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This paper presents a comprehensive review of the available literature on applications of the rough set theory. Concepts of the rough set theory are discussed for approximation, dependence and reduction of attributes, decision tables and decision rules. The applications of rough sets are discussed in pattern recognition, information processing, business and finance, industry, environment engineering, medical diagnosis and medical data analysis, system fault diagnosis and monitoring and intelligent control systems. Development trends and future efforts are outlined. An extensive list of references is also provided to encourage interested readers to pursue further investigations.

During the twentieth century mathematics has expanded at an unprecedented rate. This expansion has been accompanied by the increased application of mathematics to science. At a time when pure mathematics has been placing more and more emphasis on abstraction and the analysis of broad concepts there has been a corresponding proliferation of practical applications. This seems to have resulted from the fact that the sciences, too, have become more concerned with the discernment of general patterns in the study of nature. This search for simplifying ideas has increased the demand for ever more abstract tools of analysis.

This paper responds to ongoing calls to develop alternative management theory to guide management practice. In particular, the purpose of the paper is to demonstrate the merit of developing sustainable management theory and organizational practices that parallel conventional management theory and practices. Sustainable theory is based on a variation of virtue theory that seeks to achieve multiple forms of well-being for multiple stakeholders in the immediate as well as distant future. To illustrate the approach, the authors develop a sustainable variation of goal setting theory.

The paper includes three parts. First, the authors establish the need for developing sustainable management theory (based on virtue theory) that parallels conventional management theory. Second, the authors identify and briefly review the main tenets of goal setting theory and then describe a Sustainable variation of this theory. Finally, the authors discuss the implications of the paper for management and organization theory and practice.

The conceptual arguments for a sustainable version of goal setting theory based in virtue are supported by research and practitioner examples.

Although there is growing concern regarding the shortcomings of management theory and practice based on a materialist-individualist moral-point-of-view, few alternatives have been discussed in detail. This paper presents an alternative based in virtue theory and illustrates how it relates to goal setting theory and practice.

The purpose of this paper is to present a new method for evaluation of emergency plans for unconventional emergency events by using the soft fuzzy rough set theory and methodology.

In response to the problems of insufficient risk identification, incomplete and inaccurate data and different preference of decision makers, a new model for emergency plan evaluation is established by combining soft set theory with classical fuzzy rough set theory. Moreover, by combining the TOPSIS method with soft fuzzy rough set theory, the score value of the soft fuzzy lower and upper approximation is defined for the optimal object and the worst object. Finally, emergency plans are comprehensively evaluated according to the soft close degree of the soft fuzzy rough set theory.

This paper presents a new perspective on emergency management decision making in unconventional emergency events. Also, the paper provides an effective model for evaluating emergency plans for unconventional events.

The paper contributes to decision making in emergency management of unconventional emergency events. The model is useful for dealing with decision making with uncertain information.

Construction and demolition waste (CDW) continuously causes environmental and social problems. These formidable challenges lead to sustainable issues and are an increasingly urgent issue worldwide. Prior studies have neglected to link the triple bottom line (TBL) to a reliable estimation or empirical model for estimating CDW production performance and lack empirical sensitivity analysis in profit maximization. This study proposes an attribute analysis to build a cost–benefit analysis (CBA) to obtain profit maximization.

This study uses fuzzy set theory to develop a cost and benefit analysis (CBA) model to assess the sensitivity analysis in terms of its performance on addressing the environmental, economic and social aspects. The model is used to weigh the sum of benefits such as financial gain and total costs of actions taken to mitigate the negative impacts.

Based on the sensitivity analysis conducted, the environmental, economic and social mean scales were significantly changed, i.e. increased, and profits increased drastically. The results provide an insight into environmental legislation compliance, environmental investment and environmental impact as the cause attributes for the CDW recycling profit increase. The results prove that sensitivity analysis is viable to infer that a sustainable production performance can achieve more revenue and profit through an adequate selection of attributes regarding the TBL aspects to address the firm's uncertainty problem in multiple criteria analysis.

This study builds a CBA model to maximize profits for recycled CDW material by linking of environmental, economic and societal aspects for recycled CDW assessments. It considers a sustainability structure with criteria based on TBL aspects to assess production performance to realize the Sustainable Development Goals and presents fuzzy set theory and sensitivity analysis to solve the uncertainty problem in the construction industry.

