International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

When some coefficients of the constraints are uncertain with only their possible ranges being given, a conventional linear programming (LP) problem can be generalised to the one with set-inclusive constraints. We consider the case where the possible ranges are given by fuzzy sets in this paper. The set-inclusive constraints with fuzzy coefficients have been treated by a necessity measure. However, the usual necessity measure cannot express well the decision-maker’s requirement about the trade-off between the robustness level and the satisfaction level of the constraints. We extend the necessity measure to incorporate the trade-off between the robustness level and the satisfaction level of the constraints. We apply the extended necessity measure to LP problems with fuzzy coefficients. After the problem is formulated and reduced to the conventional programming problem, we propose a solution algorithm. Numerical examples are given to illustrate the proposed approach.

The analytic hierarchy process (AHP) provides a systematic approach to the evaluation of alternatives based on pairwise comparison matrices (PCMs) under multiple criteria. As human evaluation is not always accurate and precise, each component of a PCM showing relative importance has been expressed by an interval or a fuzzy number. In this paper, we treat a PCM whose components are represented by twofold intervals. The twofold intervals are composed of inner and outer intervals showing the range of surely acceptable values and the complement of the range of surely unacceptable values for relative importance, respectively. One may apply a fuzzy AHP approach by building a trapezoidal fuzzy number from the inner and outer intervals. However, this approach does not always fit the given information. Because the twofold interval information ambiguously specifies the range of acceptable values for the relative importance. Then we appropriately translate this information into a set of intervals including the inner interval and included in the outer interval, assuming that the decision-maker evaluates the priority weights implicitly as intervals. We investigate the decision analysis based on the twofold interval PCM. Three conflict resolution methods are proposed for treating the inconsistency in the twofold interval PCM. Parametric methods for visualizing possible alternative orderings are proposed. Numerical examples are given to demonstrate the differences between the proposed approach and the previous approaches.

End users who cannot afford to collect and label big data to train accurate deep learning (DL) models resort to Machine Learning as a Service (MLaaS) providers, who provide paid access to accurate DL models. However, the lack of transparency in how the providers’ models make predictions causes a problem of trust. A way to increase trust (and also to align with ethical regulations) is for predictions to be accompanied by explanations locally and independently generated by the end users (rather than by explanations offered by the model providers). Explanation methods using internal components of DL models (a.k.a. model-specific explanations) are more accurate and effective than those relying solely on the inputs and outputs (a.k.a. model-agnostic explanations). However, end users lack white-box access to the internal components of the providers’ models. To tackle this issue, we propose a novel approach allowing an end user to locally generate model-specific explanations for a DL classification model accessed via a provider’s API. First, we approximate the provider’s model with a local surrogate model. We then use the surrogate model’s components to locally generate model-specific explanations that approximate the explanations obtainable with white-box access to the provider’s DL model. Specifically, we leverage the surrogate model’s gradients to generate adversarial examples that counterfactually explain why an input example is classified into a specific class. Our approach only requires the end user to have unlabeled data of size $0.5\%$ of the provider’s training data and with a similar distribution; given the small size and unlabeled nature of these data, they can be assumed to be already available to the end user or even to be supplied by the provider to build trust in his model. We demonstrate the accuracy and effectiveness of our approach through extensive experiments on two ML tasks: image classification and tabular data classification. The locally generated explanations are consistent with those obtainable with white-box access to the provider’s model, thus giving end users an independent and reliable way to determine if the provider’s model is trustworthy.

In this paper we introduce a fuzzy propagation model to deal with the influence maximization (IM) problem. The IM problem for the most of existing propagation model is NP-hard. Here, we model social networks as fuzzy directed graphs to propose an application-oriented propagation process. To this aim, we investigate an interesting relationship between zero forcing set concept in graphs and IM problem in social networks. In spite of its attractive theory, its implementation is not efficient in the real world. Thus, we improve the fuzzy zero forcing set concept and suggest our fuzzy propagation model, simultaneously. Moreover, we present a polynomial time complexity algorithm to solve IM problems under the proposed propagation process. In particular, we consider a propagation parameter to control the size of the seed set and its coverage. Also, experimental results on some real world social networks show that the propagation model finds optimal and flexible seed set.

A person’s preference to select or reject certain meals is influenced by several aspects, including colour. In this paper, we study the relevance of food colour for such preferences. To this end, a set of images of meals is processed by an automatic method that associates mood adjectives that capture such meal preferences. These adjectives are obtained by analyzing the colour palettes in the image, using a method based in Kobayashi’s model of harmonic colour combinations. The paper also validates that the colour palettes calculated for each image are harmonic by developing a rating model to predict how much a user would like the colour palettes obtained. This rating is computed using a regression model based on the COLOURlovers dataset implemented to learn users’ preferences. Finally, the adjectives associated automatically with images of dishes are validated by a survey which was responded by 178 people and demonstrates that the labels are adequate. The results obtained in this paper have applications in tourism marketing, to help in the design of marketing multimedia material, especially for promoting restaurants and gastronomic destinations.