Crisp Set Research Articles

Necessary and sufficient conditions for social science undergraduates’ academic success in English medium instruction settings: a crisp set qualitative comparative analysis

ABSTRACT Previous research has examined the impact of various factors on the academic success of undergraduate students in English Medium Instruction (EMI) environments, with the aim of improving students’ academic outcomes. However, clarity regarding the necessity and sufficiency of these factors for EMI academic success remains elusive, limiting a comprehensive understanding of this phenomenon. This study used crisp-set Qualitative Comparative Analysis (csQCA) to analyse data from 16 empirical studies that investigated factors influencing the academic success of social science undergraduate students in EMI settings, using the EMI Academic Success (EMIAS) model. The findings revealed that English language proficiency emerged as a necessary and sufficient condition for EMI academic success, while students’ characteristics appeared to be a sufficient but not necessary condition. In addition, three causal configurations leading to EMI academic success were identified among four condition variables – English language proficiency, students’ characteristics, educational background, and English language support. This study contributes to a deeper understanding of the determinants of EMI academic success and highlights the importance of students’ English language proficiency and their characteristics in the context of EMI.

Difference operators on fuzzy sets

Based on the properties of the difference operator on crisp sets, a fuzzy difference operator in fuzzy logic is defined as a continuous binary operator on the closed unit interval with some boundary conditions. In this paper, the structures and properties of fuzzy difference operators are studied. The main results are: (1) Using the axiomatic approach, some generalizations of classical tautologies for fuzzy difference operators are obtained. (2) Based on the model theoretic approach, the fuzzy difference operator constructed by a nilpotent t-norm and a strong negation is characterized. (3) the paper discusses the relationship between the fuzzy difference operator and symmetric difference operator which was raised in [3].

Fuzzy Fractional Brownian Motion: Review and Extension

In traditional finance, option prices are typically calculated using crisp sets of variables. However, as reported in the literature novel, these parameters possess a degree of fuzziness or uncertainty. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. This paper presents a comprehensive review of existing work on fuzzy fractional Brownian motion and proposes an extension in the context of financial option pricing. In this paper, we define a unified framework combining fractional Brownian motion with fuzzy processes, creating a joint product measure space that captures both randomness and fuzziness. The approach allows for the consideration of individual risk preferences and beliefs about parameter uncertainties. By extending Merton’s jump-diffusion model to include fuzzy fractional Brownian motion, this paper addresses the modelling needs of hybrid systems with uncertain variables. The proposed model, which includes fuzzy Poisson processes and fuzzy volatility, demonstrates advantageous properties such as long-range dependence and self-similarity, providing a robust tool for modelling financial markets. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions.

Adopting the fuzzy approach to analyze food poverty in Italy: A study on vulnerable households using household budget survey data

Besides international efforts to address poverty and hunger, there are still many disparities among households, therefore innovative approaches and techniques are required to address the multiple facets of poverty, especially food poverty.Given the complexity in defining this phenomenon, the fuzzy approach based on an expenditure-related metric is adopted as it provides valuable insights into the Italian food poverty situation thus improving the results generally provided using by the classical binary (or crisp) set theory.By considering the equivalised household food expenditure obtained from the 2021 Italian Household Budget Survey data, the fuzzy set approach is used to measure food poverty paying particular attention to vulnerable households at a detailed territorial level. The results show that food poverty is lower in the Northern-Central regions than in Southern Italy and highlight the vulnerability of families with children and single-parent households.

Complete ranking for generalized trapezoidal fuzzy numbers and its application in supplier selection using the GTrF-CoCoSo approach

