From ranking fuzzy numbers to solving fuzzy linear programming: a comprehensive review

Solving fuzzy linear programming (FLP) requires the employment of a consistent ranking of fuzzy numbers. Ineffective fuzzy number ranking would lead to a flawed and erroneous solving approach. This paper presents a comprehensive and extensive review on fuzzy number ranking methods. Ranking techniques are categorised into six classes based on their characteristics. They include centroid methods, distance methods, area methods, lexicographical methods, methods based on decision maker's viewpoint, and methods based on left and right spreads. A survey on solving approaches to FLP is also reported. We then point out errors in several existing methods that are relevant to the ranking of fuzzy numbers and thence suggest an effective method to solve FLP. Consequently, FLP problems are converted into non-fuzzy single (or multiple) objective linear programming based on a consistent centroid-based ranking of fuzzy numbers. Solutions of FLP are then obtained by solving corresponding crisp single (or multiple) objective programming problems by conventional methods.

Solving fuzzy programming with a consistent fuzzy number ranking

 Some illustrative examples are provided to identify the ineffective and unrealistic characteristics of existing approaches to solving fuzzy linear programming (FLP) problems (with single or multiple objectives). We point out the error in existing methods concerning the ranking of fuzzy numbers and thence suggest an effective method to solve the FLP. Based on the consistent centroid-based ranking of fuzzy numbers, the FLP problems are transformed into non-fuzzy single (or multiple) objective linear programming. Solutions of FLP are then crisp single or multiple objective programming problems, which can respectively be obtained by conventional methods.

Upgrading arc median shortest path problem for an urban transportation network

In this paper, we propose an algorithm for an upgrading arc median shortest path problem for a transportation network. The problem is to identify a set of nondominated paths that minimizes both upgrading cost and overall travel time of the entire network. These two objectives are realistic for transportation network problems, but of a conflicting and noncompensatory nature. In addition, unlike upgrading cost which is the sum of the arc costs on the path, overall travel time of the entire network cannot be expressed as a sum of arc travel times on the path. The proposed solution approach to the problem is based on heuristic labeling and exhaustive search techniques, in criteria space and solution space, respectively. The first approach labels each node in terms of upgrading cost, and deletes cyclic and infeasible paths in criteria space. The latter calculates the overall travel time of the entire network for each feasible path, deletes dominated paths on the basis of the objective vector and identifies a set of Pareto optimal paths in the solution space. The computational study, using two small-scale transportation networks, has demonstrated that the algorithm proposed herein is able to efficiently identify a set of nondominated median shortest paths, based on two conflicting and noncompensatory objectives.

Optimized fuzzy association rule mining for quantitative data

With the advance of computing and electronic technology, quantitative data, for example, continuous data (i.e., sequences of floating point numbers), become vital and have wide applications, such as for analysis of sensor data streams and financial data streams. However, existing association rule mining generally discover association rules from discrete variables, such as boolean data (`O' and `l') and categorical data (`sunny', `cloudy', `rainy', etc.) but very few deal with quantitative data. In this paper, a novel optimized fuzzy association rule mining (OFARM) method is proposed to mine association rules from quantitative data. The advantages of the proposed algorithm are in three folds: 1) propose a novel method to add the smoothness and flexibility of membership function for fuzzy sets; 2) optimize the fuzzy sets and their partition points with multiple objective functions after categorizing the quantitative data; and 3) design a two-level iteration to filter frequent-item-sets and fuzzy association-rules. The new method is verified by three different data sets, and the results have demonstrated the effectiveness and potentials of the developed scheme.

Domain-driven classification based on multiple criteria and multiple constraint-level programming for intelligent credit scoring

Extracting knowledge from the transaction records and the personal data of credit card holders has great profit potential for the banking industry. The challenge is to detect/predict bankrupts and to keep and recruit the profitable customers. However, grouping and targeting credit card customers by traditional data-driven mining often does not directly meet the needs of the banking industry, because data-driven mining automatically generates classification outputs that are imprecise, meaningless, and beyond users' control. In this paper, we provide a novel domain-driven classification method that takes advantage of multiple criteria and multiple constraint-level programming for intelligent credit scoring. The method involves credit scoring to produce a set of customers' scores that allows the classification results actionable and controllable by human interaction during the scoring process. Domain knowledge and experts' experience parameters are built into the criteria and constraint functions of mathematical programming and the human and machine conversation is employed to generate an efficient and precise solution. Experiments based on various data sets validated the effectiveness and efficiency of the proposed methods. © 2006 IEEE.

