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Showing 8 results for Fuzzy Numbers

A. Doostparast Torshizi, S.r. Hejazi,
Volume 21, Issue 2 (5-2010)

In highly competitive industrial market, the concept of failure analysis is an unavoidable fact in complex industrial systems. Reliability of such systems not only depends on the reliability of each element of these systems, but also depends on occurrence of sequence of failures. In this paper, a novel approach to sequential failure analysis is proposed which is based upon fuzzy logic and the concept of Petri nets which is utilized to track all the risky behaviors of the system and to determine the potential failure sequences and then prioritizing them in order to perform corrective actions. The process of prioritizing failure sequences in this paper is done by a novel similarity measure between generalized fuzzy numbers. The proposed methodology is demonstrated with an example of two automated machine tools and two input/output buffer stocks.
Mir. B. Aryanezhad, M.j. Tarokh, M.n. Mokhtarian, F. Zaheri,
Volume 22, Issue 1 (3-2011)

  Multiple criteria decision making (MCDM) problem is one of the famous different kinds of decision making problems. In more cases in real situations, determining the exact values for MCDM problems is difficult or impossible. So, the values of alternatives with respect to the criteria or / and the values of criteria weights, are considered as fuzzy values (fuzzy numbers). In such conditions, the conventional crisp approaches for solving MCDM problems tend to be less effective for dealing with the imprecise or vagueness nature of the linguistic assessments. In this situation, the fuzzy MCDM methods are applied for solving MCDM problems. In this paper, we propose a fuzzy TOPSIS (for Order Preference by Similarity to Ideal Solution) method based on left and right scores for fuzzy MCDM problems. To show the applicability of the proposed method, two numerical examples are presented. As a result, our proposed method is precise, easy use and practical for solving MCDM problem with fuzzy data. Moreover, the proposed method considers the decision makers (DMs) preference in the decision making process. It seems that the proposed fuzzy TOPSIS method is flexible and easy to use and has a low computational volume .

Reza Morovatdar , Abdolah Aghaie , Simak Haji Yakhchali ,
Volume 22, Issue 1 (3-2011)

  In order to have better insight of project characteristics, different kinds of fuzzy analysis for project networks have been recently proposed, most of which consider activities duration as the main and only source of imprecision and vagueness, but as it is usually experienced in real projects, the structure of the network is also subject to changes. In this paper we consider three types of imprecision namely activity duration, activity existence and precedence relation existence which make our general fuzzy project network. Subsequently, a corrected forward recursion is proposed for analysis of this network. Since the convexity and normalization of traditional fuzzy numbers are not satisfied, some corrected algebraic operations are also presented. Employing the proposed method for a real project reveals that our method results in more applicable and realistic times for activities and project makespan in comparison to

Classic fuzzy PERT.
B. Moradi, H. Shakeri, S. Namdarzangeneh,
Volume 23, Issue 1 (3-2012)

Until now single values of IRR are traditionally used to estimate the time value of cash flows. Since uncertainty exists in estimating cost data, the resulting decision may not be reliable. The most commonly cited drawbacks to using the internal rate of return in evaluatton of deterministic cash flow streams is the possibility of multiple conflicting internal rates of return. In this paper we present a fuzzy methodology for solving problems of multiple IRR in any type of streams. Utilization of fuzzy cash flow allows modeling of uncertainty in estimating cost data. The approach of

-cut is to decrease the range of the final fuzzy set by increasing the degree of membership. For each fuzzy IRR in an optimum -cut, and an obtained present value of each stream, it is possible to decide on acceptance or rejection of a project according to the type of each stream (borrowing or investing). The upper bound of -cut is the worst case for borrowing and the lower bound of -cut is the worst case for investing. It is shown that both the internal rate of return and the present value are important in decision making and by analyzing the sensitivity of these values relative to the -cut variation, one can see the behavior of the project and choose a narrower fuzzy range.

M. Ameli, A. Mirzazadeh, M. Shirazi,
Volume 24, Issue 1 (2-2013)

It was suggested in 2004 by some researchers that it might be possible to improve production systems performance by applying the first and second laws of thermodynamics to reduce system entropy. Then these laws were used to modify the economic order quantity (EOQ) model to derive an equivalent entropic order quantity (EnOQ). Moreover the political instability or uncertainty of a country (as well as the whole world) leads to a much more unstable situation in the present world economy. Thus, changes in inflation take place, and it is needed to consider uncertain inflation rate. In this paper we extend the EnoQ model by considering deteriorating items with imperfect quality and price dependent demand. We also assume fuzzy inflation and discount rates.‌ A mathematical model is developed to determine the number of cycles that maximizes the present value of total revenue in a finite planning horizon. The fuzzified model for inflation and discount rate is formulated and solved by two methods: signed distance and fuzzy numbers ranking. Numerical examples are presented and results are discussed. Results show that the number of cycles decreases in fuzzy inflationary conditions. They also illustrate that defuzzification method results in more cycles than fuzzy method.
Navid Khademi, Afshin Shariat Mohaymany, Jalil Shahi, Mojtaba Rajabi,
Volume 24, Issue 3 (9-2013)

Most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. For making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. In line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or degree of membership. In this paper we propose a method for capturing the membership degree of fuzzy inequalities through discretizing the μ-axis into equidistant intervals. It calculates m in the fuzzy inequalities ≤ m and ≥m among two normal fuzzy numbers. In this method, the two μ-axis based discretized fuzzy numbers are compared point by point and at each point the degree of preferences is identified. To show its validity, this method is examined against the essential properties of fuzzy number ordering methods in [Wang, X. and E.E. Kerre, Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems, 2001. 118(3): p. 375-385.] The result provides promising outcomes that may be useful in the domain fuzzy multi criteria or multi-attribute decision making analysis and also fuzzy mathematical programming with fuzzy inequality constraints.
Eng Fateme Zare Baghabad, Dr Hassan Khademi Zare,
Volume 26, Issue 3 (9-2015)

In this paper an efficient three- stage algorithm is developed for software production cost and time estimation. First stage includes a hybrid model composed of COCOMO and Function Points methods to increase estimation accuracy. Second stage encompasses paired comparisons matrix of analytical hierarchy process to determine amount of any resources consumed in each step of software production by experts’ opinions. Third stage concludes cost and time tables of production scheduling by using Work break structure (WBS) and network models of project control. In whole of all stages of this paper, triangular fuzzy numbers are used to express uncertainty existed in succession and repetition of each production step, time of beginning, ending, the duration of each task and costs of them. Retrieved results examined by 30 practical projects conclude accuracy of 93 percent for time estimation and 92 percent for cost one. Also suggested algorithm is more accurate than COCOMOІІ 2000 algorithm as 50 percent based on examined problems.


Rahebe Keshavarzi, Mohammad Hossein Abooie,
Volume 27, Issue 2 (6-2016)

Process capability indices (PCIs) can be used as an effective tool for measuring product quality and process performance. In classic quality control there are some limitations which prevent a deep and flexible analysis because of the crisp definition of PCA‟s parameters. Fuzzy set theory can be used to add more flexibility to process capability analyses. In this study, the fuzzy X ba and MRx ba control charts are introduced to monitor continuous production process in triangular fuzzy state. Also, fuzzy PCIs are produced when SLs and measurements are triangular fuzzy numbers (TFN). For this aim, a computer program is coded in Matlab software. The fuzzy control charts is applied in Yazd fiber production plant. The results show that in continuous production processes, the better analysis will be performed by using fuzzy measurements. Also, based on the fuzzy capability indices, we can have a flexible analysis of the process performance.

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