R. Ezzati; S. Khezerloo; Z. Valizadeh; N. Mahdavi-Amiri
Volume 9, Issue 3 , May and June 2012, Pages 1-26
Abstract
We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System $(FFLS)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an $FFLS$ with a nonnegative coefficient matrix, we consider ...
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We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System $(FFLS)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an $FFLS$ with a nonnegative coefficient matrix, we consider an equivalent $FFLS$ by using an appropriate permutation to simplify fuzzy multiplications. To solve the $m times n$ permutated system, we convert it to three $m times n$ real linear systems, one being concerned with the cores and the other two being related to the left and right spreads. To decide whether the core system is consistent or not, we use the modified Huang algorithm of the class of $ABS$ methods.If the core system is inconsistent, an appropriate unconstrained least squares problem is solved for an approximate solution.The sign of each component of the solution is decided by the sign of its core. Also, to know whether the left and right spread systems are consistent or not, we apply the modified Huang algorithm again. Appropriate constrained least squares problems are solved, when the spread systems are inconsistent or do not satisfy fuzziness conditions.Then, we consider the $FFLS$ with a mixed single-signed coefficient matrix, in which each component of the coefficient matrix is either nonnegative or nonpositive. In this case, we break the $m times n$ coefficient matrix up to two $m times n$ matrices, one having only nonnegative and the other having only nonpositive components, such that their sum yields the original coefficient matrix. Using the distributive law, we convert each $m times n$ $FFLS$ into two real linear systems where the first one is related to the cores with size $m times n$ and the other is $2m times 2n$ and is related to the spreads. Here, we also use the modified Huang algorithm to decide whether these systems are consistent or not. If the first system is inconsistent or the second system does not satisfy the fuzziness conditions, we find an approximate solution by solving a respective least squares problem. We summarize the proposed approach by presenting two computational algorithms. Finally, the algorithms are implemented and effectively tested by solving various randomly generated consistent as well as inconsistent numerical test problems.
Esmaile Khorram; Vahid Nozari
Volume 9, Issue 3 , May and June 2012, Pages 27-45
Abstract
This paper studies a new multi-objective fuzzy optimization prob- lem. The objective function of this study has dierent levels. Therefore, a suitable optimized solution for this problem would be an optimized solution with preemptive priority. Since, the feasible domain is non-convex; the tra- ditional ...
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This paper studies a new multi-objective fuzzy optimization prob- lem. The objective function of this study has dierent levels. Therefore, a suitable optimized solution for this problem would be an optimized solution with preemptive priority. Since, the feasible domain is non-convex; the tra- ditional methods cannot be applied. We study this problem and determine some special structures related to the feasible domain, and using them some methods are proposed to reduce the size of the problem. Therefore, the prob- lem is being transferred to a similar 0-1 integer programming and it may be solved by a branch and bound algorithm. After this step the problem changes to solve some consecutive optimized problem with linear objective function on discrete region. Finally, we give some examples to clarify the subject.
Sunny Joseph Kalayathankal; G. Suresh Singh
Volume 9, Issue 3 , May and June 2012, Pages 47-60
Abstract
An efficient flood alarm system may significantly improve public safety and mitigate damages caused by inundation. Flood forecasting is undoubtedly a challenging field of operational hydrology and a huge literature has been developed over the years. In this paper, we first define ordered ideal intuitionistic ...
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An efficient flood alarm system may significantly improve public safety and mitigate damages caused by inundation. Flood forecasting is undoubtedly a challenging field of operational hydrology and a huge literature has been developed over the years. In this paper, we first define ordered ideal intuitionistic fuzzy sets and establish some results on them. Then, we define similarity measures between ordered ideal intuitionistic fuzzy sets (OIIFS) and apply these similarity measures to five selected sites of Kerala, India to predict potential flood.
Huei-Wen Lin; Jing-Shing Yao
Volume 9, Issue 3 , May and June 2012, Pages 61-78
Abstract
Although the classical dividend discount model (DDM) is a wellknown and widely used model in evaluating the intrinsic price of common stock, the practical pattern of dividends, required rate of return or growth rate of dividend do not generally coincide with any of the model’s assumptions. It is ...
