Journal of Intelligent & Fuzzy Systems - Volume 30, issue 2

Authors: Zhang, Haidong | He, Yanping | Xiong, Lianglin

Article Type: Research Article

Abstract: In this paper, a single-granulation dual hesitant fuzzy rough set model based on dual hesitant fuzzy tolerance relations is first introduced. By the combination of multi-granulation rough sets and the single-granulation dual hesitant fuzzy rough sets, we then develop a new multi-granulation rough set model, called a multi-granulation dual hesitant fuzzy rough set. In the multi-granulation framework, two types of multi-granulation dual hesitant fuzzy rough sets are proposed, which are named the optimistic multi-granulation dual hesitant fuzzy rough sets and pessimistic multi-granulation dual hesitant fuzzy rough sets. Finally, the relationships among the single-granulation dual hesitant fuzzy rough sets, optimistic multi-granulation …dual hesitant fuzzy rough sets and pessimistic multi-granulation dual hesitant fuzzy rough sets are investigated. Show more

Keywords: Dual hesitant fuzzy tolerance relation, Single-granulation dual hesitant fuzzy rough set, Multi-granulation dual hesitant fuzzy rough set

DOI: 10.3233/IFS-151851

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 623-637, 2016

Authors: Baghmisheh, Mahdi | Ezzati, Reza

Article Type: Research Article

Abstract: In this paper we present an efficient iterative procedure based on the triangular functions (TFs) to obtain the numerical solution of the specific nonlinear fuzzy Fredholm integral equations of the second kind. The error estimation of the proposed method is given in terms of uniform modulus of continuity. Also, we prove the stability of the method with respect to the choice of the first iteration. Finally, in order to demonstrate the accuracy and the convergence of the method, some numerical examples are included.

Keywords: Nonlinear fuzzy Fredholm integral equation, iterative procedure, triangular functions, numerical stability

DOI: 10.3233/IFS-151783

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 639-649, 2016

Authors: Tahmasbpour, A. | Borzooei, R.A. | Rashmanlou, Hossein

Article Type: Research Article

Abstract: The main purpose of this paper is to introduce the notion of bipolar f -morphism on bipolar fuzzy graphs and regular bipolar fuzzy graphs. We study the action of bipolar f -morphism on bipolar fuzzy graphs and derive some elegant results on weak and co-weak isomorphism. Also, we define d 2 -degree and total d 2 -degree of a vertex in bipolar fuzzy graphs and study (2, k )-regularity and totally (2, k )-regularity of bipolar fuzzy graphs. d 2 -degree and total d 2 -degree of a vertex in bipolar fuzzy graphs are highly utilized by computer science, geometry, …algebra, number theory and operation research. In addition these properties will also be helpful to study large bipolar fuzzy graph as a combination of small, bipolar fuzzy graphs and to derive its properties from those of the smaller ones. Show more

Keywords: Total degree, totally regular bipolar fuzzy graph, bipolar f-morphism

DOI: 10.3233/IFS-151784

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 651-658, 2016

Authors: Pan, Xianli | Xu, Yitian

Article Type: Research Article

Abstract: The support vector machine (SVM) has gained prominence in classification problems. One characteristic of it is that the optimal decision hyperplane is only determined by support vectors (SVs). Inspired by this, we propose two novel sample selection methods based on the idea of potential SVs. One is the distance-based sample selection method (DSSM), it calculates the distance between each pair of samples from different classes, and then selects those nearer to the other class as potential SVs. The other is the K-nearest neighbors (Knn)-based sample selection method (KSSM), which is presented on account of the boundary nearest SVM (BNSVM). The …BNSVM regards the nearest neighbors between two classes as potential SVs. While our KSSM extends the neighbor number from one in BNSVM to k . In addition, we present a method to choose an appropriate k . Afterwards, we do classification with these potential SVs. These selected samples contain useful information for classification which ensures the accuracy of classifiers. Moreover, the DSSM and KSSM work fast since they are only related to the distance and do not need to do iterations. Experiments conducted on small datasets and large-scaled ones show the validity of our DSSM and KSSM. Show more

Keywords: SVM, Sample selection, DSSM, KSSM

DOI: 10.3233/IFS-151785

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 659-670, 2016

Authors: Karunambigai, M.G. | Akram, Muhammad | Buvaneswari, R.

Article Type: Research Article

Abstract: In this paper, the concept of strong and superstrong vertices in intuitionistic fuzzy graphs (IFGs) are introduced. Necessary and sufficient conditions for the existence of strong and superstrong vertices in intuitionistic fuzzy graphs are discussed. Necessary and sufficient conditions for an edge to be strong in intuitionistic fuzzy graphs are also dealt and the existence of strong and superstrong vertices in strong IFGs are studied. An algorithm is defined to identify an intuitionistic fuzzy steady path between two vertices of IFGs which finds application in decision making problems.