Set theory provides a foundational approach to mathematics, and mathematics provides an abstract way of looking at social reality. The first section presents some of the elementary concepts of set theory. The second section presents a variety of examples of social reality and shows how the abstract features of reality can be modelled by set theory. The third section shows how set theory can provide a way of looking at the accounts of social reality presented in humanities disciplines such as history and literature. The fourth section briefly indicates how set theory and the concept of a structure provide a foundational approach to mathematics. The fifth section looks at the debates surrounding realism and, albeit warily, espouses mathematical social science realism.

As an increasingly important variable in the career field, career sustainability has received particular attention, yet few empirical studies have been conducted to examine its antecedents. The authors propose a moderated mediation model based on the goal-setting theory and the wise proactivity perspective for exploring when and how self-goal setting can influence career sustainability.

The authors use a time-lagged design and collect three waves of data from 1,260 teachers in basic education schools in China. The authors test the proposed hypotheses with SPSS 26.0 and Mplus 8.3.

The results show that self-goal setting positively relates to career sustainability and that career crafting plays a mediating role in this relationship. This relationship is strengthened when perceived organizational goal clarity is high.

The authors extend the application scenarios of the goal-setting theory to the field of career research and find out that self-goal setting is also a self-initiated and wise antecedent of career sustainability. From a wise proactivity perspective, the authors examine the mediating mechanism of career crafting to make positive career outcomes. Furthermore, the authors consider the impact of perceived organizational goal clarity as a boundary condition and broaden the understanding of “when to wise proactivity” from the goal-setting theory.

Due to the popularity of mobile devices and the development of artificial intelligence (AI), AI-powered mobile fitness applications (MFAs) have entered people's daily lives. However, the extant literature lacks empirical investigations that explore users' continuance usage intentions regarding AI-powered MFAs. To fill this research gap, this paper employs goal-setting theory to establish a research model for exploring how AI-enabled features (i.e. intelligence and anthropomorphism) affect users' perceptions of goal difficulties and goal specificities, which in turn affect their MFA continuance usage intentions.

This paper uses a survey method to analyze the research model, and a total of 223 responses are collected. The partial least squares (PLS) technique is utilized for data analysis.

The results show that intelligence and anthropomorphism affect the continuance usage intention of MFA users through their goal difficulty and specificity. Both intelligence and anthropomorphism positively influence goal specificity, whereas they negatively affect goal difficulty. In addition, goal specificity increases users' MFA continuance usage intention, whereas goal difficulty decreases users' continuance usage intention. The findings of this study provide theoretical contributions for AI technology adoption research and offer practical strategies for firms to retain MFA users.

Based on goal-setting theory, this study reveals that as two primary AI features of contemporary mobile fitness apps, intelligence and anthropomorphism, can increase comprehension of users' perceptions regarding goal difficulty and specificity in the context of users' continuance usage intentions toward AI-powered MFAs.

In recent years, rough set theory has evolved as one of the most promising classification techniques. One of the cardinal uses of rough set theory is its application for rule generation. The purpose of this paper is to propose a real-time fabric inspection technique. This work deals with the multi-class classification of fabric defects using rough set theory.

This technique focuses on the classification of fabric defects using the effective decision rules envisaged by rough set theory. In the proposed work, the six features of 50 images have been used for multiclass classification of fabric defects.

In this work, 40 images were used for generation of decision rules and 10 unseen images were used for validation out of which nine images are accurately predicted by the proposed technique.

The proposed method accurately identified 9 out of 10 testing defects. The obtained decision rules provide an insight about the classification method which ensures that the prediction accuracy can be improved further by framing more robust decision rules with the help of a large training data set. Thus, with the support of modern computational systems this method is potent in getting recognition from the textile industry as a real-time classification technique.

The purpose is to show that all uncountable infinite sets are self‐contradictory non‐sets.

A conceptual approach is taken in the paper.

Given the fact that the set N={x|n(x)} of all natural numbers, where n(x)=_df “x is a natural number” is a self‐contradicting non‐set in this paper, the authors prove that in the framework of modern axiomatic set theory ZFC, various uncountable infinite sets are either non‐existent or self‐contradicting non‐sets. Therefore, it can be astonishingly concluded that in both the naive set theory or the modern axiomatic set theory, if any of the actual infinite sets exists, it must be a self‐contradicting non‐set.

The first time in history, it is shown that such convenient notion as the set of all real numbers needs to be reconsidered.