Decision-making is an indispensable tool in many real-life situations. The classical set theory is insufficient to solve problems involving uncertainty and qualitative data. In order to tackle scenarios with qualitative information and imprecise boundaries, fuzzy set theory generalizes crisp sets. Thus, ranking is an essential methodology in decision-making in a fuzzy environment. In literature, generalized trapezoidal fuzzy numbers (GTrFNs) are used to model many real-life situations with imprecise, uncertain, and incomplete information. There are various techniques available to discriminate arbitrary GTrFNs. Several researchers are seeking a standard consensus technique to distinguish between arbitrary GTrFNs. The diagonal distance right position, diagonal distance left chord, diagonal distance center position, diagonal distance, and diagonal distance right chord scores are the five score functions that are used in this work to develop a complete ranking (total ordering) principle on the class of GTrFNs to distinguish arbitrary GTrFNs. To show the potentiality of the proposed method, we compare the proposed approach with the few existing approaches suggesting to rank GTrFNs. Further, we proposed a new GTrF-CoCoSo approach by incorporating the proposed complete ordering principle. Then the efficacy of the proposed ranking principle is examined in solving multi-criteria decision-making (MCDM) using the GTrF-CoCoSo approach to select the best banana supplier for food production company. Furthermore, a sensitivity analysis is presented to evaluate the performance of the suggested ranking principle with the GTrF-CoCoSo approach.

A mathematical approach to optimizing brand school placement via intuitionistic Sombor indices

The property of fuzziness is advantageous for any setting where a problem prediction and solution are intended. In comparison to the classical approach (crisp set), fuzzy graphs are beneficial as they provide greater precision and flexibility. Intuitionistic fuzzy graphs (IFGs) are generalizations of fuzzy graphs, in which each vertex is allocated an ordered pair whose first coordinate represents the membership value and whose second coordinate gives the non-membership value. Sombor indices are recently invented indices and are prime indices in describing the topology of a graph. They have demonstrated strong prediction ability in mathematical chemistry. The main aim of this research draft is to define two milestones, the fifth and sixth versions of Sombor indices in an intuitionistic fuzzy environment, IFGs are much more generalized and universal as compared to crisp graph theory, so we converted these two topological indices in this environment and then formulae for some fundamental families of graphs such as path graph, cycle graph, complete graph etc. are being derived. Our manuscript presents a novel application of opening a chain of schools of a popular brand in a certain vicinity, including the cluster center of the chain and applying intuitionistic fuzzy-based topological indices to assess their performance. With the help of this application, we highlight the practical implications and benefits of employing intuitionistic fuzzy-based techniques on the performance of schools through a comparative analysis. We checked the importance of intuitionistic fuzzy Sombor indices by presenting the application and concluded these indices can be applied to decision-making problems. With the help of the application, the efficiency of both of the intuitionistic fuzzy Sombor indices is also characterized, which must be a future efficacious tool in decision-making issues.

Beyond regression: Unpacking research of human complex systems with qualitative comparative analysis

This study underscores the effectiveness of Qualitative Comparative Analysis (QCA) when compared to conventional regression analysis (CRA) in the investigation of complex human systems. Utilizing historical secondary cross-national data from Lipset & Man (1960) spanning 18 countries, where CRA may be impractical, the research emphasizes the superior performance of QCA, specifically utilizing both crisp set QCA and fuzzy set QCA. The dataset includes variables such as democracy survival and its precursors, such as gross national product per capita, urbanization, literacy rate, and industrial labor force. In contrast to conventional regression results indicating an insignificant relationship between democracy survival and its antecedents, crisp set QCA identifies two distinct combinations of antecedents associated with high levels of democracy survival, albeit with limited solution coverage. Meanwhile, fuzzy set qualitative comparative analysis (fsQCA) reveals five combinations of antecedents linked to robust democracy survival, providing adequate solution coverage and consistency. These findings suggest that fsQCA excels in capturing the intricacies of real-life scenarios in human complex systems, offering more robust empirical solutions compared to crisp set QCA and conventional regression. As a result, researchers may find value in integrating fsQCA into their new projects focused on human complex systems.

On Maximum Guaranteed Payoff in a Fuzzy Matrix Decision-Making Problem with a Fuzzy Set of States

The current study delves into a fuzzy matrix decision-making problem involving fuzzy sets of states. It establishes that a maximum guaranteed payoff constitutes a type-2 fuzzy set defined on the real line. Additionally, it provides the associated type-2 membership function. Moreover, the paper illustrates that the maximum guaranteed payoff type-2 fuzzy set of the decision-making problem can be broken down, based on the secondary membership grades, into a finite collection of fuzzy numbers. Each of these fuzzy numbers represents the maximum guaranteed payoff of the corresponding decision-making problem with a crisp set of states. This set corresponds to a specific cut of the original fuzzy set of states. Some properties of the maximum guaranteed payoff type-2 fuzzy set are investigated, and illustrative examples are provided. Since the problem formulation is symmetrical with respect to alternatives and states of nature, the results obtained can be used in the case of a fuzzy set of alternatives.

