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Reliability analysis as one of the important research topics in engineering has been researched by a number of authors. Reliability in classical distributions is based on precise parameters. It is usually assumed that parameters of distributions are precise real numbers. However, in the real world, the data sometimes cannot be measured and recorded precisely. In this paper, the concept of fuzzy reliability is extended by the idea of generalized intuitionistic fuzzy reliability. We investigate the reliability characteristics of systems using Rayleigh lifetime distribution, in which the lifetime parameter is assumed to be generalized intuitionistic fuzzy number. Generalized intuitionistic fuzzy reliability, generalized intuitionistic fuzzy hazard function, generalized intuitionistic fuzzy mean time to failure and their cut sets are discussed when the systems follow generalized intuitionistic fuzzy Rayleigh lifetime distribution. In this approach, for every special cut set, reliability curve and hazard curve are like a band with upper and lower bound. A numerical example is given to illustrate the proposed approach. Further, reliability analysis of the series and parallel systems are done. [ABSTRACT FROM AUTHOR]

Network flows over time (also called Dynamic Network Flows) are considered as generalized form of standard (static) networks by adding an element of time. The factor of transit time on the arcs which specify the amount of time it takes for one unit of the flows to pass through a particular arc, make these networks different to traditional form of networks. While in most of network flow problems, transit times and capacities are given constant, stochastic or Fuzzy numbers, in this paper we suppose that transit times, capacities and consequently flows on arcs fall within specific ranges expressed as compact intervals. This vagueness in transit times, capacities and flows could arise in a number of ways: 1) when determining the exact capacity or transit time quantities is hard and there may happen errors in determining them which intervals reflect the measurement errors; 2) when it is impossible or even it is not needed to produce neither a distribution nor fuzzy functions but transit times, capacities and flows lie within specific ranges, or vary in time within these ranges. While determining the exact time for traveling in specific path in network transportation system is extremely difficult or almost impossible, determination of interval which can describe the range of required time for travelling in the network would be easy and fully operational. Our contribution in this paper is producing maximum flow and quickest s - t flow algorithms, first to network flows over time with interval-valued capacities and then to T-length bounded network flows over time with interval-valued transit times and capacities. [ABSTRACT FROM AUTHOR]

This paper focuses on the methods for the efficient solution of multi-objective non-linear optimization problems with uncertain parameters represented as intuitionistic fuzzy numbers. In most of the existing techniques for such problems, generally linear membership (satisfaction) functions have been used. But every real life problem cannot be justified and modeled using the linear functions, so the efficient solution methodologies from the literature such as Zimmermann's technique, Maximum additive operator technique, γ -operator technique have been extended in this paper by defining the non-linear membership functions in place of the linear ones. Unlike the classical versions of these techniques, the non-linear non-membership (dissatisfaction) functions have also been incorporated along with the memberships. Intuitionistic fuzzy number with non-linear grade functions has been introduced. Appropriate theorems have been proved to support the claims. Two numerical examples in the intuitionistic fuzzy environment from the field of manufacturing and transportation have been considered for the illustration of the proposed technique. The obtained results show the applicability and reliability of the suggested extensions and their comparison with the results obtained from that of the non-modified (traditional) techniques reflects its effectiveness. • Investigating the IF non-linear problems with conflicting objectives. • Extending three known techniques for the IF multi-objective optimization problems. • Showing the role of non-membership to resolve the conflicting nature of objectives. • Exploring wide scope of considering nonlinear satisfaction/dissatisfaction function. [ABSTRACT FROM AUTHOR]

Data Envelopment Analysis (DEA) and Multiple Objective Linear Programming (MOLP) are widely used for performance assessment in organizations. Although DEA and MOLP are similar in structure, DEA is used to assess and analyze past performance and MOLP is used to predict future performance. Several equivalence models between output-oriented DEA models and MOLP models have been proposed in the literature. However these models are not applicable to performance evaluation problems with undesirable outputs. We propose an interactive method for solving output-oriented DEA models with undesirable outputs. We show that the output-oriented BCC model of Seiford and Zhu [47] can be equivalently stated as the maximization of the minimum of several objectives over the production possibility set, which in turn is a scalarization of a multi-objective linear program. We then employ the well-known Zionts-Wallenius procedure to solve the multi-objective optimization problem. We present an example to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms. [ABSTRACT FROM AUTHOR]

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations. [ABSTRACT FROM AUTHOR]