Portfolio selection under higher moments using fuzzy multi-objective linear programming

Since asset returns have been recognized as not normally distributed, the avenue of research regarding portfolio higher moments soon emerged. To account for uncertainty and vagueness of portfolio returns as well as of higher moment risks, we proposed a new portfolio selection model employing fuzzy sets in this paper. A fuzzy multi-objective linear programming (MOLP) for portfolio optimization is formulated using marginal impacts of assets on portfolio higher moments, which are modelled by trapezoidal fuzzy numbers. Through a consistent centroid-based ranking of fuzzy numbers, the fuzzy MOLP is transformed into an MOLP that is then solved by the maximin method. By taking portfolio higher moments into account, the approach enables investors to optimize not only the normal risk (variance) but also the asymmetric risk (skewness) and the risk of fat-tails (kurtosis). An illustrative example demonstrates the efficiency of the proposed methodology comparing to previous portfolio optimization models.

Multiple visions or multiple aversions? Consumer representation, consultation and participation in maternity issues

This paper reviews the Commonwealth government's policy of 'purposeful reporting to consumers'. I argue that the notion of consumer participation is underdeveloped. Consumers' needs will not be fully met by confining consumer representation at the administrative level; that is, in assuming that consumer advocates may speak for other consumers of health care services. The partnership objective at the heart of 'purposeful reporting' may be addressed fully only when practitioners and providers recognise the reciprocal expertise of the consumer in defining their own health priorities. This would require a new model of knowledge, of ethics and of the clinical encounter. The problem is not one of information deficit but of contrasting views of knowledge.

Quality of life and multiple sclerosis: comparison between people with multiple sclerosis and people from the general population

This paper evaluated the quality of life (QOL) of people with multiple sclerosis (MS) and people from the general population. Gender differences between the 2 groups of respondents and the influence of coping style on adjustment were also evaluated. The participants were 381 (144 males, 237 females) people with MS, and 291 (101 males, 190 females) people from the general population. The results demonstrated that people with MS experienced lower levels of QOL than people from the general population for both the objective and subjective dimensions of all domains (physical health, psychological adjustment, social relationships, environmental adjustment). All coping strategies (problem-focused, focusing on the positive, detachment, wishful thinking, seeking social support) were important predictors of QOL for both males and females with MS, with wishful thinking being the strongest predictor of poor QOL. These results are discussed in terms of the various factors that impact on QOL among people with MS, and the types of coping strategies that are most adaptive in improving the QOL of people with this illness.

The relationship between religion, spirituality, psychological adjustment, and quality of life among people with multiple sclerosis

The present research was comprised of two studies that aimed to explore the role of religious and spiritual variables in the psychological adjustment and quality of life of people with Multiple Sclerosis (MS). In study 1, religious behavior and objective levels of spirituality and religiosity were not significantly related to psychological adjustment or quality of life among people with MS. Positive religious coping was negatively related to psychological adjustment and quality of life. In study 2, Intrinsic religious orientation and Quest religious orientation were related to poor psychological adjustment. Implications of the present research for people with MS and other chronic illnesses are discussed.

Coping and psychological adjustment among people with multiple sclerosis

Objective
This study was concerned with examining the coping and psychological adjustment of people with multiple sclerosis (MS) and determining how they were different in these dimensions from people from the general population. The role of severity and duration of illness as well as levels of social support on coping style and adjustment were also evaluated.

Method
The participants were 381 (144 men, 237 women) people with MS and 291 (101 men, 190 women) people from the general population.

Results
The results demonstrated that people with MS (particularly men) were less likely to adopt coping styles related to problem solving and seeking support and demonstrated poorer levels of adjustment on all dimensions. Adopting a wishful thinking coping style, as well as a lack of problem-focused coping or failure to seek social support, was also more likely to be associated with poorer psychological adjustment for both men and women with MS. Levels of health impairment were only minimally related to psychological adjustment, particularly for men.

Discussion
These findings highlight the importance of developing educational programs that include strategies to adopt more problem-focused coping strategies, so that people with MS can more readily adjust to their illness.

Combining extension matrix and integer programming for optimal concept learning

This paper proposes two integer programming models and their GA-based solutions for optimal concept learning. The models are built to obtain the optimal concept description in the form of propositional logic formulas from examples based on completeness, consistency and simplicity. The simplicity of the propositional rules is selected as the objective function of the integer programming models, and the completeness and consistency of the concept are used as the constraints. Considering the real-world problems that certain level of noise is contained in data set, the constraints in model 11 are slacked by adding slack-variables. To solve the integer programming models, genetic algorithm is employed to search the global solution space. We call our approach IP-AE. Its effectiveness is verified by comparing the experimental results with other well- known concept learning algorithms: AQ15 and C4.5.

