Fuzzy Information and Engineering

Saneifard, R.; Allahviranloo, T.

2012 Fuzzy Information and Engineering

doi: 10.1007/s12543-012-0113-1

AbstractFuzzy systems have gained more and more attention from researchers and practitioners of various fields. In such systems, the output represented by a fuzzy set sometimes needs to be transformed into a scalar value, and this task is known as the defuzzification process. Several analytic methods have been proposed for this problem, but in this paper, the researchers suggest a modified approach to the problem of defuzzification, using the bi-symmetric weighted distance between two fuzzy numbers. This defuzzification can be used as a crisp approximation with respect to a fuzzy quantity. By considering this and with benchmark between fuzzy numbers, we can present a method for ranking, which can effectively rank various fuzzy numbers and their images and overcome the shortcomings of the previous techniques. After illustrating many numerical examples, following our procedure, the ranking results become valid.

Du, Wen-Sheng; Hu, Bao-Qing; Zhao, Yan

2012 Fuzzy Information and Engineering

doi: 10.1007/s12543-012-0114-0

AbstractIn the present paper, we mainly discuss the (⊥, ⊤)-generalized fuzzy rough sets introduced by B.Q. Hu and Z.H. Huang with both constructive approach and axiomatic approach considered. In the former, we started from the investigation of the properties of the ⊥-upper and ⊤-lower approximation operators generated by binary fuzzy relations. In the latter, by defining a pair of fuzzy set-theoretic operators, we show (⊥, ⊤)-fuzzy rough approximation operators can be characterized by different sets of axioms.

Sardar, Sujit Kumar; Goswami, Sarbani; Jun, Y. B.

2012 Fuzzy Information and Engineering

doi: 10.1007/s12543-012-0115-z

AbstractThe operator semirings of a Γ-semiring have been brought into use to study Γ-semiring in terms of fuzzy subsets. This is accomplished by obtaining various relationships between the set of all fuzzy ideals of a Γ-semiring and the set of all fuzzy ideals of its left operator semiring such as lattice isomorphism between the sets of fuzzy ideals of a Γ-semiring and its operator semirings.

Jain, Aparna; Ajmal, Naseem

2012 Fuzzy Information and Engineering

doi: 10.1007/s12543-012-0116-y

AbstractThis paper is the third in a sequence of papers on categories by the same authors. In one of the papers, a new category of fuzzy sets was defined and a few results were established pertaining to that special category of fuzzy sets S. Here, the concept of a fuzzy subset of a fuzzy set is defined under the category S. Besides, the notions of images and preimages of fuzzy sets are also defined under morphisms in the category of fuzzy sets and how smoothly these images and preimages behave under the action of these morphisms is analyzed. Finally, results have been proved on algebra of morphisms of this category S.

Tapaswini, Smita; Chakraverty, S.

2012 Fuzzy Information and Engineering

doi: 10.1007/s12543-012-0117-x

AbstractThis paper targets to investigate the solution of linear and nonlinear ordinary differential equations with fuzzy initial condition. Here, two improved Euler type methods have been proposed in order to obtain numerical solution of the problem. Along with this, an exact methodology is also discussed. The obtained results are depicted in term of plots to show the efficiency of the proposed methods. The solutions are compared with the known results and are found that those obtained by the proposed methods are tighter than the results from the existing method.

Singh, Ajit Pratap; Dubey, Subodh Kant

2012 Fuzzy Information and Engineering

doi: 10.1007/s12543-012-0118-9

AbstractThe present paper develops an integrated fuzzy based model to select an optimal landfill site among the given alternative sites by using the concept of fuzzy-utility method and multi-nomial logit theory. The suitability of different landfill sites are evaluated based on some important criteria involved in the process such as accessibility and transportation; environmental, geological and climatic conditions; socioeconomic conditions; land use pattern; and safety at the selected site. These criteria are assessed qualitatively by the decision makers based on their relative degree of importance. The importance weights and ratings of each criterion have been defined in the form of triplets of triangular fuzzy numbers by taking opinion of the decision makers. The corresponding triplets of ratings of each site are used to derive the utility value of the alternative sites. A multi-nomial logit model has been applied to calculate the probability of selection of each alternative site which can help policy makers to take appropriate decisions. Finally, the proposed methodology has been applied to allocate suitable landfill sites for disposing off municipal solid waste for Pilani town which is located in Jhunjhunu district of Rajasthan. The results evaluated by the modified fuzzy utility are also compared to the outputs of a direct method which is basically based on certain linguistic aggregation operators for group decision making. Computational results clearly demonstrate that the results obtained by the proposed method are coinciding very well and prepares a basis to adopt an overall strategy for selecting appropriate landfill site for proper solid waste disposal and its management.

Jafarzadeh, Yousef

2012 Fuzzy Information and Engineering

doi: 10.1007/s12543-012-0119-8

AbstractIn this paper, a numerical procedure is proposed for the fuzzy linear Fredholm integral equations of the second kind by using splines interpolation. Besides, the convergence conditions and an upper-bound on error are derived. Finally, the advantages of the proposed method have been shown through simulation examples and comparison with Lagrange method.