An [formula omitted]-cut intervals based Fuzzy Best–Worst Method for Multi-Criteria Decision-Making

To address ambiguity arising from linguistic decision judgments, Guo and Zhao introduced a model of the well-known Multi-Criteria Decision-Making (MCDM) method, Best-Worst Method (BWM), using fuzzy sets, known as Fuzzy Best–Worst Method (FBWM). Despite its versatility, FBWM has limitations, such as criteria-weights being independent of fuzzy comparison values’ shape and reliance on approximate fuzzy arithmetic operations. In response to these limitations, we introduce a novel model of Fuzzy Best–Worst Method based on α-cut intervals. In this model, the calculation of optimal weights involves formulating an optimization problem that utilizes exact fuzzy arithmetic operations defined in terms of α-cut intervals. This approach aims to optimize the entire shape of fuzzy comparison values simultaneously. However, it turns out that, although we have proven the existence of optimal solution for this problem, solving it proves to be challenging. To resolve this issue, we approximate optimal weight set(s) using triangular fuzzy weight sets and assess the Error of Approximation (EA). The approximate weight set with the desired EA is then defuzzified to obtain a crisp weight set. In situations where there are multiple approximate weight sets with the same EA, interval-weights are calculated. Following that, we establish the necessary conditions for a Fuzzy Pairwise Comparison System (FPCS) to be consistent. Using these conditions, we calculate a lower bound of the Consistency Index (CI), providing a measure of the accuracy of weights. Finally, we discuss numerical examples and a real-world scenario, ranking of risk factors in supply chain 4.0, to validate the effectiveness of the proposed model.

Choosing Optimal Supply Radius of Transformer Substations (TSs) in Iraq’s Cities Using Geometric Programming with Neutrosophic Coefficients

Numerous uncertainties exist in various electricity power system problems due to the size, complexity, geographical distribution, and influence of unforeseen events in these systems, making it difficult for traditional mathematics tools based on crisp set theory to have an impact on and solve many power system problems. As a new branch of mathematical uncertainty techniques, the neutrosophic expert systems approach has therefore emerged with the development of electric power systems and has proven successful when correctly linked. The expert typically uses ambiguous or neutrosophic language to describe their empirical knowledge, such as "very likely," "quite likely," "if x is large, then y is very likely to occur," "x should not be less than a," etc. To design an optimal radius of power supply in the electrical transformer substation, this article presents a new method for creating primal and dual neutrosophic geometric programming problems. It also provides a numerical example to evaluate the approximate optimal economic power supply radius.

A Survey on Generalized Fuzzy Parameter-Based Fractional Programming Problem

In fuzzy sets, the elements of a universal set may belong to that set completely, may not belong to that set, or may belong partially. Therefore, fuzzy sets are called generalizations of crisp sets. Due to the diverse nature of problems in real-world situations, fuzzy set theory is found to be unable to address some of the other features of ambiguity. Therefore, researchers extended fuzzy sets to picture fuzzy sets, orthopair, intuitionistic, Pythagorean, Fermatean, neutrosophic, spherical fuzzy sets, etc. Real-world problems can be solved using the method of fractional programming. Decision-makers are trying to get good results using generalized fuzzy numbers in fractional programming problems; hence, this review paper provides a specific framework for generalized fuzzy sets and generalized fuzzy fractional programming problems. Furthermore, it is a platform for researchers who want to work on generalized fuzzy parameter-based fractional programming problems. This research paper summarizes all the basic concepts and prior research on fractional programming and generalized fuzzy linear fractional programming problems.

