Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

Explaining computer predictions with augmented appraisal degrees

An augmented appraisal degree (AAD) has been conceived as a mathematical representation of the connotative meaning in an experience-based evaluation, which depends on a particular experience or knowledge. Aiming to improve the interpretability of computer predictions, we explore the use of AADs to represent evaluations that are per- formed by a machine to predict the class of a particular object. Hence, we propose a novel method whereby predictions made using a support vector machine classification process are augmented through AADs. An illustra- tive example, in which the classes of handwritten digits are predicted, shows how the augmentation of such predictions can favor their interpretability

Water filtration by using apple and banana peels as activated carbon

Water filter is an important devices for reducing the contaminants in raw water. Activated from charcoal is used to absorb the contaminants. Fruit peels are some of the suitable alternative carbon to substitute the charcoal. Determining the role of fruit peels which were apple and banana peels powder as activated carbon in water filter is the main goal. Drying and blending the peels till they become powder is the way to allow them to absorb the contaminants. Comparing the results for raw water before and after filtering is the observation. After filtering the raw water, the reading for pH was 6.8 which is in normal pH and turbidity reading recorded was 658 NTU. As for the colour, the water becomes more clear compared to the raw water. This study has found that fruit peels such as banana and apple are an effective substitute to charcoal as natural absorbent

Rough set decision algorithms for modeling with uncertainty

The use of decision rules allows to extract information and to infer conclusions from relational databases in a reliable way, thanks to some indicators like support and certainty. Moreover, decision algorithms collect a group of decision rules that satisfies desirable properties to describe the relational system. However, when a decision table is considered within a fuzzy environment, it is necessary to extend all notions related to decision algorithms to this framework. This paper presents a generalization of these notions, highlighting the new definitions of indicators of relevance to describe decision rules and decision algorithm

On non-monotonic Choquet integrals as aggregation functions

This paper deals with non-monotonic Choquet integral, a generalization of the regular Choquet integral. The discrete non-monotonic Choquet integral is considered under the viewpoint of aggregation. In particular we give an axiomatic characterization of the class of non-monotonic Choquet integrals.We show how the Shapley index, in contrast with the monotonic case, can assume positive values if the criterion is in average a benefit, depending on its effect in all the possible coalition coalitions, and negative values in the opposite case of a cost criterion.

SVM-Based Negative Data Mining to Binary Classification

The properties of training data set such as size, distribution and the number of attributes significantly contribute to the generalization error of a learning machine. A not well-distributed data set is prone to lead to a partial overfitting model. Two approaches proposed in this dissertation for the binary classification enhance useful data information by mining negative data. First, an error driven compensating hypothesis approach is based on Support Vector Machines (SVMs) with (1+k)-iteration learning, where the base learning hypothesis is iteratively compensated k times. This approach produces a new hypothesis on the new data set in which each label is a transformation of the label from the negative data set, further producing the positive and negative child data subsets in subsequent iterations. This procedure refines the base hypothesis by the k child hypotheses created in k iterations. A prediction method is also proposed to trace the relationship between negative subsets and testing data set by a vector similarity technique. Second, a statistical negative example learning approach based on theoretical analysis improves the performance of the base learning algorithm learner by creating one or two additional hypotheses audit and booster to mine the negative examples output from the learner. The learner employs a regular Support Vector Machine to classify main examples and recognize which examples are negative. The audit works on the negative training data created by learner to predict whether an instance is negative. However, the boosting learning booster is applied when audit does not have enough accuracy to judge learner correctly. Booster works on training data subsets with which learner and audit do not agree. The classifier for testing is the combination of learner, audit and booster. The classifier for testing a specific instance returns the learner\u27s result if audit acknowledges learner\u27s result or learner agrees with audit\u27s judgment, otherwise returns the booster\u27s result. The error of the classifier is decreased to O(e^2) comparing to the error O(e) of a base learning algorithm

Bipolar and bivariate models in multi-criteria decision analysis: descriptive and constructive approaches

Multi-criteria decision analysis studies decision problems in which the alternatives are evaluated on several dimensions or viewpoints. In the problems we consider in this paper, the scales used for assessing the alternatives with respect to a viewpoint are bipolar and univariate or unipolar and bivariate. In the former case, the scale is divided in two zones by a neutral point; a positive feeling is associated to the zone above the neutral point and a negative feeling to the zone below this point. On unipolar bivariate scales, an alternative can receive both a positive and a negative evaluation, reflecting contradictory feelings or stimuli. The paper discusses procedures and models that have been proposed to aggregate multi-criteria evaluations when the scale of each criterion is of one of the two types above. We present both a constructive and a descriptive view on this question; the descriptive approach is concerned with characterizations of models of preference, while the constructive approach aims at building preferences by questioning the decision maker. We show that these views are complementary.Multiple criteria, Decision analysis, Preference, Bipolarmodels, Choquet integral

Applications of fuzzy theories to multi-objective system optimization

Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis