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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.

The purpose of this paper is to propose a novel approach of fuzzy importance‐performance analysis (FIPA) to replace conventional importance‐performance analysis (IPA) for determining critical service attributes those really need to improve for achieving superior customer satisfaction.

First, referring numerous studies, conventional IPA has some erroneous assumptions, the customer satisfaction of attribute performance has the characteristic of three‐factor theory and the novel approach which integrates natural logarithmic transformation and partial correlation analysis is feasible for acquiring the implicitly derived importance of attributes. Second, according the fact and nature of fuzziness in human perception, this study applies fuzzy set theory to revise conventional IPA. Finally, the FIPA is proposed and subsequently implemented in a Taiwanese hot spring hotel case study.

The implementation of FIPA shows the determined critical service attributes are almost completely different from those attributes acquired by conventional IPA. Hence, the application of conventional IPA may cause practitioners make incorrect decisions of improvement priorities for service attributes and direct unsuitable quality‐based marketing strategies.

The proposed FIPA which integrates fuzzy set theory, three‐factor theory, partial correlation analysis and natural logarithmic transformation avoids the erroneous assumptions of conventional IPA, considers the nature of fuzziness in human perception and includes the actual importance of service attributes. Therefore, the proposed FIPA can effectively assist business managers in determining critical service attributes to improve service quality or customer satisfaction and to achieve competitive advantage.

With the object of translating some concepts and results from classical Reliability Theory into particular types of multistate systems, this article starts by presenting some basic definitions of fuzzy systems. The concepts of fuzzy coherent and fuzzy crisp‐based systems are examined and some results on fuzzy coherent structures are presented. Both static and non‐static models are considered.

Unresolved construction dispute can be detrimental to project success. A systematic method to evaluate the seriousness of construction dispute of a construction project will assist management to take appropriate corrective actions. Evaluation of construction disputes requires an analysis on both the likelihood of occurrence and its impact, which are normally expressed by practitioners in linguistic terms. The application of classical discrete analysis will not be able to accommodate the fuzzy nature of this information. To determine how fuzzy sets theory can be applied to construction disputes evaluation (CDE), a fuzzy CDE model has been developed based on the knowledge extracted from practitioners in Hong Kong. The fuzzy CDE system consists of four components: dispute identification, dispute analysis; dispute evaluation; and dispute control. This paper describes the framework and operation of the fuzzy CDE system developed. The results indicate that CDE can be modelled by the fuzzy sets theory.

The decision-making to outsource and select the most suitable global manufacturing outsourcing partner (MOP) is complex and uncertain due to multiple conflicting qualitative and quantitative criteria as well as multiple alternatives. Vagueness and variability exist in ratings of criteria and alternatives by group of decision-makers (DMs). The paper provides a novel Stochastic Fuzzy (SF) method for evaluation and selection of agile and sustainable global MOP in uncertain and volatile business environment.

Four main selection criteria for global MOP selection were identified such as economic, agile, environmental and social criteria. Total 16 sub-criteria were selected. To consider the vagueness and variability in ratings by group of DMs, SF method using t-distribution or z-distribution was adopted. The criteria weights were determined using the Stochastic Fuzzy-CRiteria Importance Through Intercriteria Correlation (SF-CRITIC), while MOP selection was carried out using Stochastic Fuzzy-VIseKriterijumskaOptimizacija I KompromisnoResenje (SF-VIKOR) in the case study of footwear industry. Sensitivity analysis was performed to test the robustness of the proposed model. A comparative analysis of SF-VIKOR and VIKOR was made.

The worker’s wages and welfare, product price, product quality, green manufacturing process and collaboration with partners are the most important criteria for MOP selection. The MOP3 was found to be the best agile and sustainable global MOP for the footwear company. In sensitivity analysis, significance level is found to have important role in MOP ranking. Hence, the study concluded that integrated SF-CRITIC and SF-VIKOR is an improved method for MOP selection problem.

In a group decision-making, ambiguity, impreciseness and variability are found in relative ratings. Fuzzy variant Multi-Criteria Decision-Making methods cover impreciseness in ratings but not the variability. On the other hand, deterministic models do not cover either. Hence, the stochastic method based on the probability theory combining fuzzy theory is proposed to deal with decision-making problems in imprecise and uncertain environments. Most notably, the proposed model has novelty as it captures and reveals both the stochastic perspective and the fuzziness perspective in rating by group of DMs.

The proposed multi-criteria group decision-making model contributes to the sustainable and agile footwear supply chain management and will help the policymakers in selecting the best global MOP.

To the best of the authors’ knowledge, SF method has not been used to select MOP in the existing literature. For the first time, integrated SF-CRITIC and SF-VIKOR method were applied to select the best agile and sustainable MOP under uncertainty. Unlike other studies, this study considered agile criteria along with triple bottom line sustainable criteria for MOP selection. The novel method of SF assessment contributes to the literature and put forward the managerial implication for improving agility and sustainability of global manufacturing outsourcing in footwear industry.

