RENEWAL PROCESS WITH FUZZY INTERARRIVAL TIMES AND REWARDS

2003 ◽  
Vol 11 (05) ◽  
pp. 573-586 ◽  
Author(s):  
RUIQING ZHAO ◽  
BAODING LIU
Keyword(s):  
Renewal Process ◽  
Interarrival Time ◽  
Renewal Theorem ◽  
Expected Number ◽  
Fuzzy Variables ◽  
Numerical Example ◽  
Interarrival Times ◽  
Renewal Reward Theorem

This paper considers a renewal process in which the interarrival times and rewards are characterized as fuzzy variables. A fuzzy elementary renewal theorem shows that the expected number of renewals per unit time is just the expected reciprocal of the interarrival time. Furthermore, the expected reward per unit time is provided by a fuzzy renewal reward theorem. Finally, a numerical example is presented for illustrating the theorems introduced in the paper.

RENEWAL PROCESS FOR FUZZY VARIABLES

2007 ◽  
Vol 15 (04) ◽  
pp. 493-501 ◽  
Author(s):  
DUG HUN HONG
Keyword(s):  
Renewal Process ◽  
Renewal Theorem ◽  
Arrival Times ◽  
Fuzzy Variables ◽  
Continuity Assumption

Recently, Zhao and Liu [IJUFKS 11 (2003) 573–586] proposed a "fuzzy elementary renewal theorem" and "fuzzy renewal rewards theorem" for a renewal process in which the inter-arrival times and rewards are characterized as continuous fuzzy variables. The continuity assumption is restrictive. In this note, we prove the same results without the assumption of continuity of the inter-arrival times and rewards.

Monte Carlo simulation of the renewal function

1981 ◽  
Vol 18 (2) ◽  
pp. 426-434 ◽  
Author(s):  
Mark Brown ◽  
Herbert Solomon ◽  
Michael A. Stephens
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Renewal Process ◽  
Time Distribution ◽  
Interarrival Time ◽  
Renewal Function ◽  
Expected Number ◽  
Unbiased Estimators ◽  
Monte Carlo Estimation ◽  
Naive Estimator

The problem of Monte Carlo estimation of M(t) = EN(t), the expected number of renewals in [0, t] for a renewal process with known interarrival time distribution F, is considered. Several unbiased estimators which compete favorably with the naive estimator, N(t), are presented and studied. An approach to reduce the variance of the Monte Carlo estimator is developed and illustrated.

Monte Carlo simulation of the renewal function

1981 ◽  
Vol 18 (02) ◽  
pp. 426-434 ◽  
Author(s):  
Mark Brown ◽  
Herbert Solomon ◽  
Michael A. Stephens
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Renewal Process ◽  
Time Distribution ◽  
Interarrival Time ◽  
Renewal Function ◽  
Expected Number ◽  
Unbiased Estimators ◽  
Monte Carlo Estimation ◽  
Naive Estimator

The problem of Monte Carlo estimation of M(t) = EN(t), the expected number of renewals in [0, t] for a renewal process with known interarrival time distribution F, is considered. Several unbiased estimators which compete favorably with the naive estimator, N(t), are presented and studied. An approach to reduce the variance of the Monte Carlo estimator is developed and illustrated.

Possibility-Based ELECTRE II Method with Uncertain Linguistic Fuzzy Variables

2017 ◽  
Vol 31 (09) ◽  
pp. 1759016 ◽  
Author(s):  
Lidong Wang ◽  
Binquan Liao ◽  
Xiaodong Liu ◽  
Jingxia Liu
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Economic Systems ◽  
Linguistic Variables ◽  
Concordance Index ◽  
Fuzzy Variables ◽  
Numerical Example ◽  
Deviation Index ◽  
Multiple Attribute

Linguistic variables can better approximate the fuzziness of man’s thinking, which are important tools for multiple attribute decision-making problems. This paper establishes the possibility-based ELECTRE II model under the environment of uncertain linguistic fuzzy variables and uncertain weight information. By introducing the degree of possibility to ELECTRE II model, the concordance set, the discordance set and the indifferent set are obtained, respectively. Furthermore, the concordance index is redefined by considering deviation index under the same attribute, by which the strong and weak relationships are constructed, and then the rank of alternatives is obtained. A numerical example about the evaluation of socio-economic systems is employed to illustrate the convenience and applicability of the proposed method.

