Van-Nam Huynh

Multiple-attribute decision making under uncertainty: the evidential reasoning approach revisited

In multiple-attribute decision making (MADM) problems, one often needs to deal with decision information with uncertainty. During the last decade, Yang and Singh (1994) have proposed and developed an evidential reasoning (ER) approach to deal with such MADM problems. Essentially, this approach is based on an evaluation analysis model and Dempsters rule of combination in the Dempster-Shafer (D-S) theory of evidence. This paper reanalyzes the ER approach explicitly in terms of D-S theory and then proposes a general scheme of attribute aggregation in MADM under uncertainty. In the spirit of such a reanalysis, previous ER algorithms are reviewed and two other aggregation schemes are discussed. Theoretically, it is shown that new aggregation schemes also satisfy the synthesis axioms, which have been recently proposed by Yang and Xu (2002) for which any rational aggregation process should grant. A numerical example traditionally examined in published sources on the ER approach is used to illustrate the discussed techniques

A roughness measure for fuzzy sets

Recently, an attempt of integration between the theories of fuzzy sets and rough sets has resulted in providing a roughness measure for fuzzy sets [M. Banerjee, S.K. Pal, Roughness of a fuzzy set, Information Sciences 93 (1996) 235-246]. Essentially, Banerjee and Pals roughness measure depends on parameters that are designed as thresholds of definiteness and possibility in membership of the objects to a fuzzy set. In this paper we first remark that this measure of roughness has several undesirable properties, and then propose a parameter-free roughness measure for fuzzy sets based on the notion of the mass assignment of a fuzzy set. Several interesting properties of this new measure are examined. Furthermore, we also discuss how the proposed approach is used to describe the rough approximation quality of a fuzzy classification.

A Probability-Based Approach to Comparison of Fuzzy Numbers and Applications to Target-Oriented Decision Making

In this paper, we introduce a new comparison relation on fuzzy numbers based on their alpha-cut representation and comparison probabilities of interval values. Basically, this comparison process combines a widely accepted interpretation of fuzzy sets together with the uncertain characteristics inherent in the representation of fuzzy numbers. The proposed comparison relation is then applied to the issue of ranking fuzzy numbers using fuzzy targets in terms of target-based evaluations. Some numerical examples are used to illuminate the proposed ranking technique as well as to compare with previous methods. More interestingly, according to the interpretation of the new comparison relation on fuzzy numbers, we provide a fuzzy target-based decision model as a solution to the problem of decision making under uncertainty, with which an interesting link between the decision makers different attitudes about target and different risk attitudes in terms of utility functions can be established. Moreover, an application of the proposed comparison relation to the fuzzy target-based decision model for the problem of fuzzy decision making with uncertainty is provided. Numerical examples are also given for illustration.

A parametric representation of linguistic hedges in Zadeh's fuzzy logic

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh?s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.

On prioritized weighted aggregation in multi-criteria decision making

This paper deals with multi-criteria decision making (MCDM) problems with multiple priorities, in which priority weights associated with the lower priority criteria are related to the satisfactions of the higher priority criteria. Firstly, we propose a prioritized weighted aggregation operator based on ordered weighted averaging (OWA) operator and triangular norms (t-norms). To preserve the tradeoffs among the criteria in the same priority level, we suggest that the degree of satisfaction regarding each priority level is viewed as a pseudo criterion. On the other hand, t-norms are used to model the priority relationships between the criteria in different priority levels. In particular, we show that strict Archimedean t-norms perform better in inducing priority weights. As Hamacher family of t-norms provide a wide class of strict Archimedean t-norms ranging from the product to weakest t-norm, Hamacher parameterized t-norms are used to induce the priority weight for each priority level. Secondly, considering decision maker (DM)s requirement toward higher priority levels, a benchmark based approach is proposed to induce priority weight for each priority level. In particular, Lukasiewicz implication is used to compute benchmark achievement for crisp requirements; target-oriented decision analysis is utilized to obtain the benchmark achievement for fuzzy requirements. Finally, some numerical examples are used to illustrate the proposed prioritized aggregation technique as well as to compare with previous research.