A hybridized red deer and rough set clinical information retrieval system for hepatitis B diagnosis

Healthcare is a big concern in the current booming population. Many approaches for improving health are imposed, such as early disease identification, treatment, and prevention. Therefore, knowledge acquisition is highly essential at different stages of decision-making. Inferring knowledge from the information system, which necessitates multiple steps for extracting useful information, is one technique to address this problem. Handling uncertainty throughout data analysis is also another challenging task. Computer intelligence is a step forward to this end while selecting characteristics, classification, clustering, and developing clinical information retrieval systems. According to recent studies, swarm optimization is a useful technique for discovering key features while resolving real-world issues. However, it is ineffective in managing uncertainty. Conversely, a rough set helps a decision system generate decision rules. This produces decision rules without any additional information. In order to assess real-world information systems while managing uncertainties, a hybrid strategy that combines a rough set and red deer algorithm is presented in this research. In the red deer optimization algorithm, the suggested method selects the optimal characteristics in terms of the degree of dependence on the rough set. In order to determine the decision rules, further a rough set is used. The efficiency of the suggested model is also contrasted with that of the decision tree algorithm and the conventional rough set. An empirical study on hepatitis disease illustrates the viability of the proposed research as compared to the decision tree and crisp rough set. The proposed hybridization of rough set and red deer algorithm achieves an accuracy of 91.7% accuracy. The acquired accuracy for the decision tree, and rough set methods is 82.9%, and 88.9%, respectively. It suggests that the proposed research is viable.

The formation mechanism of primary health care team effectiveness : a qualitative comparative analysis research

BackgroundTeam-based care is an essential part of primary health care (PHC), and its team service delivery process is a systematic one involving multiple and complex influences. Research on the formation mechanism can help improve the effectiveness of primary health care teams (PHCTs).MethodsFirst, based on the Donabedian model, we explored the theoretical framework of a PHC team’s effectiveness formation mechanism. Semi-structured interviews were conducted with 23primary health care team members in Hangzhou, Zhejiang Province, China. A total of seven factors were then included as conditional variables using the crisp set qualitative comparative analysis (csQCA) to explore the complex influences between them and the outcome variable through univariate necessity analysis and path configuration analysis.ResultsUnivariate necessity analysis showed that only “Clear Goals” in the structural dimension were necessary for team effectiveness perception. Six pathways to good primary health care team perception of effectiveness were identified. Two of these paths were more typical.Conclusion“Clear Goals” was the core variable that should be emphasized when exploring the mechanism of PHCT formation. The results suggest that human resources in the management team should be rationally allocated, goal-oriented, and given good attention. Future studies should explore complex combinations of PHCT factors to improve the effectiveness of PHCTs.

$\mathbb{T}-$Relative Fuzzy Linear Programming for $\mathbb{T}-$Relative Fuzzy Target Coverage Problems

Optimal set covering problems are commonplace in communication, remote sensing, logistics, image processing, and network fields [3]. Thus, studies on determining optimal covering sets (sensors) of points (targets) in a region have emerged recently. One characteristic of these studies is the consideration of cases where a target is considered fully covered when it falls within a coverage area ("Boolean" coverage). Consequently, optimality solutions/methods/algorithms founded on this coverage scheme are usually too restrictive and (or) precise and so are not suitable for many complex and real life situations, which are most times plagued with ambiguity, vagueness, imprecision and approximate membership of points and (or) covering sets. Fuzzy structures have proven to be suitable for the representation and analysis of such complex systems with many successful applications. Although fuzzy sets generalizes a set, a more recent generalization for both and its related concepts is the Relative fuzzy set [1] which gives a dynamic fuzzy representation to sets. $\mathbb{T}-$Relative Fuzzy fixed points results of $\mathbb{T}-$Relative fuzzy maps were studied in [5] and recently, the concept of $\mathbb{T}-$Relative fuzzy linear programming [6] was introduced as a generalization of fuzzy linear programming. The results were applied to generalize the Boolean set based covering problems in literature to a $\mathbb{T}-$Relative fuzzy Boolean coverage one. Although, Shan et al. in [15] and others [16] - [21] have given a probabilistic coverage consideration but this lacks subjectivity in representing vagueness and imprecision inherent in most systems. In this present article the Linear Programming (LP) formulation of “A Computational Physics-based Algorithm for Target Coverage Problems" by Jordan Barry and Christopher Thron is generalized by considering a fuzzy and relative fuzzy target coverage instead of the crisp set Boolean coverage. Also we introduce the Fuzzy Linear Programming (FLP) and the $\mathbb{T}-$Relative Fuzzy Linear Programming (RFLP) for the set coverage problem which allows for ascertaining dynamic optimality with aspiration levels.