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Although the classical dividend discount model (DDM) is a wellknown and widely used model in evaluating the intrinsic price of common stock, the practical pattern of dividends, required rate of return or growth rate of dividend do not generally coincide with any of the model’s assumptions. It is just the opportunity to develop a fuzzy logic system that takes these vague parameters into account. This paper extends the classical DDMs to more realistic fuzzy pricing models in which the inherent imprecise information will be fuzzified as triangular fuzzy numbers, and introduces a novel -signed distance method to defuzzify these fuzzy parameters without considering the membership functions. Through the conscientious mathematical derivation, the fuzzy dividend discount models (FDDMs) proposed in this paper can be regarded as one more explicit extension of the classical (crisp) DDMs, so that stockholders can use it to make a specific analysis and insight into the intrinsic value of stock.
Ruixia Yan; Jianguo Zheng; Jinliang Liu; Chaoyong Qin
Volume 9, Issue 3 , May and June 2012, Pages 79-91
Abstract
To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes ...
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To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough set over dual-universes in fuzzy approximation space from two viewpoints: approximation operators and cut set of fuzzy set. Reduction of attributes and rules extraction of rough set over dual-universes in fuzzy approximation space are presented. Finally, an example of disease diagnoses expert system illustrates the possibility and eciency of rough set over dual-universes in fuzzy approximation space.
Deng-Feng Li; Jiang-Xia Nan; Zhen-Peng Tang; Ke-Jia Chen; Xiao-Dong Xiang; Fang-Xuan Hong
Volume 9, Issue 3 , May and June 2012, Pages 93-110
Abstract
The intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by Atanassov in 1983. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs of Atanassov’s triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, ...
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The intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by Atanassov in 1983. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs of Atanassov’s triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concepts and ranking order relations of Atanassov’s TIFNs are defined. A pair of bi-objective linear programming models for matrix games with payoffs of Atanassov’s TIFNs is derived from two auxiliary Atanassov’s intuitionistic fuzzy programming models based on the ranking order relations of Atanassov’s TIFNs defined in this paper. An effective methodology based on the weighted average method is developed to determine optimal strategies for two players. The proposed method in this paper is illustrated with a numerical example of the market share competition problem.
Wanli Liu; Xiaoqiu Song; Qiuzhao Zhang; Shubi Zhang
Volume 9, Issue 3 , May and June 2012, Pages 111-126
Abstract
Introducing more types of integrals will provide more choices todeal with various types of objectives and components in real problems. Firstly,in this paper, a (T) fuzzy integral, in which the integrand, the measure andthe integration result are all multi-valued, is presented with the introductionof ...
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Introducing more types of integrals will provide more choices todeal with various types of objectives and components in real problems. Firstly,in this paper, a (T) fuzzy integral, in which the integrand, the measure andthe integration result are all multi-valued, is presented with the introductionof T-norm and T-conorm. Then, some classical results of the integral areobtained based on the properties of T-norm and T-conorm mainly. The pre-sented integral can act as an aggregation tool which is especially useful inmany information fusing and data mining problems such as classi cation andprogramming.
Amir Abbas Rassafi; Roohollah Rezaei; Mehdi Hajizamani
Volume 9, Issue 3 , May and June 2012, Pages 127-146
Abstract
One of the most important stages in the urban transportation planning procedure is predicting the rate of trips generated by each trac zone. Currently, multiple linear regression models are frequently used as a prediction tool. This method predicts the number of trips produced from, or attracted to ...
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One of the most important stages in the urban transportation planning procedure is predicting the rate of trips generated by each trac zone. Currently, multiple linear regression models are frequently used as a prediction tool. This method predicts the number of trips produced from, or attracted to each trac zone according to the values of independent variables for that zone. One of the main limitations of this method is its huge dependency on the exact prediction of independent variables in future (horizon of the plan). The other limitation is its many assumptions, which raise challenging questions of its application. The current paper attempts to use fuzzy logic and its capabilities to estimate the trip generation of urban zones. A fuzzy expert system is introduced, which is able to make suitable predictions using uncertain and inexact data. Results of the study on the data for Mashhad (Lon: 59.37 E, Lat: 36.19 N) show that this method can be a good competitor for multiple linear regression method, specially, when there is no exact data for independent variables.