Optimal stopping in a continuous search model

1986 ◽  
Vol 23 (02) ◽  
pp. 514-518 ◽  
Author(s):  
Dror Zuckerman
Keyword(s):  
Optimal Stopping ◽  
Renewal Process ◽  
Control Level ◽  
Market Price ◽  
Stopping Time ◽  
Control Limit ◽  
Interarrival Time ◽  
Search Model ◽  
Job Offers ◽  
Constant Cost

We examine a continuous search model in which rewards (e.g. job offers in a search model in the labor market, price offers for a given asset, etc.) are received randomly according to a renewal process determined by a known distribution function. The rewards are non-negative independent and have a common distribution with finite mean. Over the search period there is a constant cost per unit time. The searcher's objective is to choose a stopping time at which he receives the highest available reward (offer), so as to maximize the net expected discounted return. If the interarrival time distribution in the renewal process is new better than used (NBU), it is shown that the optimal stopping strategy possesses the control limit property. The term ‘control limit policy' refers to a strategy in which we accept the first reward (offer) which exceeds a critical control level ξ.

A note on filtered Markov renewal processes

1981 ◽  
Vol 18 (03) ◽  
pp. 752-756
Author(s):  
Per Kragh Andersen
Keyword(s):  
Renewal Process ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
Markov Renewal Processes ◽  
The Moment

A Markov renewal theorem necessary for the derivation of the moment formulas for a filtered Markov renewal process stated by Marcus (1974) is proved and its applications are outlined.

Optimal strategies in a risk selection investment model

2000 ◽  
Vol 32 (02) ◽  
pp. 518-539
Author(s):  
David Assaf ◽  
Yuliy Baryshnikov ◽  
Wolfgang Stadje
Keyword(s):  
Optimal Strategies ◽  
Concave Function ◽  
Investment Model ◽  
Interarrival Time ◽  
Objective Functions ◽  
Constant Rate ◽  
Optimal Value ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Interarrival Times

We study the following stochastic investment model: opportunities occur randomly over time, following a renewal process with mean interarrival time d, and at each of them the decision-maker can choose a distribution for an instantaneous net gain (or loss) from the set of all probability measures that have some prespecified expected value e and for which his maximum possible loss does not exceed his current capital. Between the investments he spends money at some constant rate. The objective is to avoid bankruptcy as long as possible. For the case e>d we characterize a strategy maximizing the probability that ruin never occurs. It is proved that the optimal value function is a concave function of the initial capital and uniquely determined as the solution of a fixed point equation for some intricate operator. In general, two-point distributions suffice; furthermore, we show that the cautious strategy of always taking the deterministic amount e is optimal if the interarrival times are hyperexponential, and, in the case of bounded interarrival times, is optimal ‘from some point on’, i.e. whenever the current capital exceeds a certain threshold. In the case e = 0 we consider a class of natural objective functions for which the optimal strategies are non-stationary and can be explicitly determined.

scholarly journals Delayed Renewal Process with Uncertain Random Inter-Arrival Times

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1943
Author(s):  
Xiaoli Wang ◽  
Gang Shi ◽  
Yuhong Sheng
Keyword(s):  
Random Process ◽  
Renewal Process ◽  
Random Variable ◽  
Random Delay ◽  
Renewal Theorem ◽  
Arrival Times ◽  
Chance Distribution ◽  
Renewal Rate ◽  
First Arrival

An uncertain random variable is a tool used to research indeterminacy quantities involving randomness and uncertainty. The concepts of an ’uncertain random process’ and an ’uncertain random renewal process’ have been proposed in order to model the evolution of an uncertain random phenomena. This paper designs a new uncertain random process, called the uncertain random delayed renewal process. It is a special type of uncertain random renewal process, in which the first arrival interval is different from the subsequent arrival interval. We discuss the chance distribution of the uncertain random delayed renewal process. Furthermore, an uncertain random delay renewal theorem is derived, and the chance distribution limit of long-term expected renewal rate of the uncertain random delay renewal system is proved. Then its average uncertain random delay renewal rate is obtained, and it is proved that it is convergent in the chance distribution. Finally, we provide several examples to illustrate the consistency with the existing conclusions.

On excess life in certain renewal processes

1981 ◽  
Vol 18 (02) ◽  
pp. 378-389 ◽  
Author(s):  
Barry C. Arnold ◽  
Richard A. Groeneveld
Keyword(s):  
Markov Chain ◽  
Linear Combination ◽  
Renewal Process ◽  
Interarrival Time ◽  
Renewal Processes ◽  
Life Distributions ◽  
Discrete Markov Chain ◽  
Absorption Probabilities

Excess life distributions for discrete renewal processes may be computed by using elementary discrete Markov chain concepts involving absorption probabilities. Excess life distributions in general may then be obtained by approximating the renewal process under study by a suitably chosen sequence of discrete renewal processes. The technique is illustrated in the cases of renewal processes with interarrival distributions which are a linear combination of two exponentials and uniform [0, 1]. A related algorithm is described for computer generated approximations of excess life distributions corresponding to continuous interarrival time distributions with an increasing c.d.f. Conditions for convergence of this algorithm are examined.

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