Necessary and Sufficient Conditions for a Stability of the Concepts of Stable Interior and Stable Exterior via Neutrosophic Crisp Sets

The general direction for generating any stable neutrosophic crisp topology is through base or the stable neutrosophic crisp interior concept, which is closed in the finite intersection process and not closed in the union process, likewise the stable neutrosophic crisp exterior is closed in the finite union process but not closed in finite intersection. Our research deals with finding necessary and sufficient condition for the finite union and finite intersection to be closed respectively using the concept of confused crisp sets.

Stable Neutrosophic Crisp Topological Space

The significance and influence of neutrosophic crisp set theory in numerous scientific domains, particularly topology, led us to construct a new definition of topology based on neutrosophic crisp sets, allowing us to regulate its key mathematical ideas. Therefore, we constructed this definition and dubbed it stable neutrosophic crisp topology, where we went over the key idea which is the interior with the vital features.

Fatores explicativos da morosidade das demarcações de terras indígenas no Brasil

Abstract The administrative processes of recognizing Indigenous Lands (ILs) in Brazil can take decades to complete. Indigenous peoples who live in unrecognized ILs are more vulnerable to a series of rights violations, which makes the completion of demarcation processes urgent. This article aims to answer the following question: why do some demarcation processes take longer than others? We listed five conditions found in the literature on the demarcation of indigenous lands that can delay them. Next, we applied the qualitative comparative analysis (QCA) method in its crisp set mode to 40 cases of IL demarcation. We present two conclusions: the presence of economic interests is an important condition to explain the long duration of some demarcation processes, but it is neither necessary nor sufficient, and the conjunction of this factor with the judicialization of the demarcation process explains most cases of long-term demarcations.

Reliability analysis of parted rope injuries during ship mooring operation under neutrosophic environments

At the national and international levels, many efforts have been made over recent decades to ensure the safety of ships at sea. In marine environments, crews face serious concerns during parted rope injuries during ship mooring operation. This problem can be tackled with the help of failure probability analysis which plays a vital role in detecting and eliminating the aforesaid threats in maritime transportation. Therefore, determining the fundamental causes of parted rope injuries during ship mooring operation is essential for maritime safety researchers. When the failure probability values of basic events are exact, conventional fault tree analysis has previously been successfully applied to determine the cause of failure of the top events. However, sometimes the failure information provided by different analysts for mooring operation may be uncertain and inconsistent. To properly address this important issue, the proposed research reflects a novel approach by extending crisp sets, fuzzy sets, and intuitionistic fuzzy sets into neutrosophic sets. The aforesaid approach is used to compute failure probabilities and reliability intervals for truth-membership, indeterminacy-membership and falsity-membership functions, along with a measure of how much each basic failure event contributes to the failure of the top event. The results obtained by incorporating the proposed approach are compared with those obtained using earlier approaches.

On a value of a matrix game with fuzzy sets of player strategies

The present paper investigates a fuzzy matrix game with fuzzy sets of player strategies. We construct a game value with the help of Zadeh's extension principle in combination with an approach to fuzzy matrix games worked out by Liu and Kao. We prove that the FSs of players strategies in a fuzzy matrix game generate a game value in the form of a type-2 fuzzy set (T2FS) on the real line. Furthermore, the corresponding type-2 membership function is given. It is shown that the T2FS of the game value can be decomposed according to the secondary membership grades into a finite collection of fuzzy numbers. Each of them is the value of the corresponding fuzzy matrix game for crisp sets of player strategies. These sets are the corresponding cuts of the original fuzzy sets of player strategies. Illustrative examples are given.

On Kemeny Optimization Scheme for Fuzzy Set of Relations

The present paper investigated the aggregation of individual preferences into a group fuzzy preference relation for a fuzzy set of decision-makers (DMs). This aggregation is based on the Kemeny optimization scheme. It was proven that this group relation is a Type-2 fuzzy relation (T2FR). The decomposition approach was used to analyze the group T2FR. It is shown that the group T2FR can be decomposed according to secondary membership grades into a finite collection of Type-1 fuzzy relations. Each of them is a group fuzzy relation for a crisp set of DMs, which is the corresponding α-cut of the original fuzzy set of DMs. Illustrative examples are given.