Clouds, p-boxes, fuzzy sets, and other uncertainty representations in higher dimensions

Uncertainty modeling in real-life applications comprises some serious problems such as the curse of dimensionality and a lack of sufficient amount of statistical data. In this paper we give a survey of methods for uncertainty handling and elaborate the latest progress towards real-life applications with respect to the problems that come with it. We compare different methods and highlight their relationships. We introduce intuitively the concept of potential clouds, our latest approach which successfully copes with both higher dimensions and incomplete information

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.

State‐of‐the‐Art Nonprobabilistic Finite Element Analyses

The finite element analysis of a mechanical system is conventionally performed in the context of deterministic inputs. However, uncertainties associated with material properties, geometric dimensions, subjective experiences, boundary conditions, and external loads are ubiquitous in engineering applications. The most popular techniques to handle these uncertain parameters are the probabilistic methods, in which uncertainties are modeled as random variables or stochastic processes based on a large amount of statistical information on each uncertain parameter. Nevertheless, subjective results could be obtained if insufficient information unavailable and nonprobabilistic methods can be alternatively employed, which has led to elegant procedures for the nonprobabilistic finite element analysis. In this chapter, each nonprobabilistic finite element analysis method can be decomposed as two individual parts, i.e., the core algorithm and preprocessing procedure. In this context, four types of algorithms and two typical preprocessing procedures as well as their effectiveness were described in detail, based on which novel hybrid algorithms can be conceived for the specific problems and the future work in this research field can be fostered

A multi-attribute decision making procedure using fuzzy numbers and hybrid aggregators

The classical Analytical Hierarchy Process (AHP) has two limitations. Firstly, it disregards the aspect of uncertainty that usually embedded in the data or information expressed by human. Secondly, it ignores the aspect of interdependencies among attributes during aggregation. The application of fuzzy numbers aids in confronting the former issue whereas, the usage of Choquet Integral operator helps in dealing with the later issue. However, the application of fuzzy numbers into multi-attribute decision making (MADM) demands some additional steps and inputs from decision maker(s). Similarly, identification of monotone measure weights prior to employing Choquet Integral requires huge number of computational steps and amount of inputs from decision makers, especially with the increasing number of attributes. Therefore, this research proposed a MADM procedure which able to reduce the number of computational steps and amount of information required from the decision makers when dealing with these two aspects simultaneously. To attain primary goal of this research, five phases were executed. First, the concept of fuzzy set theory and its application in AHP were investigated. Second, an analysis on the aggregation operators was conducted. Third, the investigation was narrowed on Choquet Integral and its associate monotone measure. Subsequently, the proposed procedure was developed with the convergence of five major components namely Factor Analysis, Fuzzy-Linguistic Estimator, Choquet Integral, Mikhailov‘s Fuzzy AHP, and Simple Weighted Average. Finally, the feasibility of the proposed procedure was verified by solving a real MADM problem where the image of three stores located in Sabak Bernam, Selangor, Malaysia was analysed from the homemakers‘ perspective. This research has a potential in motivating more decision makers to simultaneously include uncertainties in human‘s data and interdependencies among attributes when solving any MADM problems

Uncertainty in Quantitative Risk Analysis - Characterisation and Methods of Treatment

The fundamental problems related to uncertainty in quantitative risk analyses, used in decision making in safety-related issues (for instance, in land use planning and licensing procedures for hazardous establishments and activities) are presented and discussed, together with the different types of uncertainty that are introduced in the various stages of an analysis. A survey of methods for the practical treatment of uncertainty, with emphasis on the kind of information that is needed for the different methods, and the kind of results they produce, is also presented. Furthermore, a thorough discussion of the arguments for and against each of the methods is given, and of different levels of treatment based on the problem under consideration. Recommendations for future research and standardisation efforts are proposed

Development and characterisation of error functions in design

As simulation is increasingly used in product development, there is a need to better characterise the errors inherent in simulation techniques by comparing such techniques with evidence from experiment, test and inservice. This is necessary to allow judgement of the adequacy of simulations in place of physical tests and to identify situations where further data collection and experimentation need to be expended. This paper discusses a framework for uncertainty characterisation based on the management of design knowledge leading to the development and characterisation of error functions. A classification is devised in the framework to identify the most appropriate method for the representation of error, including probability theory, interval analysis and Fuzzy set theory. The development is demonstrated with two case studies to justify rationale of the framework. Such formal knowledge management of design simulation processes can facilitate utilisation of cumulated design knowledge as companies migrate from testing to simulation-based design

Evaluation of e-learning web sites using fuzzy axiomatic design based approach

High quality web site has been generally recognized as a critical enabler to conduct online business. Numerous studies exist in the literature to measure the business performance in relation to web site quality. In this paper, an axiomatic design based approach for fuzzy group decision making is adopted to evaluate the quality of e-learning web sites. Another multi-criteria decision making technique, namely fuzzy TOPSIS, is applied in order to validate the outcome. The methodology proposed in this paper has the advantage of incorporating requirements and enabling reductions in the problem size, as compared to fuzzy TOPSIS. A case study focusing on Turkish e-learning websites is presented, and based on the empirical findings, managerial implications and recommendations for future research are offered

Modeling systems thinking in action among higher education leaders with fuzzy multi-criteria decision making

The college and university systems are more complex and required persistent approach towards adoption and transformation. Highly vulnerable environment portrays the need to visualize the regular and strategic issues with the larger perspectives as a whole and develop a model which is more focused towards sustainability and reformation. The current study has attempted to conceptualize systems thinking in action model which consists of four stages of action cycle; diagnosis and analysis, modeling, intervention and review and lessons learned. This is attempting to evaluate the systems thinking among the educational leaders in higher education in Thailand through the fuzzy multi-criteria decision-making method. The study has found that leaders are adopting systems thinking in the moderate level, however, the first three stages are found less in practice and more in perceived importance. The study found that there is higher need of calling for collaborative, cooperative and participation of stakeholders’ involvement. The study has further given managerial implications