M-best solutions for a class of fuzzy constraint satisfaction problems
International Research and Training Centre of Information Technologies and Systems, National Academy of Science of Ukraine（乌克兰国家科学院国际信息技术与系统研究培训中心）；Czech Technical University in Prague（布拉格捷克理工大学）
Michail Schlesinger, Boris Flach, Evgeniy Vodolazskiy
The article considers one of the possible generalizations of constraint satisfaction problems where relations are replaced by multivalued membership functions. In this case operations of disjunction and conjunction are replaced by maximum and minimum, and consistency of a solution becomes multivalued rather than binary. The article studies the problem of finding d most admissible solutions for a given d. A tractable subclass of these problems is defined by the concepts of invariants and polymorphisms similar to the classic constraint satisfaction approach. These concepts are adapted in two ways. Firstly, the correspondence of "invariant-polymorphism" is generalized to (min,max) semirings. Secondly, we consider non-uniform polymorphisms, where each variable has its own operator, in contrast to the case of one operator common for all variables. The article describes an algorithm that finds $d$ most admissible solutions in polynomial time, provided that the problem is invariant with respect to some non-uniform majority operator. It is essential that this operator needs not to be known for the algorithm to work. Moreover, even a guarantee for the existence of such an operator is not necessary. The algorithm either finds the solution or discards the problem. The latter is possible only if the problem has no majority polymorphism.
Cairo University（开罗大学）；Faculty of Science（理学院）；Department of Mathematics（数学系）
In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to Łukasiewicz logic. The MaxSAT problem for a set of formulae Φ is the problem of finding an assignment to the variables in Φ that satisfies the maximum number of formulae. Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem (WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness.
Xi’an Jiaotong University（西安交通大学）；University of Electronic Science and Technology of China（电子科技大学）
We apply the Ordered Weighted Averaging (OWA) operator in multi-criteria decision-making. To satisfy different kinds of uncertainty, measure based dominance has been presented to gain the order of different criterion. However, this idea has not been applied in fuzzy system until now. In this paper, we focus on the situation where the linguistic satisfactions are fuzzy measures instead of the exact values. We review the concept of OWA operator and discuss the order mechanism of fuzzy number. Then we combine with measure-based dominance to give an overall score of each alternatives. An example i…
A weighted constraint satisfaction problem (WCSP) is a constraint satisfaction problem in which preferences among solutions can be expressed. Bucket elimination is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory required to apply bucket elimination is too high, a heuristic method based on it (denominated mini-buckets) can be used to calculate bounds for the optimal solution. Nevertheless, the curse of dimensionality makes these techniques impractical on large scale problems. In response to this situation, we present a memetic algorithm …
University of York（约克大学）；University College Cork（科克大学学院）；Uppsala University（乌普萨拉大学）
We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement an efficient linear time algorithm for enforcing generalised arc consistency on such a multiset ordering constraint. Experimental results on several problem domains show considerable promise.
International Institute of Information Technology Bhubaneswar（布巴内斯瓦尔国际信息技术学院）
Minesweeper is a popular spatial-based decision-making game that works with incomplete information. As an exemplary NP-complete problem, it is a major area of research employing various artificial intelligence paradigms. The present work models this game as Constraint Satisfaction Problem (CSP) and Markov Decision Process (MDP). We propose a new method named as dependents from the independent set using deterministic solution search (DSScsp) for the faster enumeration of all solutions of a CSP based Minesweeper game and improve the results by introducing heuristics. Using MDP, we implement mach…
Hamilton Institute, National University of Ireland Maynooth（爱尔兰国立大学梅努斯分校汉密尔顿研究所）；University of Toulouse（图卢兹大学）
We show that several important resource allocation problems in wireless networks fit within the common framework of Constraint Satisfaction Problems (CSPs). Inspired by the requirements of these applications, where variables are located at distinct network devices that may not be able to communicate but may interfere, we define natural criteria that a CSP solver must possess in order to be practical. We term these algorithms decentralized CSP solvers. The best known CSP solvers were designed for centralized problems and do not meet these criteria. We introduce a stochastic decentralized CSP so…
University of Manouba（马努巴大学）；National School of Computer Science（国立计算机科学学院）；University of Strasbourg（斯特拉斯堡大学）；Taibah University（塔伊巴大学）；College of Computer Science and Engineering（计算机科学与工程学院）
