Fuzzy Information and Engineering

Kumar, Amit; Gupta, Anila

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0062-0

AbstractMukherjee and Basu proposed a new method for solving fuzzy assignment problems. In this paper, some fuzzy assignment problems and fuzzy travelling salesman problems are chosen which cannot be solved by using the fore-mentioned method. Two new methods are proposed for solving such type of fuzzy assignment problems and fuzzy travelling salesman problems. The fuzzy assignment problems and fuzzy travelling salesman problems which can be solved by using the existing method, can also be solved by using the proposed methods. But, there exist certain fuzzy assignment problems and fuzzy travelling salesman problems which can be solved only by using the proposed methods. To illustrate the proposed methods, a fuzzy assignment problem and a fuzzy travelling salesman problem is solved. The proposed methods are easy to understand and apply to find optimal solution of fuzzy assignment problems and fuzzy travelling salesman problems occurring in real life situations.

Liu, Hong; Huang, Zhen; Gao, Hong-yi; Zeng, Qing-heng

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0063-z

AbstractThe factors affecting performance of fractured wells are analyzed in this work. The static and dynamic geologic data of fractured well and fracturing treatment parameters obtained from 51 fractured wells in sand reservoirs of Zhongyuan oilfield are analyzed by applying the grey correlation method. Ten parameters are screened, including penetrability, porosity, net thickness, oil saturation, water cut, average daily production, and injection rate, amount cementing front spacer, amount sand-carrying agent and amount sand. With the novel Radial Basis Function neural network model based on immune principles, 13 parameters of 42 wells out of 51 are used as the input samples and the stimulation ratios as the output samples. The nonlinear interrelationship between the input samples and output samples are investigated, and a productivity prediction model of optimizing fracture design is established. The data of the rest 7 wells are used to test the model. The results show that the relative errors are all less than 7%, which proves that the novel Radial Basis Function neural network model based on immune principles has less calculation, high precision and good generalization ability.

Sebastian, Sabu; Ramakrishnan, T.V.

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0064-y

AbstractIn this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multi-fuzzy sets, a method for obtaining Atanassov's intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov's intuitionistic fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh's fuzzy set theory, Atanassov's intuitionsitic fuzzy set theory and L-fuzzy set theory.

Zhang, Qian-sheng; Li, Bi

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0065-x

AbstractThis paper focuses on presentation of a method to bidirectional interval-valued fuzzy approximate reasoning by employing a weighted similarity measure between the fact and the antecedent (or consequent) portion of production rule in which the vague terms are represented by interval-valued fuzzy concepts rather than plain fuzzy sets. The proposed method is more reasonable and flexible than the one presented in the paper by Chen [Fuzzy Sets and Systems, 91(1997), 339–353] due to the fact that it not only can deal with multidimensional interval-valued fuzzy reasoning scheme, but also consider the different importance degree of linguistic variables in production rule and that of elements in each universe.

De, P. K.; Rawat, Apurva

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0066-9

AbstractIn business and industry it becomes very difficult for a manager to take concrete decision regarding inventory, as the data available to him are not always certain. Because uncertainty arises in demand, set-up resources & capacity constraints of an inventory planning system, it could be more justified to consider these factors in an elastic form. Therefore, with these uncertain data, fuzziness can be applied and the problem of inventory can be controlled. In the present paper, an inventory model without shortage has been considered in a fuzzy environment, by considering real-life data from the LPG store of Banasthali University. Triangular fuzzy numbers have been used to consider the ordering and holding costs. For defuzzification, signed-distance method has been used to compute the optimum order quantity.

Peng, Jin

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0067-8

AbstractDecision making in real world is usually made in fuzzy environment and subject to fuzzy risks. The value at risk (VaR) is a widely used tool in risk management and the average value at risk (AVaR) is a risk measure which is a superior alternative to VaR. In this paper, we present a methodology for fuzzy risk analysis based on credibility theory. First, we present the new concepts of the credibilistic VaR and credibilistic AVaR. Next, we examine some properties of the proposed credibilistic VaR and credibilistic AVaR. After that, a kind of fuzzy simulation algorithms are given to show how to calculate them. Finally, a numerical example is illustrated. The proposed credibilistic VaR and credibilistic AVaR are suitable for use in many real problems of fuzzy risk analysis.

Kumar, Amit; Kaur, Amarpreet

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0068-7

AbstractTo the best of our knowledge till now there is no method in the literature to find the exact fuzzy optimal solution of unbalanced fully fuzzy transportation problems. In this paper, the shortcomings and limitations of some of the existing methods for solving the problems are pointed out and to overcome these shortcomings and limitations, two new methods are proposed to find the exact fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as LR flat fuzzy numbers. To show the advantages of the proposed methods over existing methods, a fully fuzzy transportation problem which may not be solved by using any of the existing methods, is solved by using the proposed methods and by comparing the results, obtained by using the existing methods and proposed methods. It is shown that it is better to use proposed methods as compared to existing methods.

Guo, Si-zong; Song, Tao

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0069-6

AbstractIn this paper we introduced the definition of interval-valued fuzzy numbers based on the definition of interval-valued fuzzy set and the operations of real fuzzy numbers by extension principle, defined the operations of interval-valued fuzzy numbers and their distance, and gave their structured element representations and operations of them by using the fuzzy structured element method. The work of this paper is an expansion of the research of real fuzzy numbers.