فهرست مطالب
 Volume:14 Issue:1, 2017
 تاریخ انتشار: 1395/12/15
 تعداد عناوین: 11


Pages 121Intervalvalued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decisionmaking preference. Hence, this paper proposes a group generalized intervalvalued intuitionistic fuzzy soft set (GGIVIFSS) which contains the basic description by intervalvalued intuitionistic fuzzy soft set (IVIFSS) on the alternatives and a group of expert's evaluation of it. It contributes the following threefold: 1) A generalized intervalvalued intuitionistic fuzzy soft set (GIVIFSS) is proposed by introducing an intervalvalued intuitionistic fuzzy parameter, which reflects a new and senior expert's opinion on the basic description. The operations, properties and aggregation operators of GIVIFSS are discussed. 2) Based on GIVIFSS, a GGIVIFSS is then proposed to reduce the impact of decisionmaking preference by introducing more parameters by a group of experts. Its important operations, properties and the weighted averaging operator are also defined. 3) A multiattribute group decision making model based on GGIVIFSS weighted averaging operator is built to solve the group decision making problems in the more universal IVIF environment, and two practical examples are taken to validate the efficiency and effectiveness of the proposed model.Keywords: Group decision making, Intervalvalued intuitionistic fuzzy set, Generalized intervalvalued intuitionistic fuzzy soft set, Soft set

Pages 2341The current study set to extend a new VIKOR method as a compromise ranking approach to solve multiple criteria decisionmaking (MCDM) problems through intuitionistic fuzzy analysis. Using compromise method in MCDM problems contributes to the selection of an alternative as close as possible to the positive ideal solution and far away from the negative ideal solution, concurrently. Using Atanassov intuitionistic fuzzy sets (AIFSs) may simultaneously express the degree of membership and nonmembership to decision makers (DMs) to describe uncertain situations in decisionmaking problems. The proposed intuitionistic fuzzy VIKOR indicates the degree of satisfaction and dissatisfaction of each alternative with respect to each criterion and the relative importance of each criterion, respectively, by degrees of membership and nonmembership. Thus, the ratings for the importance of criteria, DMs, and alternatives are in linguistic variables and expressed in intuitionistic fuzzy numbers. Using IFS aggregation operators and with respect to subjective judgment and objective information, the most suitable alternative is indicated among potential alternatives. Moreover, practical examples illustrate the procedure of the proposed method.Keywords: Multiple criteria decision making (MCDM), Decision makers (DMs), Atanassov intuitionistic fuzzy sets (AIFSs), Intuitionistic fuzzy numbers

Pages 4360Support Vector Regression (SVR) solves regression problems based on the concept of Support Vector Machine (SVM). In this paper, a new model of SVR with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. Using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadratic optimization problem. The proposed method is illustrated by several simulated data and real data sets for both models (linearand nonlinear) with probabilistic constraints.Keywords: Probabilistic constraints, Support Vector Machine, Support Vector Regression, Quadratic programming, Probability function, Monte Carlo simulation

Pages 6175In this paper, we determine necessary and sufficient Tauberian conditions under which convergence in Pringsheim's sense of a double sequence of fuzzy numbers follows from its $(C,1,1)$ summability. These conditions are satisfied if the double sequence of fuzzy numbers is slowly oscillating in different senses. We also construct some interesting double sequences of fuzzy numbers.Keywords: Fuzzy numbers, Double sequences, Slow oscillation, Summability $(C, 1, 1)$, Tauberian theorems

Pages 7787Let $R$ be a commutative ring with identity and $M$ be an $R$module. Let $FSpec(M)$ denotes the collection of all prime fuzzy submodules of $M$. In this regards some basic properties of Zariski topology on $FSpec(M)$ are investigated. In particular, we prove some equivalent conditions for irreducible subsets of this topological space and it is shown under certain conditions $FSpec(M)$ is a $T_0$space or Hausdorff.Keywords: Fuzzy prime submodule, Fuzzy prime spectrum, Zariski topology, Irreducible subset

Pages 8997In this paper, a local approach to the concept of Hudetz $g$entropy is presented. The introduced concept is stated in terms of Hudetz $g$entropy. This representation is based on the concept of $g$ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.Keywords: $g$entropy, $g$ergodic decomposision, Hudetz correction

Pages 99113In this paper, we introduce the probabilistic normed groups. Among other results, we investigate the continuity of inner automorphisms of a group and the continuity of left and right shifts in probabilistic groupnorm. We also study midconvex functions defined on probabilistic normed groups and give some results about locally boundedness of such functions.Keywords: Probabilistic normed groups, Invariant probabilistic metrics, Distributionalslowly varying functions, Midconvex functions

Pages 115130In this paper, we firstly show that the $N$dual operation of the right residual implication, which is induced by a leftconjunctive right arbitrary $\vee$distributive left semiuninorm, is the right residual coimplication induced by its $N$dual operation. As a dual result, the $N$dual operation of the right residual coimplication, which is induced by a leftdisjunctive right arbitrary $\wedge$distributive left semiuninorm, is the right residual implication induced by its $N$dual operation. Then, we demonstrate that the $N$dual operations of the left semiuninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left semiuninorms. Finally, we reveal the relationships between conjunctive right arbitrary $\vee$distributive left semiuninorms induced by implications and disjunctive right arbitrary $\wedge$distributive left semiuninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle.Keywords: Fuzzy connective, Implication, Coimplication, Left semiuninorm, Neutrality principle

Pages 131144Matroids are important combinatorial structures and connect closely with graphs. Matroids and graphs were all generalized to fuzzy setting respectively. This paper tries to study connections between fuzzy matroids and fuzzy graphs. For a given fuzzy graph, we first induce a sequence of matroids from a sequence of crisp graph, i.e., cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matroid, is then constructed by using the sequence of matroids. An equivalent description of graphic fuzzy matroids is given and their properties of fuzzy bases and fuzzy circuits are studied.Keywords: Fuzzy graph, Partial fuzzy subgraph, Cycle, Fuzzy matroid

Pages 145162In this paper, we introduce the notion of $M$fuzzifying interval spaces, and discuss the relationship between $M$fuzzifying interval spaces and $M$fuzzifying convex structures.
It is proved that the category {\bf MYCSA2} can be embedded in the category {\bf MYIS} as a reflective subcategory, where {\bf MYCSA2} and {\bf MYIS} denote the category of $M$fuzzifying convex structures of $M$fuzzifying arity $\leq 2$ and the category of $M$fuzzifying interval spaces, respectively.
Under the framework of $M$fuzzifying interval spaces, subspaces and product spaces are presented and some of their fundamental properties are obtained.Keywords: $M$fuzzifying interval spaces, $M$fuzzifying convex structures, $M$fuzzifying interval preserving functions, Subspaces, Product spaces 
Pages 163181In this paper we classify fuzzy subgroups of a rank3 abelian group $G = \mathbb{Z}_{p^n} \mathbb{Z}_p \mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in \cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) nonisomorphic maximal chains of subgroups and (v) classes of isomorphic fuzzy subgroups of $G$. Illustrative examples are provided.Keywords: Equivalence, Fuzzy subgroup, Maximal chain, Keychain, Distinguishing factor, Isomorphism