Fuzzy Time Research Articles

The Fuzzy Optimization Algorithm to Solve Customer’s Highest Satisfaction Under Fuzzy Time

The fuzzy completion time and customer request are two main uncertain factors in the process of the actual workshop production. The scheduling model under uncertain situation based on fuzzy mathematics is established in this paper. The average customer satisfaction acts as the objective of the model. Next, a novel hybrid algorithm is obtained through improving the mutation operation of genetic algorithm on the basis of simulated annealing algorithm. The customers can determine the priority through the process time of the process route to evaluate the effectiveness of the process route. The effectiveness and superiority of the proposed algorithm are verified through the contrast experiment with the existing algorithms.

Production flows scheduling subject to fuzzy processing time constraints

Effective sequencing and scheduling of material handling systems (MHSs) have a major impact on the productivity of a manufacturing system. Since the main function of a MHS is to supply the right materials at the right locations at the right time, the design of automated guided vehicles (AGVs) fleet-oriented, distributed and scalability-robust control policies ensuring deadlock-free operations is of crucial importance. In this context, a given design of a flexible manufacturing system (FMS) where vehicles serve workstations located along different modes of cyclic guided paths in a 3D environment composed of rails/lifts/hoists is considered. Furthermore, fuzzy processing time constraints on transportation operations, a production flows scheduling problem subject to an assumed set of constraints imposed by admissible production routes and schedules of AGV fleet in a given MHS are considered. Since this type of problem can be treated as a fuzzy constraint satisfaction problem, the main objective is to provide analytical formulas enabling the avoidance of time-consuming computer-simulation-based calculations of AGV fleet schedules, as well as vehicles deadlock and collisions, while keeping the throughput at the maximum achievable level. Results of computational experiments assessing the scalability of the proposed method are presented as well.

Adaptive Fuzzy Sliding Mode Control of MEMS Gyroscope with Finite Time Convergence

This paper presents adaptive fuzzy finite time sliding mode control of microelectromechanical system gyroscope with uncertainty and external disturbance. Firstly, fuzzy system is employed to approximate the uncertainty nonlinear dynamics. Secondly, nonlinear sliding mode hypersurface and double exponential reaching law are selected to design the finite time convergent sliding mode controller. Thirdly, based on Lyapunov methods, adaptive laws are presented to adjust the fuzzy weights and the system can be guaranteed to be stable. Finally, the effectiveness of the proposed method is verified with simulation.

RENEWAL AND RENEWAL REWARD THEORIES FOR T-INDEPENDENT FUZZY RANDOM VARIABLES

Recently, Wang et al. [Computers and Mathematics with Ap-plications 57 (2009) 1232-1248.] and Wang and Watada [Information Sci-ences 179 (2009) 4057-4069.] studied the renewal process and renewal reward process with fuzzy random inter-arrival times and rewards under the T-independence associated with any continuous Archimedean t-norm. But, their main results do not cover the classical theory of the random elementary renewal theorem and random renewal reward theorem when fuzzy random variables degenerate to random variables, and some given assumptions relate to the membership function of the fuzzy variable and the Archimedean t-norm of the results are restrictive. This paper improves the results of Wang and Watada and Wang et al. from a mathematical per-spective. We release some assumptions of the results of Wang and Watada and Wang et al. and completely generalize the classical stochastic renewal theorem and renewal rewards theorem.

Optimum Solar Panel Implementation Using DC-DC Boost Converter Controlled by Fuzzy Logic Controller

This paper proposes the implementation of a simple fuzzy logic controller (FLC) for a DC-DC boost converter based on a microcontroller to obtain maximum power from the solar system with the maximum power point tracking (MPPT) method. The system includes a solar panel, DC-DC boost converter, the fuzzy logic controller implemented on Arduino Uno for controlling on/off time of MOSFET of the boost converter, voltage divider and optocoupler circuit. This paper presents a fuzzy logic real time code in the Arduino language for ATmega328 microcontroller on the Arduino UNO board. The designed system increases the efficiency of the solar panel based on experimental results.

