FuzzySTAR: Fuzzy set theory of axiomatic design review

Product development involves multiple phases. Design review (DR) is an essential activity formally conducted to ensure a smooth transition from one phase to another. Such a formal DR is usually a multicriteria decision problem, involving multiple disciplines. This paper proposes a systematic framework for DR using fuzzy set theory. This fuzzy approach to DR is considered particularly relevant for several reasons. First, information available at early design phases is often incomplete and imprecise. Second, the relationships between the product design parameters and the review criteria cannot usually be exactly expressed by mathematical functions due to the enormous complexity. Third, DR is frequently carried out using subjective expert judgments with some degree of uncertainty. The DR is defined as the reverse mapping between the design parameter domain and design requirement (review criterion) domain, as compared with Suh's theory of axiomatic design. Fuzzy sets are extensively introduced in the definitions of the domains and the mapping process to deal with imprecision, uncertainty, and incompleteness. A simple case study is used to demonstrate the resulting fuzzy set theory of axiomatic DR.published_or_final_versio

Vop\v{e}nka's Alternative Set Theory in the Mathematical Canon of the 20th Century: Author's Translation from Czech

Vop\v{e}nka's Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem's construction of a nonstandard model of arithmetic, and its inception has been explicitly mentioned as an attempt to axiomatize Robinson's Nonstandard Analysis. Vop\v{e}nka preferred working in an axiomatic theory to investigating its individual models; he also viewed other areas of nonclassical mathematics through this prism. This article is a contribution to the mapping of the mathematical neighbourhood of the Alternative Set Theory, and at the same time, it submits a challenge to analyze in more detail the genesis and structure of the philosophical links that eventually influenced the Alternative Set Theory.Comment: This is the author's translation into English of her paper published originally in Czech. 14 page

Fuzzy Supernova Templates I: Classification

Modern supernova (SN) surveys are now uncovering stellar explosions at rates that far surpass what the world's spectroscopic resources can handle. In order to make full use of these SN datasets, it is necessary to use analysis methods that depend only on the survey photometry. This paper presents two methods for utilizing a set of SN light curve templates to classify SN objects. In the first case we present an updated version of the Bayesian Adaptive Template Matching program (BATM). To address some shortcomings of that strictly Bayesian approach, we introduce a method for Supernova Ontology with Fuzzy Templates (SOFT), which utilizes Fuzzy Set Theory for the definition and combination of SN light curve models. For well-sampled light curves with a modest signal to noise ratio (S/N>10), the SOFT method can correctly separate thermonuclear (Type Ia) SNe from core collapse SNe with 98% accuracy. In addition, the SOFT method has the potential to classify supernovae into sub-types, providing photometric identification of very rare or peculiar explosions. The accuracy and precision of the SOFT method is verified using Monte Carlo simulations as well as real SN light curves from the Sloan Digital Sky Survey and the SuperNova Legacy Survey. In a subsequent paper the SOFT method is extended to address the problem of parameter estimation, providing estimates of redshift, distance, and host galaxy extinction without any spectroscopy.Comment: 26 pages, 12 figures. Accepted to Ap

Axiomatic Analysis of the Semi-Fuzzy Poverty Indices MIf and PGf

Every poverty index can be classified into one of the two major classes; classical indices and fuzzy indices; except for the semi-fuzzy poverty indices such as PGf and MIf which hybridize between the theory of classical sets and that of fuzzy sets, which makes their axiomatic analysis very special since it uses both classical and fuzzy mathematical tools. In order to better exploit and characterize the PGf and MIf indices, we propose in this paper an axiomatic analysis by mathematically demonstrating, on the one hand, the satisfaction of these two indices of a set of axioms most desirable by economists, which shows their performance in describing poverty. On the other hand, we discuss their limits according to three axioms that we demonstrate in order to improve the formula of these semi-fuzzy indices of poverty

A method of classification for multisource data in remote sensing based on interval-valued probabilities

An axiomatic approach to intervalued (IV) probabilities is presented, where the IV probability is defined by a pair of set-theoretic functions which satisfy some pre-specified axioms. On the basis of this approach representation of statistical evidence and combination of multiple bodies of evidence are emphasized. Although IV probabilities provide an innovative means for the representation and combination of evidential information, they make the decision process rather complicated. It entails more intelligent strategies for making decisions. The development of decision rules over IV probabilities is discussed from the viewpoint of statistical pattern recognition. The proposed method, so called evidential reasoning method, is applied to the ground-cover classification of a multisource data set consisting of Multispectral Scanner (MSS) data, Synthetic Aperture Radar (SAR) data, and digital terrain data such as elevation, slope, and aspect. By treating the data sources separately, the method is able to capture both parametric and nonparametric information and to combine them. Then the method is applied to two separate cases of classifying multiband data obtained by a single sensor. In each case a set of multiple sources is obtained by dividing the dimensionally huge data into smaller and more manageable pieces based on the global statistical correlation information. By a divide-and-combine process, the method is able to utilize more features than the conventional maximum likelihood method

Design and Evaluation of Ballast Water Management Systems using Modified and Hybridised Axiomatic Design Principles

There are two major motivations to this research. The first is based on the concerns raised at the International Maritime Organisation (IMO) MEPC 67 and 68 meetings regarding the capacity of some type-approved Ballast Water Management (BWM) Systems to meet the performance standard (D-2) of the BWM Convention at-all-times and in all conditions. The second is based on the reluctance expressed by some ship- owners to install the system onboard their ships as a Lloyd\u27s list survey suggested. In this work, an attempt was made to address these issues and concerns using a set of criteria stipulated in Regulation D-5.2 of the BWM Convention which provides the framework for reviewing and evaluating the practical concepts of managing ballast water, developing a conceptual model for managing ballast water and minimizing the contributions of human-error to BWM System performance by analyzing the associated operational human factors. Firstly, the design of a conceptual model of managing ballast water and the evaluation of some established practical concepts of BWM were achieved by using a suitable technique (Axiomatic Design or AD) which was selected via a robust procedure. The two axioms of Axiomatic Design (information and independence) were used to evaluate four different concepts of managing ballast water as well as develop a BWM Convention-compliant conceptual design matrix model respectively. Based on data collected from ballast water management experts, Post-loading Onshore Ballast Water Management System was shown to be the most appropriate ballast water management concept with respect to the Regulation D-5.2 set of criteria. This presents a paradigm shift in expert preference from traditional shipboard systems to onshore systems with respect to the IMO-criteria. The pathway for improved performance of the Convention-compliant design matrix was subsequently determined and prioritised using Sufield model of Altshuler\u27s theory of inventive problem solving (TRIZ). Lastly, a 5-step algorithm was developed to minimise operator errors in the BWM System’s operation. Fatigue and training were found to have the greatest impact on operator performance

A fuzzy hierarchical multiple criteria group decision support system - Decider - and its applications

Decider is a Fuzzy Hierarchical Multiple Criteria Group Decision Support System (FHMC-GDSS) designed for dealing with subjective, in particular linguistic, information and objective information simultaneously to support group decision making particularly on evaluation. In this chapter, the fuzzy aggregation decision model, functions and structure of Decider are introduced. The ideas to resolve decision and evaluation problems we have faced in the development and application of Decider are presented. Two real applications of the Decider system are briefly illustrated. Finally, we discuss our further research in this area. © 2011 Springer-Verlag Berlin Heidelberg