages ranged from 11 to 13, all attending the elementary educational level of a public school in the city of Porto Alegre. In order to examine the effective use of predictions, a reading task with parts of a fable was presented in paper cards, as well as questions about the story to stimulate the use of those strategies. The verbal protocol of self-revelation was adopted to verify the participants´ textual level of consciousness. The results showed that most of the students managed to deal with reading prediction, making pertinent anticipations, although 27% of them were unsuccessful. In relation to the textual consciousness in the use of this strategy, just over half of the students showed metalinguistic behavior, being capable to explain the generative bases of their predictions efficiently using both intratextual and extratextual information. Nevertheless, 47% of the pupils were not able to achieve the goal, since they responded the questions in a confusing and mistaken manner or used vague and imprecise information while showing evidences of how they had processed the question. Considering the educational context, the research results suggested that both the use of the reading prediction and its conscious awareness are relevant topics to be applied in Portuguese language classes, for they provide the teacher with information concerning the possibilities and difficulties on students´ reading process.

Medical Image Thresholding Using Genetic Algorithm and Fuzzy Membership Functions

Thresholding is one of the important steps in image analysis process and used extensively in different image processing techniques. Medical image segmentation plays a very important role in surgery planning, identification of tumours, diagnosis of organs, etc. In this article, a novel approach for medical image segmentation is proposed using a hybrid technique of genetic algorithm and fuzzy logic. Fuzzy logic can handle uncertain and imprecise information. Genetic algorithms help in global optimization, gives good results in noisy environments and supports multi-objective optimization. Gaussian, trapezoidal and triangular membership functions are used separately for calculating the entropy and finding the fitness value. CPU time, Root Mean Square Error, sensitivity, specificity, and accuracy are calculated using the three membership functions separately at threshold levels 2, 3, 4, 5, 7 and 9. MRI images are considered for applying the proposed method and the results are analysed. The experimental results obtained prove the effectiveness and efficiency of the proposed method.

Aggregating and Ranking Method for the Evaluation of Product Design Materials

A new MCDM model based on a triangular intuitionistic fuzzy (TIF) aggregating and ranking model is proposed for the evaluation of adhesive materials used in joining fibre-reinforced plastic. The new model which uses the triangular intuitionistic fuzzy numbers (TIFN), TIF aggregating operators and the TIF ranking functions provides a more accurate method for assessing uncertain or imprecise information in the decision-making process. The model addresses the MCDM problem in which the available information cannot be assessed with exact numbers and requires the use of a more holistic approach which is a drawback in the existing MCDM methods used in the evaluation of design materials in literature. The result from the evaluation shows that the alternative T3 (Polyurethane) has the best chances of been used in joining the FRP with respect to the fracture mechanics-based criteria. With the ranking result presented, the study can conclude that the procedure used for the evaluation of the adhesive material has led to the selection of the best adhesive material for joining the FRP elements.

A Novel Hybrid Approach: Grid Partition and Rough Set-Based Fuzzy Rule Generation for Accurate Dataset Classification

Accurate dataset classification is a fundamental task in various domains such as machine learning, pattern recognition, and data mining. This research proposes a novel hybrid approach that combines grid partitioning, rough set-based feature reduction, and fuzzy rule generation to enhance classification accuracy and interpretability. The approach begins with the partitioning of the dataset into a grid of cells, enabling localized analysis and capturing intricate patterns. Next, rough set-based feature reduction is applied to identify essential features and reduce dimensionality. This process helps overcome the curse of dimensionality commonly associated with complex datasets. Subsequently, fuzzy rule generation is employed, leveraging linguistic variables and membership functions to represent imprecise and uncertain information. This enhances interpretability by providing transparent decision-making rules. To evaluate the effectiveness of the proposed approach, comparative analysis with traditional classification methods, including decision trees, support vector machines, and neural networks, is conducted. The results demonstrate the superiority or at least comparability of the hybrid approach in terms of classification accuracy, computational complexity, and interpretability. However, it is essential to acknowledge the limitations of the research, such as the sensitivity to grid size and the interpretability-performance trade-off. Future research can focus on refining the approach by exploring optimal grid size selection methods and mitigating the interpretability-performance trade-off.The findings of this research contribute to the advancement of accurate dataset classification techniques. The proposed hybrid approach offers improved classification accuracy, handles complex datasets effectively, and enhances interpretability through fuzzy rules. The practical implications of the research span domains such as bioinformatics, IoT, and financial analysis. Overall, this research provides a foundation for further exploration, refinement, and real-world applications of the hybrid approach in accurate dataset classification scenarios.

