Theory of fuzzy integrals and its applications

Real-life decisions are usually made in the state of uncertainty such as randomness and fuzziness. How do we model optimization problems in uncertain environments? How do we solve these models? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas, hybrid intelligent algorithms, and applications in system reliability design, project scheduling problem, vehicle routing problem, facility location problem, and machine scheduling problem. Researchers, practitioners and students in operations research, management science, information science, system science, and engineering will find this work a stimulating and useful reference.

Theory and practice of uncertain programming

This survey provides a structured and comprehensive overview of research on security and privacy in computer and communication networks that use game-theoretic approaches. We present a selected set of works to highlight the application of game theory in addressing different forms of security and privacy problems in computer networks and mobile applications. We organize the presented works in six main categories: security of the physical and MAC layers, security of self-organizing networks, intrusion detection systems, anonymity and privacy, economics of network security, and cryptography. In each category, we identify security problems, players, and game models. We summarize the main results of selected works, such as equilibrium analysis and security mechanism designs. In addition, we provide a discussion on the advantages, drawbacks, and future direction of using game theory in this field. In this survey, our goal is to instill in the reader an enhanced understanding of different research approaches in applying game-theoretic methods to network security. This survey can also help researchers from various fields develop game-theoretic solutions to current and emerging security problems in computer networking.

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Game theory meets network security and privacy

This chapter is an overview of past and present works dealing with fuzzy intervals and their operations. A fuzzy interval is a fuzzy set in the real line whose level-cuts are intervals. Particular cases include usual real numbers and intervals. Usual operations on the real line canonically extend to operations between fuzzy quantities, thus extending the usual interval (or error) analysis to membership functions. What is obtained is a counterpart of random variable calculus, but where, contrary to the latter case, there is no compensation between variables. Many results pertaining to basic properties of fuzzy interval analysis are summed up in the chapter. Computational methods are presented, exact or approximate ones, based on parametric representations, or level-cut approximations. The generalized fuzzy variable calculus involving interactive variables is also discussed with emphasis on triangular-norm based fuzzy additions. Dual ‘optimistic’ operations on fuzzy intervals, i.e., with maximal error compensation are also presented; its interest lies in providing tools for solving fuzzy interval equations. This chapter also contains a reasoned survey of methods for comparing and ranking fuzzy intervals. The chapter includes some historical background, as well as pointers to applications in mathematics and engineering.

Fuzzy Interval Analysis

A new method for solving fully fuzzy linear programming problems

Linear programming problems and ranking of fuzzy numbers

Fuzzy linear programming models to solve fuzzy matrix games

On the use of the ranking function approach to solve fuzzy matrix games in a direct way

A new method to solve zero‐sum two‐person games with imprecise values in their matrices of pay‐offs is suggested. The natural lack of precision generated by the use of fuzzy numbers in a fuzzy game requires the use of subjective criteria by the players in the resolution model. We apply a ranking function, the Average Value, which allows the decision makers to take into account their subjectivity. The use of this function raises again the solution of the fuzzy game when two criteria, one for each player, are used.

Lourdes Campos

Papers

Linear programming problems and ranking of fuzzy numbers

Fuzzy linear programming models to solve fuzzy matrix games

On the use of the ranking function approach to solve fuzzy matrix games in a direct way

Fuzzy matrix games considering the criteria of the players

Further contributions to the study of the average value for ranking fuzzy numbers