The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a variety of applications, such as Computing With Words. In this paper, we highlight this utility and introduce a distance measure which takes the direction between sets into account. We provide details of its application for normal and non-normal, as well as convex and non-convex fuzzy sets. We demonstrate the new distance measure using real data from the MovieLens dataset and establish the benefits of measuring the direction between fuzzy sets.

This paper aims at providing a preliminary discussion on how to deal with spatio-temporal information in the context of behaviour recognition. It draws comparison with how humans reason in other areas, such as law, and discusses some of the pros and cons of formalisms for handling uncertainty, starting with probability theory, continuing with the Dempster-Shafer theory, and concluding with fuzzy logic.

One of the most difficult tasks in value function approximation for Markov Decision Processes is finding an approximation architecture that is expressive enough to capture the important structure in the value function, while at the same time not overfitting the training samples. Recent results in non-parametric approximate linear programming (NP-ALP), have demonstrated that this can be done effectively using nothing more than a smoothness assumption on the value function. In this paper we extend these results to the case where samples come from real world transitions instead of the full Bellman equation, adding robustness to noise. In addition, we provide the first max-norm, finite sample performance guarantees for any form of ALP. NP-ALP is amenable to problems with large (multidimensional) or even infinite (continuous) action spaces, and does not require a model to select actions using the resulting approximate solution.

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 generated through extensive simulation from NSOU, Kolkata, India in terms of its execution times. The proposed FILP models are compared with commonly used heuristic viz. ILP approach on experimental data which gives an idea about quality of heuristic. The techniques are also compared with different Artificial Intelligence based heuristics for ETP with respect to best and mean cost as well as execution time measures on Carter benchmark datasets to illustrate its effectiveness. FILP takes an appreciable amount of time to generate satisfactory solution in comparison to other heuristics. The formulation thus serves as good benchmark for other heuristics. The experimental study presented here focuses on producing a methodology that generalizes well over spectrum of techniques that generates significant results for one or more datasets. The performance of FILP model is finally compared to the best results cited in literature for Carter benchmarks to assess its potential. The problem can be further reduced by formulating with lesser number of allocation variables it without affecting optimality of solution obtained. FLIP model for ETP can also be adapted to solve other ETP as well as combinatorial optimization problems.

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 doing this we accomplish two things viz., (i) ease of describing human knowledge involving vague concepts and (ii) enhanced ability to develop cost-effective solution to real-world problem. The multi-valued nature of Fuzzy Sets allows handling uncertain and vague information. It is a model-less approach and a clever disguise of Probability Theory. We give comparative simulation results of both approaches and discuss the Computational Complexity. To the best of our knowledge, this is the first work on comparative study of Transportation Problem using Probabilistic and Fuzzy Uncertainties.

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 values of each cells in the transportation table. For finding the initial solution of the transportation problem we use the Fuzzy Vogel Approximation Method and for determining the optimality of the obtained solution Fuzzy Modified Distribution Method is used. The fuzzification of the cost of the transportation problem is discussed with the help of a numerical example. Finally, we discuss the computational complexity involved in the problem. To the best of our knowledge, this is the first work on obtaining the solution of the transportation problem using fuzzy trapezoidal numbers.

In India financial markets have existed for many years. A functionally accented, diverse, efficient and flexible financial system is vital to the national objective of creating a market driven, productive and competitive economy. Today markets of varying maturity exist in equity, debt, commodities and foreign exchange. In this work we attempt to generate prediction rules scheme for stock price movement at Bombay Stock Exchange using an important Soft Computing paradigm viz., Rough Fuzzy Multi Layer Perception. The use of Computational Intelligence Systems such as Neural Networks, Fuzzy Sets, Genetic Algorithms, etc. for Stock Market Predictions has been widely established. The process is to extract knowledge in the form of rules from daily stock movements. These rules can then be used to guide investors. To increase the efficiency of the prediction process, Rough Sets is used to discretize the data. The methodology uses a Genetic Algorithm to obtain a structured network suitable for both classification and rule extraction. The modular concept, based on divide and conquer strategy, provides accelerated training and a compact network suitable for generating a minimum number of rules with high certainty values. The concept of variable mutation operator is introduced for preserving the localized structure of the constituting Knowledge Based sub-networks, while they are integrated and evolved. Rough Set Dependency Rules are generated directly from the real valued attribute table containing Fuzzy membership values. The paradigm is thus used to develop a rule extraction algorithm. The extracted rules are compared with some of the related rule extraction techniques on the basis of some quantitative performance indices. The proposed methodology extracts rules which are less in number, are accurate, have high certainty factor and have low confusion with less computation time.

Type-1 fuzzy logic has frequently been used in control systems. However this method is sometimes shown to be too restrictive and unable to adapt in the presence of uncertainty. In this paper we compare type-1 fuzzy control with several other fuzzy approaches under a range of uncertain conditions. Interval type-2 and non-stationary fuzzy controllers are compared, along with 'dual surface' type-2 control, named due to utilising both the lower and upper values produced from standard interval type-2 systems. We tune a type-1 controller, then derive the membership functions and footprints of uncertainty from the type-1 system and evaluate them using a simulated autonomous sailing problem with varying amounts of environmental uncertainty. We show that while these more sophisticated controllers can produce better performance than the type-1 controller, this is not guaranteed and that selection of Footprint of Uncertainty (FOU) size has a large effect on this relative performance.

We propose a reinforcement learning solution to the \emph{soccer dribbling task}, a scenario in which a soccer agent has to go from the beginning to the end of a region keeping possession of the ball, as an adversary attempts to gain possession. While the adversary uses a stationary policy, the dribbler learns the best action to take at each decision point. After defining meaningful variables to represent the state space, and high-level macro-actions to incorporate domain knowledge, we describe our application of the reinforcement learning algorithm \emph{Sarsa} with CMAC for function approximation. Our experiments show that, after the training period, the dribbler is able to accomplish its task against a strong adversary around 58% of the time.

The Dominance-based Rough Set Approach (DRSA) is an extension of Rough Sets Theory to handle multicriteria classification problems by authorizing preference-ordered attributes. The DRSA assumes the existence of a single decision table while real-world decision problems imply generally several experts with different decision tables. The objective of this paper is to propose an algorithm for the aggregation of a set of decision tables, as a first step for approximating these tables. The algorithm is illustrated using real-world data.