Observer and control design in partially observable finite Markov chains

The controllable Partially Observable Markov Decision Process (POMDP) framework has proven to be useful in different domains where one is constrained to provide incomplete information of the structure and the parameters of the problem. Sometimes, it is not easy to track and measure accurately some state variables, and it may be more effective to make decisions based on imprecise information. This paper is focused on the design of an observer (which is unknown) for a class of ergodic homogeneous finite Markov chains with partially observable states. The main goal of the proposed method is the derivation of formulas for computing an observer, and as a result, on optimal control policy. For solving the problem, we introduce a new variable, which involves the product of the policy, the observation kernel and the distribution vector. We derive the formulas to recover the variables of interest. This work considers a dynamic environment for learning the parameters of the POMDP model. The construction of the adaptive policies is based on an identification approach, where we estimate the elements of the transition matrices and utility matrices by counting the number of unobserved experiences. A numerical example is presented to illustrate the practical implications of the theoretical issues applied to a portfolio optimization problem. These findings are important and new to the literature.

A practical review and taxonomy of fuzzy expert systems: methods and applications

PurposeExpert systems are computer-based systems that mimic the logical processes of human experts or organizations to give advice in a specific domain of knowledge. Fuzzy expert systems use fuzzy logic to handle uncertainties generated by imprecise, incomplete and/or vague information. The purpose of this paper is to present a comprehensive review of the methods and applications in fuzzy expert systems.Design/methodology/approachThe authors have carefully reviewed 281 journal publications and 149 conference proceedings published over the past 37 years since 1982. The authors grouped the journal publications and conference proceedings separately accordingly to the methods, application domains, tools and inference systems.FindingsThe authors have synthesized the findings and proposed useful suggestions for future research directions. The authors show that the most common use of fuzzy expert systems is in the medical field.Originality/valueFuzzy logic can be used to manage uncertainty in expert systems and solve problems that cannot be solved effectively with conventional methods. In this study, the authors present a comprehensive review of the methods and applications in fuzzy expert systems which could be useful for practicing managers developing expert systems under uncertainty.

Strengths of Exaggerated Tsunami-Originated Placenames: Disaster Subculture in Sanriku Coast, Japan

Disaster-originated placename is a kind of disaster subculture that is used for a practical purpose of identifying a location while reminding the past disaster experience. They are expected to transmit the risks and knowledge of high-risk low-frequency natural hazards, surviving over time and generations. This paper compares the perceptions to tsunami-originated placenames in local communities having realistic and exaggerated origins in Sanriku Coast, Japan. The reality of tsunami-originated placenames is first assessed by comparing the tsunami run-ups indicated in the origins and that of the tsunami in the Great East Japan Earthquake 2011 using GIS and digital elevation model. Considerable proportions of placenames had exaggerated origins, but the group interviews to local communities revealed that origins indicating unrealistic tsunami run-ups were more believed than that of the more realistic ones. We discuss that accurate hazard information will be discredited if it contradicts to the people’s everyday life and the desire for safety, and even imprecise and ambiguous information can survive if it is embedded to a system of local knowledge that consistently explains the various facts in a local area that requires explanation.