The purpose of this paper lies in the combination of fuzzy set and interval grey set, namely, considering the fuzzy set theory, rough set theory and grey system theory. The paper then presents a unified form (or symbol system) which can be more useful to describe a wide variety of theories.

Considering the lower bounds and upper bounds of interval grey set are classical set, this paper draws lessons from the classical set to fuzzy set transition mode which was advanced by Professor Zadeh. The paper puts forward the concept of interval fuzzy set, and then relaxes the constraints of the lower bound of interval fuzzy set to make it more widely used in actual uncertain problems.

For the examples which have been given in the paper, interval fuzzy set and its three theorems are proved practical and flexible.

The theorems proved in the paper can be used as a useful extension to the classical fuzzy set, which can also be applied to fuzzy clustering, fuzzy classification, fuzzy pattern recognition and so on.

The paper puts forward the concept of interval fuzzy set and the three theorems of interval fuzzy set and proves their practicability and flexibility. The theorems can be used for further study on interval fuzzy set.

Improvements in quality have a very important role to play in services because such improvements add greater flexibility and give clients greater confidence in the services provided. Therefore, this paper aims to describe a framework for measuring quality in the provision of the service by using a SERVQUAL scale and fuzzy operators.

In this approach, a framework to assess quality in service provision is put forward which applies the SERVQUAL scale as an instrument of data collection. Fuzzy set theory is proposed and applied within this framework as a technique to make a quantitative assessment of the quality of the provision of services. A case study is used to illustrate how to apply this framework for this purpose. The data were processed and transformed into a fuzzy environment, and fuzzy numbers and operators were applied to the analysis of customers' assessment with regard to the dimensions of quality in the service provided.

The study demonstrated the differences between evaluations of the dimensions of quality assessed, and differences of the same customer in relation to these dimensions. The main points raised were the importance given by customers to the dimensions, and the gaps between customers' perceptions and expectations, when fuzzy numbers were used to assess levels of service quality, and to evaluating the prioritization of service quality.

This paper proposes the use of fuzzy theory within a framework by making a linguistic analysis when dealing with data collected in a SERVQUAL scale so as to assess service quality. The data were measured by examining the gap between customers' perceptions and expectations. The framework describes the phases of this assessment, and uses fuzzy operators.

The purpose of this paper is to shed light on the relationship between the Internet Financial Reporting (IFR) levels and corporate characteristics. It is assumed that the relationship between the disclosure level and its determinants is known. Nevertheless, the results of the empirical studies confirm that it is a naive assumption. As a result, the author suggests refusing the conventional methods of econometric analysis.

The research methodology consisted of four stages: First, the author tried to select the “best” model using the Akaike Information Criterion (AIC). Second, the author checked out the stability of the relationship between corporate disclosure level and its determinants. Third, the regression analysis was used. Finally, the author proposed a “genetic-fuzzy system” for studying the determinants of corporate disclosure. The firms' yearly data collected consisted of a random sample of 152 Tunisian companies' websites.

The results show that the variables that should be used to explain the level of IFR are firm size, ownership concentration, firm performance and liquidity. The Chow forecast test shows that there is a significant and large difference between the actual and the predicted values. Consequently, the author suggests using non-parametric methods, particularly a methodology based on fuzzy logic concepts and genetic algorithms. This technique would allow the author to discover the true form of the relationship between the disclosure level and its determinants. Regarding the hypotheses of this study, the findings of the “genetic-fuzzy system” validate all the hypotheses. Indeed, the arguments of the agency theory, the signaling theory, and the political cost hypothesis were supported using the “genetic-fuzzy system.”

The originality of the paper lies in providing a new research methodology based on several statistical tools for dealing with an important research topic in accounting and finance, i.e. the determinants of IFR. The results of this study can be considered as a starting point to develop a unified methodology.

An attempt is made to save the law of excluded middle in fuzzy set theory. This is done by mapping the sentences of axiomatic set theory to a Boolean algebra, prior to assigning numerical values. With a simple choice of Boolean algebra a probability interpretation emerges.

Sets out to provide an understanding of the theory of fuzzy logic by supplying background details concerning its evolution in mathematics and computer science. Once a basic understanding of the theory is obtained, then it is easier to understand the implications for computer applications. Fuzzy logic processors and compilers have facilitated the development of expert systems that typically use a lot of imprecise data. These expert systems have been used successfully as control units in industrial settings and as decision support systems in hospital settings. Fuzzy logic has been found to be a practical and viable form of artificial intelligence that mitigates the current drawbacks of other forms of artificial intelligence. But the really exciting development that is poised to emerge is the introduction of fuzzy logic appliances. These appliances employ an expert system on a chip that is able to mimic the range of flexibility of the human mind, while utilizing resources more efficiently.