Land Cover Classification Using the Proposed Texture Model and Fuzzy k-NN Classifier

Texture feature is a decisive factor in pattern classification problems because texture features are not deduced from the intensity of current pixel but from the grey level intensity variations of current pixel with its neighbors. In this chapter, a new texture model called multivariate binary threshold pattern (MBTP) has been proposed with five discrete levels such as -9, -1, 0, 1, and 9 characterizing the grey level intensity variations of the center pixel with its neighbors in the local neighborhood of each band in a multispectral image. Texture-based classification has been performed with the proposed model using fuzzy k-nearest neighbor (fuzzy k-NN) algorithm on IRS-P6, LISS-IV data, and the results have been evaluated based on confusion matrix, classification accuracy, and Kappa statistics. From the experiments, it is found that the proposed model outperforms other chosen existing texture models.

Supply Chain Network Design in Uncertain Environment

Dynamic environment imposes such conditions that make it necessary for companies to consider sources of uncertainty in designing core business processes and optimizing supply chain operations. Efficient management of a supply system requires an integrated approach towards various operational functions and related source of uncertainties. Uncertain conditions in supply network design problem such as market demands, delivery time, and facility capacity are considered and incorporated by many studies at the mathematical programming formulations as well. In this chapter, extensive review of existing SCND literature, brief overview and classification on uncertainty sources, useful strategies to deal uncertainties, model formulation with uncertain/stochastic parameters, efficient developed solution methodologies, and improvement adjustment mechanisms are discussed. Lastly, some directions for further research in this area are suggested.

Optimality Principles for Fuzzy Dual Uncertain Systems

This chapter considers the extension of the calculus of variations to the optimization of a class of fuzzy systems where the uncertainty of variables and parameters is represented by symmetrical triangular membership functions. The concept of fuzzy dual numbers is introduced, and the consideration of the necessary differentiability conditions for functions of dual variables leads to the definition of fuzzy dual functions. It is shown that when this formalism is adopted to represent performance indexes for uncertain optimization problems, the calculus of variations can be used to establish necessary optimality conditions as an extension to this case of the Euler-Lagrange equation. Then the chapter discusses the propagation of uncertainty when the fuzzy dual formalism is adopted for the state representation of a time continuous system. This leads to the formulation of a fuzzy dual optimization problem for which necessary optimality conditions, corresponding to an extension of Pontryagine's optimality principle, are established.

A Fuzzy Measure of Vulnerability for the Optimization of Vehicle Routing Problems With Time Windows

In a vehicle routing problem (VRP) with time windows, the start of service needs to take place within the customer time window. Due to uncertainty on travel times, vehicles might arrive late at a customer's site. A VRP is mostly solved to minimize a total cost criterion (travel time, travel distance, fixed and variable vehicle costs). But the dispatcher might also take into consideration the risk of non-conformance with the service agreement to start service within the time window. Therefore, a measure of risk, called “vulnerability of a solution,” is developed to serve as a second criterion. This chapter develops such a measure based on a distance metric and investigates its strengths and weaknesses.

Selected Topics in Robust Optimization

In this chapter, the authors give a brief introduction to important concepts of RO paradigm. The remainder of the chapter is organized as follows: Section 2 gives an introduction on optimization under uncertainty, and presents brief comparisons among the well-known sub-fields of optimization under uncertainty such as RO, stochastic programming (SP), and fuzzy optimization (FO). Section 3 presents important methodologies of RO paradigm. Section 4 gives insights about alternative ways of choosing the uncertainty set. Section 5 shows alternative methods of assessing the quality of a robust solution and presents miscellaneous topics. Finally, Section 6 summarizes conclusions and gives future research directions.

Advances in Fuzzy Dynamic Programming

This chapter considers the use of fuzzy dual numbers to model and solve through dynamic programming process mathematical programming problems where uncertainty is present in the parameters of the objective function or of the associated constraints. It is only supposed that the values of the uncertain parameters remain in known real intervals and can be modelled with fuzzy dual numbers. The interest of adopting the fuzzy dual formalism to implement the sequential decision-making process of dynamic programming is discussed and compared with early fuzzy dynamic programming. Here, the comparison between two alternatives is made considering not only the cumulative performance but also the cumulative risk associated with previous steps in the dynamic process, displaying the traceability of the solution under construction as it is effectively the case with the classical deterministic dynamic programming process. The proposed approach is illustrated in the case of a long-term airport investment planning problem.

A Study of Fully Fuzzy Linear Fractional Programming Problems by Signed Distance Ranking Technique

The aim of this chapter is to study fully fuzzy linear fractional programming (FFLFP) problems where all coefficients of the decision variables and parameters are characterized by triangular fuzzy numbers. To deal with this, the authors have first to transform FFLFP problems to fuzzy linear programming (FLP) problems by using Charnes and Cooper method and then use signed distance ranking to convert fuzzy linear programming (FLP) problems to crisp linear programming (LP) problems. The proposed method is solved by using the simplex method to find the optimal solution of the problem. The authors have studied sensitivity analysis to determine changes in the optimal solution of the fully fuzzy linear fractional programming (FFLFP) problems resulting from changes in the parameters. To demonstrate the proposed method, one numerical example is solved.

Experimental Investigation for Performance Optimization of Biodiesel-Fueled Diesel Engine Using Taguchi-Gray Relational Analysis

The objective of this analysis is to determine optimum parameters for maximum performance and minimum emission for biodiesel-fueled diesel engine. The experiments were designed using Taguchi L25 orthogonal array. Five parameters—fuel blend, load, speed, injection timing, and injection pressure—each with five levels were selected. Cylinder pressure, exhaust temperature, brake thermal efficiency, brake specific fuel consumption, carbon monoxide, unburned hydrocarbons, nitric oxide, and smoke were response parameters. Optimum combination of parameters was determined by grey relational analysis. The confirmatory test was performed at optimum combination. The grey relational grade and signal-to-noise ratio was determined. The contribution of individual parameter was determined by ANOVA analysis. Optimum performance was obtained at 80% load and 1900 rpm speed with B50 fuel at injection timing of 15.50 BTDC with 225 bar injection pressure. Finally, grey relational grade was improved by 3.7%.

Grey Optimization Problems Using Prey-Predator Algorithm

The optimization problems are the problem of finding the best parameter values which optimize the objective functions. The optimization methods are divided into two types: deterministic and non-deterministic methods. Metaheuristic algorithms fall in the non-deterministic solution methods. Prey-predator algorithm is one of the well-known metaheuristic algorithms developed for optimization problems. It has gained popularity within a short time and is used in different applications, and it is an easy algorithm to understand and also to implement. The grey systems theory was initialized as uncertain systems. Each grey system is described with grey numbers, grey equations, and grey matrices. A grey number has uncertain value, but there is an interval or a general set of numbers, within that the value lies is known. In this chapter, the author will review and show that grey system modeling is very useful to use with prey-predator algorithm. The benchmark functions, grey linear programming, and grey model GM (1,1) are used as examples of grey system.

A Survey on Grey Optimization

This chapter provides a literature review of optimization problems in the context of grey system theory, as proposed by various authors. The chapter explains the binary interactive algorithm approach as a problem-solving method for linear programming and quadratic programming problems with uncertainty and a genetic-algorithm-based approach as a second problem-solving scheme for linear programming, quadratic programming, and general nonlinear programming problems with uncertainty. In the chapter, details on the computation procedures involved for solving the aforementioned optimization problems with uncertainty are presented and results from these two approaches are compared and contrasted. Finally, possible future work area in the subject is suggested.