Multi-objective Integration of Flexible Collaborative Planning and Fuzzy Flexible Lot-Splitting Scheduling Based on the Pareto Optimal

Since that a job usually contains several working procedures in actual production, and it’s hard to optimize the flexible collaborative planning, the flexible lot splitting and scheduling of the job simultaneously in batch production mode, a model for multiobjective integration of flexible collaborative planning and fuzzy lot-splitting scheduling is established. We take four performance indicators below which are the most common as standards to optimize the model: average delivery satisfaction, fuzzy total cost, fuzzy completion time and average credibility of job tardiness, and then a multi-objective algorithm based on the Pareto optimal is established. In this algorithm, we design the integrated coding scheme, which include collaboration chromosome, lot-splitting chromosome and scheduling chromosome, meanwhile the Pareto optimal scheme is designed. Finally, the efficiency of the model and algorithm is proved by the simulation.

An economic production quantity problem with backorders and fuzzy cycle times

Optimization models combining Economic Production Quantity models and fuzzy set theory are important to the process industry as they are capable of modeling the numerous uncertainties inherent in t...

Hybrid Genetic Algorithm Based on Chaotic Migration Strategy for Solving Flow Shop Scheduling Problem with Fuzzy Delivery Time

In this paper, a hybrid genetic algorithm based on a chaotic migration strategy (HGABCM) for solving the flow shop scheduling problem with fuzzy delivery times is proposed. First, the initial population is divided into several sub-populations, and each sub-population is isolated and evolved. Next, these offspring are further optimized by a strategy that combines NEH heuristic algorithm proposed by M. Navaz, J.-E. Enscore, I. Ham in 1983 with a newly designed algorithm that has excellent local search capability, thereby enhancing the strategy’s local search capability. Then, the concept of a chaotic migration sequence is introduced to guide the ergodic process of the migration of individuals effectively so that information is exchanged sufficiently among sub-populations and the process of falling into a local optimal solution is thereby avoided. Finally, several digital simulations are provided to demonstrate the effectiveness of the algorithm proposed in this paper.

A priori least expected time paths in fuzzy, time-variant transportation networks

Dynamics and fuzziness are two significant characteristics of real-world transportation networks. To capture these two features theoretically, this article proposes the concept of a fuzzy, time-variant network characterized by a series of time-dependent fuzzy link travel times. To find an effective route guidance for travelers, the expected travel time is specifically adopted as an evaluation criterion to assess the route generation process. Then the shortest path problem is formulated as a multi-objective 0–1 optimization model for finding the least expected time path over the considered time horizon. Different from the shortest path problem in dynamic and random networks, an efficient method is proposed in this article to calculate the fuzzy expected travel time for each given path. A tabu search algorithm is designed for the problem to generate the best solution under the framework of linear weighted methods. Finally, two numerical experiments are performed to verify the effectiveness and efficiency of the model and algorithm.

Dissipative Analysis and Synthesis of Control for TS Fuzzy Markovian Jump Neutral Systems

This paper is focused on stochastic stability and strictly dissipative control design for a class of Takagi-Sugeno (TS) fuzzy neutral time delayed control systems with Markovian jumps. The main aim of this paper is to design a strictly dissipative controller such that the closed-loop TS fuzzy control system is stochastically stable, and also the disturbance rejection attenuation is obtained to a given level by means of theH∞performance index. Intensive analysis is carried out to obtain sufficient conditions for the existence of desired dissipative controller which ensures both the stochastic stability and the strictly dissipative performance. The main advantage of the proposed technique is that it is possible to obtain the dissipative controller with less control effort and also, as special cases, robustH∞control with the prescribedH∞performance under given constraints and passivity control can be obtained for the considered systems. Also, the existence condition of the fuzzy dissipative controller can be obtained in terms of linear matrix inequalities. Finally, a practical example based on truck-trailer model is provided to demonstrate the effectiveness and feasibility of the proposed design technique.

Optimal production run length for an imperfect production process with allowable shortages in fuzzy random environments

In this article, we develop a model to determine the economic production run length for a deteriorating production system and allowable shortages in fuzzy random environments. Based on the credibility measure of fuzzy event, the economic production quantity model with fuzzy random elapsed time can be transformed into a crisp model when deriving the expected total cost per unit time. The optimal production run length is proved to exist and be unique. Bounds for the optimal production run length are provided. Furthermore, the bisection method searching for the optimal production run length is designed. The relevant applications of the model are outlined. Finally, a numerical example is given to confirm the proposed model.