Constraint satisfaction problem (CSP) has been actively used for modeling and solving a wide range of complex real-world problems. However, it has been proven that developing efficient methods for solving CSP, especially for large problems, is very difficult and challenging. Existing complete methods for problem-solving are in most cases unsuitable. Therefore, proposing hybrid CSP-based methods for problem-solving has been of increasing interest in the last decades. This paper aims at proposing a novel approach that combines incomplete and complete CSP methods for problem-solving. The proposed…
We explore the problem of step-wise explaining how to solve constraint satisfaction problems, with a use case on logic grid puzzles. More specifically, we study the problem of explaining the inference steps that one can take during propagation, in a way that is easy to interpret for a person. Thereby, we aim to give the constraint solver explainable agency, which can help in building trust in the solver by being able to understand and even learn from the explanations. The main challenge is that of finding a sequence of simple explanations, where each explanation should aim to be as cognitively…
The purpose of this paper is to point to the usefulness of applying a linear mathematical formulation of fuzzy multiple criteria objective decision methods in organising business activities. In this respect fuzzy parameters of linear programming are modelled by preference-based membership functions. This paper begins with an introduction and some related research followed by some fundamentals of fuzzy set theory and technical concepts of fuzzy multiple objective decision models. Further a real case study of a manufacturing plant and the implementation of the proposed technique is presented. Em…
We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly produce a single satisfying assignment. Our first CSP solver, called Perturbed Blief Propagation, smoothly interpolates two well-known inference procedures; it starts as BP and ends as a Gibbs sampler, which produces a single sample from the set of solutions. Moreover we apply a similar perturbation scheme to SP to produce another CSP solver, Perturbed Survey Pro…
Suuplier selection is one of the most important functions of a purchasing department. Since by deciding the best supplier, companies can save material costs and increase competitive advantage.However this decision becomes compilcated in case of multiple suppliers, multiple conflicting criteria, and imprecise parameters. In addition the uncertainty and vagueness of the experts' opinion is the prominent characteristic of the problem. therefore an extensively used multi criteria decision making tool Fuzzy AHP can be utilized as an approach for supplier selection problem. This paper reveals the ap…
Fuzzy rule based classification systems are one of the most popular fuzzy modeling systems used in pattern classification problems. This paper investigates the effect of applying nine different T-norms in fuzzy rule based classification systems. In the recent researches, fuzzy versions of confidence and support merits from the field of data mining have been widely used for both rules selecting and weighting in the construction of fuzzy rule based classification systems. For calculating these merits the product has been usually used as a T-norm. In this paper different T-norms have been used fo…
NIIT University（NIIT大学）；Netaji Subhas Open University（内塔吉·苏巴斯开放大学）
ETP is NP Hard combinatorial optimization problem. It has received tremendous research attention during the past few years given its wide use in universities. In this Paper, we develop three mathematical models for NSOU, Kolkata, India using FILP technique. To deal with impreciseness and vagueness we model various allocation variables through fuzzy numbers. The solution to the problem is obtained using Fuzzy number ranking method. Each feasible solution has fuzzy number obtained by Fuzzy objective function. The different FILP technique performance are demonstrated by experimental data generate…
Netaji Subhas Open University（内塔吉·苏巴斯开放大学）；St. Xavier’s College（圣沙勿略学院）
The Fuzzy Modeling has been applied in a wide variety of fields such as Engineering and Management Sciences and Social Sciences to solve a number Decision Making Problems which involve impreciseness, uncertainty and vagueness in data. In particular, applications of this Modeling technique in Decision Making Problems have remarkable significance. These problems have been tackled using various theories such as Probability theory, Fuzzy Set Theory, Rough Set Theory, Vague Set Theory, Approximate Reasoning Theory etc. which lack in parameterization of the tools due to which they could not be appli…
Optimization is becoming a crucial element in industrial applications involving sustainable alternative energy systems. During the design of such systems, the engineer/decision maker would often encounter noise factors (e.g. solar insolation and ambient temperature fluctuations) when their system interacts with the environment. In this chapter, the sizing and design optimization of the solar powered irrigation system was considered. This problem is multivariate, noisy, nonlinear and multiobjective. This design problem was tackled by first using the Fuzzy Type II approach to model the noise fac…