A Target-Based Decision-Making Approach to Consumer-Oriented Evaluation Model for Japanese Traditional Crafts

This paper deals with the evaluation of Japanese traditional crafts, in which product items are assessed according to the so-called “Kansei” features by means of the semantic differential method. For traditional crafts, decisions on which items to buy or use are usually influenced by personal feelings/characteristics; therefore, we shall propose a consumer-oriented evaluation model targeting these specific requests by consumers. Particularly, given a consumers request, the proposed model aims to define an evaluation function that quantifies how well a product item meets the consumers feeling preferences. An application to evaluating patterns of Kutani porcelain is conducted to illustrate how the proposed evaluation model works, in practice.

A Linguistic Screening Evaluation Model in New Product Development

The screening of new product ideas is critically very important in new product development (NPD). Due to the incompleteness of information available and the qualitative nature of most evaluation criteria regarding NPD process, a fuzzy linguistic approach may be necessary for new-product screening, making use of linguistic assessments and the fuzzy-set-based computation. However, an inherent limitation of such a fuzzy linguistic approach is the loss of information caused by approximation processes, which eventually implies a lack of precision in the final results. This limitation even becomes more critical when applying the approach to new product screening. This paper proposes an approach to new product go/stop evaluation at the front end in NPD, based on the 2-tuple linguistic representation and the so-called preference-preserving transformation. It is shown that the proposed approach always yields a consistent result, while maintaining the flexibility for managers in making their decisions as in the fuzzy-set-based approach. Ultimately, this approach enhances the fuzzy-logic-based screening model proposed in the previous studies by overcoming the mentioned limitation. A case study taken from the literature is used to illuminate the proposed technique and to compare with the previous technique based on fuzzy computation.

Adaptively entropy-based weighting classifiers in combination using Dempster-Shafer theory for word sense disambiguation

In this paper we introduce an evidential reasoning based framework for weighted combination of classifiers for word sense disambiguation (WSD). Within this framework, we propose a new way of defining adaptively weights of individual classifiers based on ambiguity measures associated with their decisions with respect to each particular pattern under classification, where the ambiguity measure is defined by Shannons entropy. We then apply the discounting-and-combination scheme in Dempster-Shafer theory of evidence to derive a consensus decision for the classification task at hand. Experimentally, we conduct two scenarios of combining classifiers with the discussed method of weighting. In the first scenario, each individual classifier corresponds to a well-known learning algorithm and all of them use the same representation of context regarding the target word to be disambiguated, while in the second scenario the same learning algorithm applied to individual classifiers but each of them uses a distinct representation of the target word. These experimental scenarios are tested on English lexical samples of Senseval-2 and Senseval-3 resulting in an improvement in overall accuracy.

Decision making under uncertainty with fuzzy targets

This paper discusses the issue of how to use fuzzy targets in the target-based model for decision making under uncertainty. After introducing a target-based interpretation of the expected value on which it is shown that this model implicitly assumes a neutral behavior on attitude about the target, we examine the issue of using fuzzy targets considering different attitudes about the target selection of the decision maker. We also discuss the problem for situations on which the decision maker’s attitude about target may change according to different states of nature. Especially, it is shown that the target-based approach can provide an unified way for solving the problem of fuzzy decision making with uncertainty about the state of nature and imprecision about payoffs. Several numerical examples are given for illustration of the discussed issues.

Integrated Uncertainty in Knowledge Modelling and Decision Making

• Uncertainty formalisms: Bayesian probability, Dempster-Shafer theory, imprecise probability, random sets, rough sets, fuzzy sets & interval-based models. • Modelling uncertainty & inconsistency in big data • Learning and reasoning with uncertainty • Information fusion & knowledge integration in uncertain environments • Decision making under various types of uncertainty • Aggregation operators • Copulas for dependence modelling • Granular and soft computing • Computational intelligence Application