An economic production quantity problem with backorders and fuzzy cycle times

Optimization models combining Economic Production Quantity models and fuzzy set theory are important to the process industry as they are capable of modeling the numerous uncertainties inherent in this context. In this paper, we incorporate backorders i.e the inventory to go below zero in a fuzzy Economic Production Quantity EPQ model. The uncertainties in the backorders for different products are modeled using triangular possibility distributions. We present an example describing a typical decision making problem in the paper industry to illustrate our model.

Using Metric Distance Ranking Method to Find Intuitionistic Fuzzy Critical Path

Network analysis is a technique which determines the various sequences of activities concerning a project and the project completion time. The popular methods of this technique which is widely used are the critical path method and program evaluation and review techniques. The aim of this paper is to present an analytical method for measuring the criticality in an (Atanassov) intuitionistic fuzzy project network. Vague parameters in the project network are represented by (Atanassov) intuitionistic trapezoidal fuzzy numbers. A metric distance ranking method for (Atanassov) intuitionistic fuzzy numbers to a critical path method is proposed. (Atanassov) Intuitionistic fuzzy critical length of the project network is found without converting the (Atanassov) intuitionistic fuzzy activity times to classical numbers. The fuzzified conversion of the problem has been discussed with the numerical example. We also apply four different ranking procedures and we compare it with metric distance ranking method. Comparison reveals that the proposed ranking method is better than other raking procedures.

Continuous review inventory model with reducing lost sales rate under fuzzy stochastic demand and variable lead time

The present study considers a continuous review inventory system for the inventory model involving fuzzy random demand, variable lead-time with lost-sales (backorder) caused by stock-out. Two forms of capital investment cost function viz. logarithmic and power are employed to reduce the lost-sales rate. We first formulate the basic model mathematically by assuming expected demand as triangle fuzzy number along with the capital investment to reduce lost-sales rate. As a result, the demand during lead-time is fuzzy random variable which is the linear sum of the weekly demand during the lead-time period. Consequently, the total weekly cost of this model is also fuzzy random in nature. Hence the expected total weekly cost is fuzzy valued function. To defuzzify the expected total weekly cost, we use the signed distance method. A computer program using the software MATLAB is developed to obtain the optimal solution and provide numerical examples to illustrate the models. Moreover, sensitivity analysis is carried out with respect to the key parameters.

Fuzzy Time in Linear Temporal Logic

In the past years, the adoption of adaptive systems has increased in many fields of computer science, such as databases and software engineering. These systems are able to automatically react to events by collecting information from the external environment and generating new events. However, the collection of data is often hampered by uncertainty and vagueness. The decision-making mechanism used to produce a reaction is also imprecise and cannot be evaluated in a crisp way, as it depends on vague temporal constraints expressed by humans. Logic has been extensively used as an abstraction to express vagueness in the satisfaction of system properties, as well as to enrich existing modeling formalisms. However, existing attempts to fuzzify the temporal modalities still have some limitations. Existing fuzzy temporal languages are generally obtained from classical temporal logic by replacing classical connectives or propositions with their fuzzy counterparts. Hence, these languages do not allow us to represent temporal properties, such as “almost always” and “soon,” in which the notion of time is inherently fuzzy. To overcome these limitations, we propose a temporal framework, fuzzy-time temporal logic (FTL), to express vagueness on time. This framework formally defines a set of fuzzy temporal modalities that can be customized by choosing a specific semantics for the connectives. The semantics of the language is sound, and the introduced modalities respect a set of mutual relations. We also prove that under the assumption that all events are crisp, FTL reduces to linear temporal logic (LTL). Moreover, for some of the possible fuzzy interpretations of the connectives, we identify adequate sets of temporal operators, from which it is possible to derive all of the other ones.

Probabilistic distributions of ordinal statistics in the analysis of super-short fuzzy and incomplete time series

The paper presents results of a stage of research devoted to approaches to an estimation of rate of risky behavior. The paper contains the description of ways of formation of the specified estimation of the rate on the basis of the maximum and minimum interval, and also an median interval between the behavior episodes. A solution of the problem is based on formation and the analysis of formulas for distribution (and joint distribution) functions corresponding to ordinal statistics, distribution density, and also on a choice of values of their parameters. Several approaches to the analysis of quality of the received estimations are offered.

