Iranian journal of fuzzy systems
Volume:10 Issue: 4, Aug 2013

In the framework of fuzzy algebras with fuzzy equalities and a complete lattice as a structure of membership values, we investigate fuzzy equational classes. They consist of special fuzzy algebras ful lling the same fuzzy identities, de ned with respect to fuzzy equalities. We introduce basic notions and the corresponding operators of universal algebra: construction of fuzzy subalgebras, homomorphisms and direct products. We prove that every fuzzy equational class is closed under these three operators, which means that such a class is a fuzzy variety.

In the literature, several numerical methods are proposed for solving nth-order fuzzy linear diff erential equations. However, till now there are only two analytical methods for the same. In this paper, the fuzzy Kolmogorov''s di fferential equations, obtained with the help of fuzzy Markov model of piston manufacturing system, are solved by one of these analytical methods and illustrated that the obtained solution does not represent a fuzzy number. To resolve the drawback of existing method, a new analytical method is proposed for solving nth-order fuzzy linear di fferential equations. Furthermore, the advantage of proposed method over existing method is also discussed.

Recently, tuning the weights of the rules in Fuzzy Rule-Base Classification Systems is researched in order to improve the accuracy of classification. In this paper, a margin-based optimization model, inspired by Support Vector Machine classifiers, is proposed to compute these fuzzy rule weights. This approach not only considers both accuracy and generalization criteria in a single objective function, but also is independent of any order in presenting data patterns or fuzzy rules. It has a global optimum solution and needs only one regularization parameter C to be adjusted. In addition, a rule reduction method is proposed to eliminating low weighted rules and having a compact rule-base. This method is compared with some greedy, reinforcement and local search rule weighting methods on 13 standard datasets. The experimental results show that, the proposed method significantly outperforms the other ones especially from the viewpoint of generalization.

In this paper, a fuzzy version of the analytic form of Hahn-Banach extension theorem is given. As application, the Hahn-Banach theorem for $r$-fuzzy bounded linear functionals on $r$-fuzzy normed linear spaces is obtained.

Nowadays energy is one of the most essential needs of human being and it can be considered as the basic prerequisite of social and economic development. Hence, many of the correlations and legislations of a country are affected by it. Since Iran has huge source of gas and oil, it has turned to a fossil fuel oriented county. But as oil and gas sources are non-renewable ones and cannot be replaced, it is essential for every country to focus on Renewable Energy Sources (RES). So today is the time of studying and investing on RES to be able to exploit them in the time of oil and gas crisis. In the past, the choice among alternative sources was based on the cost minimization, but ranking the RES options’ is a complex task. The objective of this paper is determining the best renewable energy alternative for Sistan & Baluchestan province of Iran by using interval Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method. In the application of the proposed methodology the most appropriate renewable energy alternative is determined fuel cell and biomass for the mentioned province.

Bilevel linear programming is a decision making problem with a two-level decentralized organization. The textquotedblleft leadertextquotedblright~ is in the upper level and the textquotedblleft followertextquotedblright, in the lower. Making a decision at one level affects that at the other one. In this paper, bilevel linear programming with inexact parameters has been studied and a method is proposed to solve a fuzzy bilevel linear programming using interval bilevel linear programming.

Recently, Abbasbandy and Asady have been proposed a modification of the distance based approach, namely ``sign distance method''. However, in this paper, it is shown that this method has some drawbacks, i.e., the result is not consistent with human intuition for special cases and this method cannot always logically infer ranking order of the images of the fuzzy numbers. In this paper, we present a revised method which can avoid these problems for ranking fuzzy numbers. Also, we present several properties for revised sign distance method while the original method does not have some of them.

This note studies the relationship between Hutton''s quasi-uniformities and Shi''s quasi-uniformities. It is shown that when $L$ satisfies``multiple choice principle«for co-prime elements, the category of Hutton''s quasi-uniform spaces is a bireflective full subcategory of the category of Shi''s quasi-uniform spaces. Especially, if the remote-neighborhood mapping defined by Shi preserves arbitrary joins, then the two categories are isomorphic to each other.

In this paper, the notion of cyclic $varphi$-contraction in fuzzy metric spaces is introduced and a fixed point theorem for this type of mapping is established. Meantime, an example is provided to illustrate this theorem. The main result shows that a self-mapping on a G-complete fuzzy metric space has a unique fixed point if it satisfies the cyclic $varphi$-contraction. Afterwards, some results in connection with the fixed point are given.

We develop a theory of stratified $LM$-filters which generalizes the theory of stratified $L$-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices $L$ and $M$. If $L$ and $M$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $L$-filters. Based on the stratified $LM$-filters, a general theory of lattice-valued convergence spaces can be developed.