Iranian journal of fuzzy systems
Volume:10 Issue: 6, Dec 2013

The prevalent communications networks suffer from lack of spectrum and spectrum inefficiency. This has motivated researchers to develop cognitive radio (CR) as a smart and dynamic radio access promised solution. A major challenge to this new technology is how to make fair assignment of available spectrum to unlicensed users, particularly for smart grids communication. This paper introduces an innovative approach to this key challenge in CR networks based on an empowered ant colony system (ACS) using fuzzy logic (FL). In order to evaluate performance of the proposed fuzzy logic-ant colony system spectrum assignment algorithm (FLACS-SAA), authors have particularly studied its performance versus the color sensitive graph coloring (CSGC) approach as well as a variety of bio-inspired based techniques referenced in the literature.

Triangular intuitionistic fuzzy numbers (TIFNs) is a special case of intuitionistic fuzzy (IF) set and the ranking of TIFNs is an important problem. The aim of this paper is to develop a new methodology for ranking TIFNs by using multiattribute decision making methods (MADM). In this methodology, the value and ambiguity indices of TIFNs may be considered as the attributes and the TIFNs in comparison are seen as the alternatives. A compromise ratio method for fuzzy MADM is developed based on the concept that larger TIFN should close to the maximum value index and is far away from the minimum ambiguity index simultaneously. The proposed ranking method is applied to solve multiattribute decision making problems in which the ratings of alternatives on attributes are expressed by using TIFNs. Numerical examples are examined to demonstrate the implementation process and applicability of the proposed method in this paper. Furthermore, a comparison analysis of the proposed method is conducted to show its advantages over other methods.

The engineers can frequently encounter with the situation to select the optimum option among the alternatives related with tunneling operations. The optimum choice can be selected by the experienced engineers taking into consideration their judgment and intuition. However, decision-making methods can offer to the engineers to support their optimum selection for a particular application in a scientific way. The Fuzzy Analytical Hierarchy Process (FAHP) is one of the multi attribute decision-making (MADM) methods utilizing structured pair-wise comparisons. This paper presents an application of the FAHP method to the selection of the optimum support design for water transporting tunnel in Naien. The methodology considers six main criteria, considering: displacement values for determined history locations, factor of safety (FOS), cost (total cost), time, mechanization and applicability factor for the selection of support design. The displacements and stress values were obtained by using the finite difference program FLAC2D as the numerical studies have been widely used by engineers examining the response of tunnels, in advance. After carrying out several numerical models for different support designs, the FAHP method was incorporated to evaluate these support designs according to the pre-determined criteria. These studies show that such FAHP application can effectively assist engineers to evaluate the alternatives support system for tunnels.

For any lacunary sequence $theta = (k_{r})$, we define the concepts of $S_{theta}-$limit point and $S_{theta}-$cluster point of a sequence of fuzzy numbers $X = (X_{k})$. We introduce the new sets $Lambda^{F}_{S_{theta}}(X)$, $Gamma^{F}_{S_{theta}}(X)$ and prove some inclusion relaions between these and the sets $Lambda^{F}_{S}(X)$, $Gamma^{F}_{S}(X)$ introduced in ~cite{Ayt:Slpsfn} by Aytar [S. Aytar, Statistical limit points of sequences of fuzzy numbers, Inform. Sci. 165 (2004) 129-138]. Later, we find restriction on the lacunary sequence $theta = (k_{r})$ for which the sets $Lambda^{F}_{S_{theta}}(X)$ and $Gamma^{F}_{S_{theta}}(X)$ respectively coincides with the sets $Lambda^{F}_{S}(X)$ and $Gamma^{F}_{S}(X)$.

We obtain two fixed point theorems for a kind of $varphi $-contractions in complete fuzzy metric spaces, which are applied to easily deduce intuitionistic versions that improve and simplify the recent results of X. Huang, C. Zhu and X. Wen.

In this paper, by presenting some notions and theorems, we obtain different types of fuzzy topologies. In fact, we obtain some Lowen-type and Chang-type fuzzy topologies on general fuzzy automata. To this end, first we define a Kuratowski fuzzy interior operator which induces a Lowen-type fuzzy topology on the set of states of a max- min general fuzzy automaton. Also by proving some theorems, we can define two fuzzy closure (two fuzzy interior) operators on the certain sets related to a general fuzzy automaton and then according to these notions we give some theorems and obtain some different Chang-type fuzzy topologies.

In this paper, the notion of fuzzy semicompactness degrees is introduced in $L$-fuzzy topological spaces by means of the implication operation of $L$. Characterizations of fuzzy semicompactness degrees in $L$-fuzzy topological spaces are obtained, and some properties of fuzzy semicompactness degrees are researched.

In this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. Explicit formulas are given for dihedral groups $D_{2n}$, quasi-dihedral groups $QD_{2^n}$, generalized quaternion groups $Q_{4n}$ and modular $p$-groups $M_{p^n}$.

module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.In this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for subsets of the universe.

Ngcibi, Murali and Makamba [Fuzzy subgroups of rank two abelian $p$-group, Iranian J. of Fuzzy Systems {bf 7} (2010), 149-153] considered the number of fuzzy subgroups of a finite abelian $p$-group $mathbb{Z}_{p^m}times mathbb{Z}_{p^n}$ of rank two, and gave explicit formulas for the cases when $m$ is any positive integer and $n=1,2,3$. Even though their method can be used for the cases when $n=4,5,ldots$ by using inductive arguments, it does not provide an explicit formula for that number for an arbitrarily given positive integer $n$. In this paper we give a complete answer to this problem. Thus for arbitrarily given positive integers $m$ and $n$, an explicit formula for the number of fuzzy subgroups of $mathbb{Z}_{p^m}times mathbb{Z}_{p^n}$ is given.

The purpose of this paper is to study the fuzzy fractional differential equations. We prove that fuzzy fractional differential equation is equivalent to the fuzzy integral equation and then using this equivalence existence and uniqueness result is establish. Fuzzy derivative is consider in the Goetschel-Voxman sense and fractional derivative is consider in the Riemann Liouville sense. At the end, we give the applications of the main result.

In this paper we study a representation of a fuzzy subgroup $mu$ of a group $G$, as a product of indecomposable fuzzy subgroups called the components of $mu$. This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and some of their properties to prove this theorem. We illustrate with some examples.