Fuzzy Decision Trees in Medical Decision Making Support Systems

Fuzzy decision trees represent classification knowledge more naturally to the way of human thinking and are more robust in tolerating imprecise, conflict, and missing information. Decision Making Support Systems are used widely in clinical medicine because decisions play an important role in diagnostic processes. Decision trees are a very suitable candidate for induction of simple decision-making models with the possibility of automatic learning. The goal of this paper is to demonstrate a new approach for predictive data mining models in clinical medicine. This approach is based on induction of fuzzy decision trees. This approach allows us to build decision-making modesl with different properties (ordered, stability etc.). Three new types of fuzzy decision trees (non-ordered, ordered and stable) are considered in the paper. Induction of these fuzzy decision trees is based on cumulative information estimates. Results of experimental investigation are presented. Predictive data mining is becoming an essential instrument for researchers and clinical practitioners in medicine. Using new approaches based on fuzzy decision trees allows to increase the prediction accuracy. Decision trees are a very suitable candidate for induction using simple decision-making models with the possibility of automatic and AI learning.

Generalization of non-intrusive imprecise stochastic simulation for mixed uncertain variables

Abstract Non-intrusive Imprecise Stochastic Simulation (NISS) is a recently developed general methodological framework for efficiently propagating the imprecise probability models and for estimating the resultant failure probability functions and bounds. Due to the simplicity, high efficiency, stability and good convergence, it has been proved to be one of the most appealing forward uncertainty quantification methods. However, the current version of NISS is only applicable for model with input variables characterized by precise and imprecise probability models. In real-world applications, the uncertainties of model inputs may also be characterized by non-probabilistic models such as interval model due to the extreme scarcity or imprecise information. In this paper, the NISS method is generalized for models with three kinds of mixed inputs characterized by precise probability model, non-probabilistic models and imprecise probability models respectively, and specifically, the interval model and distributional p-box model are exemplified. This generalization is realized by combining Bayes rule and the global NISS method, and is shown to conserve all the advantages of the classical NISS method. With this generalization, the three kinds of inputs can be propagated with only one set of function evaluations in a pure simulation manner, and two kinds of potential estimation errors are properly addressed by sensitivity indices and bootstrap. A numerical test example and the NASA uncertainty quantification challenging problem are solved to demonstrate the effectiveness of the generalized NISS procedure.

Distance and similarity measures of Pythagorean fuzzy sets based on the Hausdorff metric with application to fuzzy TOPSIS

Pythagorean fuzzy sets (PFSs) were proposed by Yager in 2013 to treat imprecise and vague information in daily life more rigorously and efficiently with higher precision than intuitionistic fuzzy sets. In this paper, we construct new distance and similarity measures of PFSs based on the Hausdorff metric. We first develop a method to calculate a distance between PFSs based on the Hasudorff metric, along with proving several properties and theorems. We then consider a generalization of other distance measures, such as the Hamming distance, the Euclidean distance, and their normalized versions. On the basis of the proposed distances for PFSs, we give new similarity measures to compute the similarity degree of PFSs. Some examples related to pattern recognition and linguistic variables are used to validate the proposed distance and similarity measures. Finally, we apply the proposed methods to multicriteria decision-making by constructing a Pythagorean fuzzy Technique for Order Preference by Similarity to an Ideal Solution and then present a practical example to address an important issue related to social sector. Numerical results indicate that the proposed methods are reasonable and applicable and also that they are well suited in pattern recognition, linguistic variables, and multicriteria decision-making with PFSs.

Robust Adaptive Wideband Beamforming Based on Time Frequency Distribution

Many robust adaptive wideband beamforming algorithms have been carried out to preserve the signal of interest, but their performance can be still degraded by the mismatches of steering vector and covariance matrix. Therefore, in this paper, a novel robust adaptive wideband beamformer based on the time-frequency distribution is proposed, which can achieve high output signal-to-interference-plus-noise ratio close to the optimal one even with perturbed array manifold and limited snapshots. It transforms the received signal into the time-frequency domain, and gives a method to select the single-source points of wideband signals. With the single-source points, it reconstructs the interference-plus-noise covariance matrix and estimates the steering vector without using the imprecise prior information about the array manifold, guaranteeing high estimation accuracy. Simulation results demonstrate that the proposed method outperforms other adaptive wideband beamformers, and achieves excellent output performance over a broad range of direction and sensor position errors even with small number of snapshots.