The development and validation of the impact of multiple sclerosis scale and the symptoms of multiple sclerosis scale

Objective

To develop and validate the Impact of Multiple Sclerosis Scale (IMSS) and the Symptoms of Multiple Sclerosis Scale (SMSS) using the Extended Disability Status Scale (EDSS) for construct validity.
Design

Panel design involving test-retest over 4 months.
Setting

A mailed survey.
Participants

Volunteers with a diagnosis of multiple sclerosis (MS) recruited from an MS support service in Australia: 193 people (mean age, 39y) and 150 people participated at time 1 and time 2, respectively.
Interventions

Not applicable.
Main Outcome Measures

Principal components analyses, the Cronbach α, and descriptive statistics for the 2 scales; correlations for construct validity with the EDSS and retest; and confirmatory factor analysis to test the stability of IMSS and SMSS components over time.
Results

The IMSS yielded 5 independent and reliable components; the SMSS yielded 3 components; both component structures were stable over time. These scales showed convergent validity with the EDSS.
Conclusions

The IMSS and SMSS are psychometrically sound scales suitable for clinical and research purposes to assess the symptoms and impact of MS.

Comparability of dietary patterns assessed by multiple dietary assessment methods: results from the 1946 British Cohort

Objective: The aim of this study is to evaluate the consistency of dietary patterns assessed through the use of a dietary recall and a 5-day food diary. Design: Participants (n=2265) of a longitudinal study of health and development completed 48-h dietary recall at interview, followed by a 5-day food diary and with the 24 h immediately preceding the interview analysed separately as a 24-h recall. Mean intakes of foods and nutrients were calculated and dietary patterns were assessed using exploratory factor analysis, using the method of principal components. Paired t-tests and correlation coefficients were used to compare the three dietary assessment methods. Results: Five distinct dietary patterns were identified using the food diary and the 48-h recall but were less consistent on the 24-h recall.  Correlations between factor scores on the 48-h recall and the food diary (r=0.13–0.67) were higher than those between the 24-h recall and food diary (r=-0.01–0.59). The recall methods were effective at ranking subjects according to food and nutrient intakes, with the 48-h recall and food diary showing higher correlations in both males and females. Conclusions: This study indicates that a 48-h recall effectively characterises dietary patterns in British adults when compared to a food diary and ranks participants appropriately with respect to most nutrients and foods and is superior to a single 24-h recall. These results have implications for longitudinal studies where maximising response rates to repeat dietary assessment tools is essential.

Multiple criteria sustainability modelling

This paper describes the research supported by a recent AIQS research grant to develop a computer-based tool for sustainability modeling using multiple criteria. The model enables a sustainability index with an accept/reject threshold of one that has the potential to completely replace traditional net present value methods. Minimum performance benchmarks are prescribed and must be observed - often by trading off performance across the full criteria set. Sustainability is shown to be capable of objective (numeric) analysis for new projects, existing facilities, or indeed any product or asset. A combination of investor-centred and community-centred motivations can also be explored in the model. Known as SINDEX, the tool has industry-wide application, both locally and abroad, and represents a paradigm shift in project evaluation techniques. Furthermore, its multi-discipline considerations underscore the importance of a team approach to sustainability modeling and the need for people to work more closely together when dealing with complex problems

Producing a GIS based multiple criteria analysis tool for regional sustainability assessment: the problem of weighting

Decision support tools will be useful in guiding regions to sustainability. These need to be simple but effective at identifying, for regional managers, areas most in need of initiatives to progress sustainability. Multiple criteria analysis (MCA) is often used as a decision support tool for a wide range of applications. This method allows many criteria to be considered at one time. It does this by giving a ranking of possible options based on how closely each option meets the criteria. Thus, it is suited to the assessment of regional sustainability as it can consider a number of indicators simultaneously and demonstrates how sustainability can vary at small scales across the region. Coupling MCA with GIS to produce maps, allows this analysis to become visual giving the manager a picture of sustainability across the region. To do this each indicator is standardised to a common scale so that it can be compared to other indicators. A weighting is then applied to each indicator to calculate weighted summation for each area in the region. This paper argues that this is the critical step in developing a useful decision support tool. A study being conducted in south west Victoria demonstrates that the weights chosen can have a dramatic impact on the results of the sustainability assessment. It is therefore imperative that careful consideration be given to determining indicator weights in a way that is objective and fully considers the impact of that indicator on regional sustainability.