11256201
On the normalization of interval and fuzzy weights
The normalization of interval and fuzzy weights is often necessary in multiple criteria decision analysis (MCDA) under uncertainty, especially in analytic hierarchy process (AHP) with interval or fuzzy judgements. The existing normalization methods based on interval arithmetic and fuzzy arithmetic are found flawed and need to be revised. This paper presents the correct normalization methods for interval and fuzzy weights and offers relevant theorems in support of them. Numerical examples are examined to show the correctness of the proposed normalization methods and their differences from those existing normalization methods.
37194320
The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty
Abstract The evidential reasoning (ER) approach is a method for multiple attribute decision analysis (MADA) under uncertainties. It improves the insightfulness and rationality of a decision making process by using a belief decision matrix (BDM) for problem modelling and the Dempster–Shafer (D–S) theory of evidence for attribute aggregation. The D–S theory provides scope and flexibility to deal with interval uncertainties or local ignorance in decision analysis, which is not explored in the original ER approach and will be investigated in this paper. Firstly, interval uncertainty will be defined and modelled in the ER framework. Then, an extended ER algorithm, IER, is derived, which enables the ER approach to deal with interval uncertainty in assessing alternatives on an attribute. It is proved that the original ER algorithm is a special case of the IER algorithm. The latter is demonstrated using numerical examples.
6142906
Multiple attribute decision making based on fuzzy preference information on alternatives: Ranking and weighting
This paper investigates the multiple attribute decision making (MADM) problem with fuzzy preference information on alternatives and proposes an eigenvector method to rank them. Three optimization models are introduced to assess the relative importance weights of attributes in a MADM problem, which integrate subjective fuzzy preference relations and objective information in different ways. Since the decisions these models lead to are based on both subjective and objective information, they are more balanced and credible than those that consider only one type of information. An example is provided to illustrate the application of the proposed models.
46223238
Environmental impact assessment using the evidential reasoning approach
Environmental impact assessment (EIA) problems are often characterised by a large number of identified environmental factors that are qualitative in nature and can only be assessed on the basis of human judgments, which inevitably involve various types of uncertainties such as ignorance and fuzziness. So, EIA problems need to be modelled and analysed using methods that can handle uncertainties. The evidential reasoning (ER) approach provides such a modelling framework and analysis method. In this paper the ER approach will be applied to conduct EIA analysis for the first time. The environmental impact consequences are characterized by a set of assessment grades that are assumed to be collectively exhaustive and mutually exclusive. All assessment information, quantitative or qualitative, complete or incomplete, and precise or imprecise, is modelled using a unified framework of a belief structure. The original ER approach with a recursive ER algorithm will be introduced and a new analytical ER algorithm will be investigated which provides a means for using the ER approach in decision situations where an explicit ER aggregation function is needed such as in optimisation problems. The ER approach will be used to aggregate multiple environmental factors, resulting in an aggregated distributed assessment for each alternative policy. A numerical example and its modified version are studied to illustrate the detailed implementation process of the ER approach and demonstrate its potential applications in EIA.
18488788
A preference aggregation method through the estimation of utility intervals
In this paper, a preference aggregation method is developed for ranking alternative courses of actions by combining preference rankings of alternatives given on individual criteria or by individual decision makers. In the method, preference rankings are viewed as constraints on alternative utilities, which are normalized, and linear programming models are constructed to estimate utility intervals, which are weighted and averaged to generate an aggregated utility interval. A simple yet pragmatic interval ranking method is used to compare and/or rank alternatives. The final ranking is generated as the most likely ranking with certain degrees of belief. Three numerical examples are examined to illustrate the potential applications of the proposed method.
16424206
A general multiple attribute decision-making approach for integrating subjective preferences and objective information
A general multiple attribute decision-making (MADM) approach is proposed to integrate subjective preferences and objective information and to assess the relative weights of attributes, where subjective preferences are expressed either by a fuzzy preference relation on decision alternatives or by a pairwise comparison matrix on the relative weights of attributes or by both of them and objective information is expressed by a decision matrix. Three special cases of the approach are investigated, which are the weighted least deviation norm (WLDN), the weighted least-square deviation norm (WLSDN) and the weighted minimax deviation norm (WMDN) approaches. The extension of the general approach to group decision-making and the choice of decision parameters are also discussed. A numerical example is examined to show the applications of the proposed MADM approaches.
15293150
On achievable error exponents for watermarking
Probability-of-error exponents have recently been derived for watermarking systems based on spread-spectrum and quantization-index modulation methods. This paper takes this work one step further and presents minmax error exponents for any embedding scheme and any attack (subject to distortion constraints) at all rates below capacity. The decoders used are universal: they do not know the attck used. Randomized codes outperform deterministic codes, except in the case of memoryless attacks where the same performance is obtained using either kind of code.
39861836
A Novel Method for Eye Features Extraction
Extraction of the eye features, like the pupil center and radius, eye corners and eyelid contours from the frontal face images often provides us useful cues in many important applications, such as face recognition, facial expression recognition and 3D face modeling from 2D images. Assuming the rough eye window is known, the color information, Gabor features are extracted from the eye window and then these two features and their mutual relationship have been incorporated into the design of our algorithm. Firstly, after the pupil center is detected in H channel of HSV color space, the pupil radius is estimated and refined. Secondly, eye corners are localized using eye-corner filter based on Gabor feature space. Finally, eyelid curves are fitted by spline function. The new algorithm has been tested on our SJTU database and some other pictures taken from the web. The experimental results show that our algorithm has high accuracy and is robust under different conditions.
3032688
Statistical Identification of Key Phrases for Text Classification
Algorithms for text classification generally involve two stages, the first of which aims to identify textual elements (words and/or phrases) that may be relevant to the classification process. This stage often involves an analysis of the text that is both language-specific and possibly domain-specific, and may also be computationally costly. In this paper we examine a number of alternative keyword-generation methods and phrase-construction strategies that identify key words and phrases by simple, language-independent statistical properties. We present results that demonstrate that these methods can produce good classification accuracy, with the best results being obtained using a phrase-based approach.
299693
Geometry-based semantic ID for persistent and interoperable reference in feature-based parametric modeling
In current feature-based parametric design systems, the reusability principle is not fully supported as it was expected. Unpredictability and ambiguity of models often happen during design modification within one system as well as among different systems. This reference deficiency significantly reduces the power of feature-based parametric modeling, where geometry re-evaluation generates unexpected shapes. In this paper, a sufficient condition of B-Rep variance based on geometry continuity in parametric complex Euclidean (P^pC^3) space is proposed. Shape and relation parameters are differentiated in P^pC^3, thus parametric family can be defined. A semantic id scheme based on continuity of geometry is developed to solve the problem of naming persistency and to improve interoperability of CAD feature modeling. Hierarchical namespaces localize entity creation and identification. All geometric and topological entities are referred uniformly based on surface ids, and topology semantics is retained in id itself.
5870530
Mathematical models and properties of games
Games are a decision process under competition where opponent players compete for the maximum gain or a success state in the same environment according to the same rules of the game. Games are conventionally dealt with payoff tables based on random strategies that are found inadequate to describe the dynamic behaviors of games and to rigorously predict the outcomes of games. This paper presents a formal treatment of games by a set of mathematical models for both the layouts and behaviors of games. A formal model of games is introduced, based on which the properties of games in terms of decision strategies and serial matches are described. A wide range of generic zero-sum and nonzero-sum games are formally modeled and analyzed using the mathematical models of games.