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Bojnord, Iran

Ameri R.,University of Tehran | Dehghan O.,Bojnord University
Computers and Mathematics with Applications

We introduce and study fuzzy hypervector spaces based on fuzzy singletons. In this regard by considering the notion of fuzzy singletons, we characterize a fuzzy hypervector space fuzzily spanned by a fuzzy subset. Then we use these results to introduce the concept of fuzzy freeness of a fuzzy subset μ of a hypervector space V and finally we characterize it in terms of linear independence in the usual sense. © 2011 Elsevier Ltd. All rights reserved. Source

Bakhshi M.,Bojnord University
Iranian Journal of Fuzzy Systems

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore, the Fundamental Homomorphism Theorem is established. Finally, it is proved that the class of all fuzzy convex lattice-ordered subgroups of a lattice-ordered group G forms a complete Heyting sublattice of the lattice of fuzzy subgroups of G. Source

Rezaee B.,Bojnord University
Journal of Intelligent and Fuzzy Systems

In fuzzy models, redundancy may be present in the form of similar fuzzy sets, especially in the construction of a fuzzy system from a set of given training examples. In this paper, a simple formula for calculating the degree of similarity of Trapezoidal membership functions is derived in order to merge similar membership functions and hence to obtain a more transparent rule-base with a minimum number of membership functions. A simplification algorithm by using the proposed similarity measure has been applied to fuzzy models of nonlinear functions approximation. © 2012-IOS Press and the authors. All rights reserved. Source

Husseinzadeh Kashan A.,Islamic Azad University at Tehran | Rezaee B.,Bojnord University | Karimiyan S.,International Institute of Earthquake Engineering and Seismology
Pattern Recognition

Fuzzy data clustering plays an important role in practical use and has become a prerequisite step for decision-making in fuzzy environment. In this paper we propose a new algorithm, called FuzzyGES for unsupervised fuzzy clustering based on adaptation of the recently proposed Grouping Evolution Strategy (GES). To adapt GES for fuzzy clustering we devise a fuzzy counterpart of the grouping mutation operator typically used in GES, and employ it in a two phase procedure to generate a new clustering solution. Unlike conventional clustering algorithms which should get the number of clusters as an input, FuzzyGES tries to determine the true number of clusters as well as providing the optimal cluster centroids after several iterations. The proposed approach is validated through using several data sets and results are compared with those of fuzzy c-means algorithm, particle swarm optimization algorithm (PSO), differential evolution (DE) and league championship algorithm (LCA). We also investigate the performance of FuzzyGES through using different cluster validity indices. Our results indicate that FuzzyGES is fast and provides acceptable results in terms of both determining the correct number of clusters and the accurate cluster centroids. © 2012 Elsevier Ltd. Source

Oghaz N.M.,Bojnord University | Haghighi B.,Islamic Azad University at Neyshabur | Alavianmehr M.M.,Shiraz University of Technology | Ghiamati E.,Birjand University
Journal of Solution Chemistry

A robust and efficient procedure is presented for calculating the solubility parameter. An analytical equation for internal pressure is proposed. Through a simple relation reported by Verdier and Andersen (fluid phase equilibrium 231: 125-137, 2005), one can easily find the solubility parameter via our analytical equation for the internal pressure. Also, the radial distribution function (RDF) of a Lennard-Jones LJ (12, 6) fluid, proposed by Xu and Hu (fluid phase equilibrium 30: 221-228, 1986), has been employed to calculate the internal pressure of normal alkanes from methane to decane. Their solubility parameters were evaluated according to the calculated values of the internal pressure. A comparison between the experimental and the estimated values demonstrated a very good agreement between them. © 2013 Springer Science+Business Media New York. Source

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