Meghnad Saha Institute of Technology（梅格纳德·萨哈技术学院）；Netaji Subhas Open University（苏巴斯·钱德拉·鲍斯开放大学）；St. Xavier’s College（圣沙勿略学院）；Indian Institute of Technology（印度理工学院）
Transportation Problem is an important problem which has been widely studied in Operations Research domain. It has been often used to simulate different real life problems. In particular, application of this Problem in NP Hard Problems has a remarkable significance. In this Paper, we present the closed, bounded and non empty feasible region of the transportation problem using fuzzy trapezoidal numbers which ensures the existence of an optimal solution to the balanced transportation problem. The multivalued nature of Fuzzy Sets allows handling of uncertainty and vagueness involved in the cost v…
Meghnad Saha Institute of Technology（梅格纳德·萨哈技术学院）；Netaji Subhas Open University（内塔吉·苏巴斯开放大学）
Transportation Problem is an important aspect which has been widely studied in Operations Research domain. It has been studied to simulate different real life problems. In particular, application of this Problem in NP- Hard Problems has a remarkable significance. In this Paper, we present a comparative study of Transportation Problem through Probabilistic and Fuzzy Uncertainties. Fuzzy Logic is a computational paradigm that generalizes classical two-valued logic for reasoning under uncertainty. In order to achieve this, the notation of membership in a set needs to become a matter of degree. By…
School of Electrical and Information Engineering, University of the Witwatersrand（威特沃特斯兰德大学电气与信息工程学院）
An ensemble based approach for dealing with missing data, without predicting or imputing the missing values is proposed. This technique is suitable for online operations of neural networks and as a result, is used for online condition monitoring. The proposed technique is tested in both classification and regression problems. An ensemble of Fuzzy-ARTMAPs is used for classification whereas an ensemble of multi-layer perceptrons is used for the regression problem. Results obtained using this ensemble-based technique are compared to those obtained using a combination of auto-associative neural ne…
The domain model is one of the important components used by adaptive learning systems to automatically generate customized courses for the learners. In this paper our contribution is to propose a new tool for implementation of a domain model based on fuzzy relationships among concepts. This tool allows the experts and teachers to find the best parameters in order to adapt the learners's differences.
Bankruptcy prediction is very important for all the organization since it affects the economy and rise many social problems with high costs. There are large number of techniques have been developed to predict the bankruptcy, which helps the decision makers such as investors and financial analysts. One of the bankruptcy prediction models is the hybrid model using Fuzzy C-means clustering and MARS, which uses static ratios taken from the bank financial statements for prediction, which has its own theoretical advantages. The performance of existing bankruptcy model can be improved by selecting th…
Shahid Beheshti University（沙希德·贝赫什提大学）；Amirkabir University of Technology（阿米尔卡比尔理工大学）
In this paper, a novel stepwise learning approach based on estimating desired premise parts' outputs by solving a constrained optimization problem is proposed. This learning approach does not require backpropagating the output error to learn the premise parts' parameters. Instead, the near best output values of the rules premise parts are estimated and their parameters are changed to reduce the error between current premise parts' outputs and the estimated desired ones. Therefore, the proposed learning method avoids error backpropagation, which lead to vanishing gradient and consequently getti…
Khulna University of Engineering & Technology（库尔纳工程技术大学）
The Decision Support System (DSS) contains more than one antecedent and the degrees of strength of the antecedents need to be combined to determine the overall strength of the rule consequent. The membership values of the linguistic variables in Fuzzy have to be combined using an aggregation operator. But it is not feasible to predefine the form of aggregation operators in decision making. Instead, each rule should be found based on the feeling of the experts and on their actual decision pattern over the set of typical examples. Thus this work illustrates how the choice of aggregation operator…
A fuzzy adaptive metaheuristic algorithm for identifying sustainable, economical, lightweight, and earthquake-resistant reinforced concrete cantilever retaining walls
School of Information and Physical Sciences, The University of Newcastle（新castle大学信息与物理科学学院）；Department of Civil Engineering, University of Memphis（Memphis大学土木工程系）；Faculty of Engineering and Information Technology, University of Technology Sydney（悉尼技术大学工程与信息技术学院）