Fuzzy multi objective transportation model based on new ranking index on generalized LR fuzzy numbers

In this paper, we present a new method for analyzing a fuzzy multi objective transportation problem using a linear programming model based on a new method for ranking generalized LR fuzzy numbers. First, we present a new method for ranking generalized LR fuzzy numbers from its λ-cut.To the best of our knowledge till now there is no method in the literature to find the ranking order of the generalized LR fuzzy numbers to various linear and non-linear functions of LR fuzzy numbers from its  -cut based on area, mode and spread. Our method can efficiently rank various LR fuzzy numbers, their images and crisp numbers which are consider to be a special case of fuzzy numbers (normal/nonnormal, triangular/trapezoidal, and general), which could not be ranked by the existing ranking methods. Our ranking method also satisfies the linearity property condition. For the corroboration, we used some comparative examples of different existing methods to illustrate the advantages of the proposed method.The reference functions of LR fuzzy numbers of fuzzy multi objective transportation problem are considered to be linear and non-linear functions. This paper develops a procedure to derive the fuzzy objective value of the fuzzy multi objective transportation problem, in that the fuzzy cost coefficients and the fuzzy time are LR fuzzy numbers. The method is illustrated with an example by various cases.

Method of recognising facial image using fuzzy measure

The proposed work is a mathematical and morphological erosion calculation method through defuzzification. It defines a λ-fuzzy set measure in all subsets of defuzzification, which measures degrees of inclusion on the fuzzy set measure of each subset, replaces as a result of the fuzzy integral by performing defuzzification of images within the mask of such measures, and defines a fuzzy morphological calculation operator by an erosion on the basis of the fuzzy set measure. The experimental results show 92% of the heterogeneous template matching and 98% of the matching based on the fuzzy set measure. The heterogeneous matching and the average fuzzy matching time took 27.4 and 12.3 s, respectively. The proposed method achieved not only reduction in detecting time by skipping the templates but also the more strong detections on the facial colour and the face in the similar background when compared with the heterogeneous template-matching method.

Development of a fuzzy-queue-based stochastic quadratic program for water resources planning

In this study, a fuzzy-queue (FQ)-based inexact stochastic quadratic programming (SQP) method is developed through coupling FQ technique with inexact SQP. FQ-SQP improves upon the existing stochastic programming methods by considering the effects of queuing phenomenon during the water resources allocation process. FQ-SQP cannot only handle uncertainties expressed as interval values, random variables, and fuzzy sets, but also tackle nonlinearity in the objective function; more importantly, it can reflect the effects of FQ on water resources allocation and system benefit. The FQ-SQP model is applied to a case study of planning water resources management, where FM/FM/1 (fuzzy exponential interarrival time, fuzzy exponential service time, and one server) queue is incorporated within the SQP modeling framework. Based on α-cut analysis technique, interval solutions with fuzzy arrival and service rates have been generated, which result in different water resources allocation patterns as well as changed waiting water amounts and system benefits. Results indicate that consideration of queuing problem impacts on water resources allocation can provide more useful information for decision makers and gain in-depth insights into the effects of queuing problems for water resources allocation.

Fuzzy Logic-Based Round Trip Time Scaling and Scheduling in High Speed TCP Stacks

Network management and control is a complex problem that requires intelligent, control methodologies to obtain satisfactory performance. Round trip time (RTT) scaling mechanism has been introduced for changing congestion window and to perform congestion control satisfactorily in all circumstances. This paper presents a fuzzy RTT scaling (FRTTS) scheme that performs RTT scaling and RTT scheduling for different high speed transmission control protocol (TCP) networks. In this scheme, RTT samples are allocated requesting application by using RTT scheduling factor and RTT samples are scaled for an application by using RTT scaling factor. A RTT scaler placed at the end node performs the RTT scheduling as well as RTT scaling. We also apply a FRTTS scheme on different high speed TCP’s namely high-TCP (H-TCP) and scalable-TCP(S-TCP) and demonstrates that it provides better performance than non fuzzy scheme. The scheme has been extensively simulated to test the performance in terms of flow rate, RTT flows, packet size and congestion window size. The results show that FRTTS scheme provides better performance than non fuzzy scheme which employs dynamic RTT scheduling and RTT scaling.