Fourier‐Motzkin elimination method in MOLP problems

This paper introduces a method for finding the non‐dominated set in criterion space of an MOLP problem based on Fourier–Motzkin Elimination. The method incorporates a procedure that eliminates decision variables from constraints and transforms a feasible region from decision space to criterion space. While avoiding characterization of the efficient set in decision space, it finds the non‐dominated set in criterion space. After the decision maker's most preferred criterion vector has been identified, the corresponding efficient solutions can be found by backward substitution. The method was implemented in MATLAB using a tabular form and computational experiments were conducted. The results indicate that although the method performs well for relatively small problems, it can be computationally intensive for larger problems. Nonetheless, the method is intuitively appealing and it provides useful insights into the geometry and theory of MOLP. As such it makes it a valuable educational tool for students of multi‐criteria decision analysis. Copyright © 2003 John Wiley & Sons, Ltd.     

An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems using chance constrained conditions

Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this paper, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using chance constrained programming techniques, the stochastic programming problems are transformed into deterministic ones. As a fusion of stochastic approaches and fuzzy ones, after determining the fuzzy goals of the decision maker, interactive fuzzy satisficing methods to derive a satisficing solution for the decision maker by updating the reference membership levels is presented. Copyright © 2003 John Wiley & Sons, Ltd.     

消费者基于选择集的情境效应

消费者基于选择集的情境效应颠覆了传统的理性选择理论,表明了情境对消费者偏好和选择的系统性影响。情境效应主要的类型有吸引效应和折衷效应。情境效应具有感知偏差、风险和负面情绪规避以及信息推理等方面的内在机理。选择集结构和特征及消费者等因素都对情境效应产生影响,而情境效应会影响消费者偏好的构建。未来情境效应研究将会向复杂属性组合、复杂购买情境和新情境效应的发现等方面拓展。     

Feature selection using Ant Colony Optimization (ACO) and Road Sign Detection and Recognition (RSDR) system

Road Sign Detection and Recognition (RSDR) is aimed to enable drivers maintain basic functionality with the aim of identifying and notifying driver through the existing restrictions so that the process is a success on the present widened road. Examples for RSDR include ‘traffic light ahead’ or ‘pedestrian crossing’ signs. An innovative RSDR system has been introduced which comprises of pre-processing, edge detection, feature extraction, features selection and Ensemble Fuzzy Support Vector Machine (EFSVM) classifier. Feature selection is carried out successfully by deployment of Ant Colony Optimization (ACO) algorithm to determine most prominent and definitive features. These features are then fed into the ensemble SVM to enable both road side traffic detection as well as recognition. Suggested system’s performance is analyzed and evaluated with respect to road signs having a capable recognition rate.     

Parameter selection based on fuzzy logic to improve UAV path-following algorithms

In order to steer an Unmanned Aerial Vehicle (UAV) and make it follow a desired trajectory, a high level controller is needed. Depending on the control algorithm, one or more parameters have to be tuned, having their values high impact on the performance. In most of the works, these parameters are taken as constant. In this paper, we apply fuzzy logic to select the parameters of the control law and compare this approach with the tuning by constant parameters and with another adjusting method based on the kinematic analysis of the equations of the UAV. After many simulations of the quadrotor following randomly generated paths, we have proved that the fuzzy tuning law is not only a good and feasible solution, but also more general as it can be applied to any trajectory.     

Small wonders of the Indian market

Heavy competition in India in almost all product categories, due to diversification by large and medium companies and increased entry of multinationals, has restricted the growth of domestic companies. Previously, large companies enjoyed high profit margins by targeting premium priced products in the upper strata of Indian society. High levels of competition from equally reputed brands have not only decreased the companies' market share but also created price wars, reducing profit margins and limiting market growth. This has motivated companies to consider the lower classes and the rural segments, which they had previously ignored. By targeting these segments with products in small packs at lower price points, companies have experienced great success. At the same time, small packs also pose some challenges for the companies. This paper explains the importance of small packs for market expansion in various product categories within the Indian market, drawing on several examples to support the views of the authors. Copyright © 2004 Henry Stewart Publications.     

LÉVY HIERARCHY IN WEAK SET THEORIES

We investigate the interactions of formula complexity in weak set theories with the axioms available there. In particular, we show that swapping bounded and unbounded quantification preserves formula complexity in presence of the axiom of foundation weakened to an arbitrary set base, while it does not if the axiom of foundation is further weakened to a proper class base. More attention is being paid to the necessary axioms employed in the positive results, than to the combinatorial strength of the positive results themselves.     

Propositions, Sets, and Worlds

If we agree with Michael Jubien that propositions do not exist, while accepting the existence of abstract sets in a realist mathematical ontology, then the combined effect of these ontological commitments has surprising implications for the metaphysics of modal logic, the ontology of logically possible worlds, and the controversy over modal realism versus actualism. Logically possible worlds as maximally consistent proposition sets exist if sets generally exist, but are equivalently expressed as maximally consistent conjunctions of the same propositions in corresponding sets. A conjunction of propositions, even if infinite in extent, is nevertheless itself a proposition. If sets and hence proposition sets exist but propositions do not exist, then whether or not modal realism is true depends on which of two apparently equivalent methods of identifying, representing, or characterizing logically possible worlds we choose to adopt. I consider a number of reactions to the problem, concluding that the best solution may be to reject the conventional model set theoretical concept of logically possible worlds as maximally consistent proposition sets, and distinguishing between the actual world alone as maximally consistent and interpreting all nonactual merely logically possible worlds as submaximal. I am grateful to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Royal Netherlands Academy of Arts and Sciences (KNAW), for supporting this among related research projects in philosophical logic and philosophy of mathematics during my Resident Research Fellowship in 2005-2006.     

Single and double alternation learning in rats: The role of set size and correction

In many experiments, rats have evidenced extreme difficulty mastering alternation patterns. In three experiments, we explored rats’ ability to learn double alternation patterns and possible reasons behind their past difficulties with such patterns. In Experiment 1, rats learned single and double alternation patterns. In the second and third experiment, we explored the role of correction and interference from stimulus set size on rats’ learning of double alternation patterns. Our results showed that rats easily learned both single and double alternation patterns and that stimulus set size had no noticeable effect on learning double alternation patterns. Findings additionally evidenced that correction played an important role in rats’ learning double alternation patterns.