Keywords: Strong vertex, superstrong vertex, cycle IFG, strong IFG

DOI: 10.3233/IFS-151786

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 671-678, 2016

Authors: Li, Erqiang | Shi, Fugui

Article Type: Research Article

Abstract: In this paper, motivated by the free product of crisp matroids, the free product of M -fuzzifying matroids is defined when M is a finite Boolean algebra and a number of fundamental properties of the operation are derived. Parallel to crisp matroids, the minors of M -fuzzifying matroids are described in terms of the M -fuzzifying truncation operator and its dual, the M -fuzzifying Higgs lift operator.

Keywords: M-fuzzifying matroid, Free product of M-fuzzifying matroids, M-fuzzifying truncation, M-fuzzifying Higgs lift

DOI: 10.3233/IFS-151788

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 679-690, 2016

Authors: Yao, Dengbao | Liu, Xiaoxing | Zhang, Xu | Wang, Cuicui

Article Type: Research Article

Abstract: The main purpose of the paper is to develop a general analytical framework of uncertainty measures, which provides a fresh new look into the uncertain information of hesitant fuzzy sets (HFSs). We first refine the axiomatic principles of hesitant fuzzy entropy based on the fuzzy factor and hesitant factor, and propose some distance-based entropy formulas of HFSs. Then, a novel hesitant fuzzy cross-entropy is defined to measure the discrimination of uncertain information of different HFSs. Meanwhile, the relationship between cross-entropy and entropy of HFSs is also discussed, and the hesitant fuzzy entropy may be divided into arithmetic average of fuzzy …entropy and hesitant entropy. Moreover, some parameterized uncertainty measures are investigated, and two comparative examples are presented to demonstrate their reasonability. Finally, we apply these proposed measures in multiple attribute decision-making problem to illustrate their efficiency and applicability. Show more

Keywords: Hesitant fuzzy entropy, fuzzy factor, hesitant factor, cross-entropy, parameterized uncertainty measures

DOI: 10.3233/IFS-151790

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 691-703, 2016

Authors: Rafiee, R. | Khalookakaie, R. | Ataei, M. | Jalali, S.M.E. | Sereshki, F. | Azarfar, A.

Article Type: Research Article

Abstract: A fuzzy expert semi-quantitative (FESQ) method is presented to analyze the parameters influencing rock mass cavability in block caving mines. In the proposed method, fuzzy numbers are used to allow the incorporation of uncertainty in coding the interaction matrix. Since in the classic ESQ method a fixed single value is defined as the interaction between two parameters, based on one expert view, it seems necessary to improve the method to be able to cover different views of different experts. To illustrate the application of the proposed method, first the parameters influencing the cavability in the block caving mines are selected, …then a matrix of interaction between parameters are introduced using fuzzy numbers. Every fuzzy number has its own membership function designed based on experts’ views. Finally the dominant and subordinated parameters are determined and interpreted by fuzzy logic. The proposed fuzzy codding method is very useful in humanistic decision making systems with existence of uncertainty, vagueness and imprecision. Show more

Keywords: ESQ codding, fuzzy numbers, cavability, RES

DOI: 10.3233/IFS-151791

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 705-715, 2016

Authors: Zhai, Junhai | Li, Ta | Wang, Xizhao

Article Type: Research Article

Abstract: Motivated by the idea of cross-validation, a novel instance selection algorithm is proposed in this paper. The novelties of the proposed algorithm are that (1) it cross selects the important instances from the original data set with a committee, (2) it can deal with the problem of selecting instance from large data sets. We experimentally compared our algorithm with five state-of-the-art approaches which are CNN, ENN, RNN, MCS, and ICF on 3 artificial data sets and 6 UCI data sets, including 4 large data sets, ranking from 130K to 4898K in size. The experimental results show that the proposed algorithm …is very efficient and effective, especially on large data sets. Show more

Keywords: Instances selection, extreme learning machine, K–L divergence, large data sets

DOI: 10.3233/IFS-151792

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 717-728, 2016

Authors: Atagün, Akın Osman | Aygün, Emin

Article Type: Research Article

Abstract: In this paper, we introduce two new operations on soft sets, called inverse production and characteristic production, by using Molodtsov’s definition of the soft sets. We prove that the set of all soft sets over a universe U is an abelian group under the each operations and called “the inverse group of soft sets” and “the characteristic group of soft sets”. We finally show that these groups are isomorphic.

Keywords: Soft set, group structure, inverse group of soft sets, characteristic group of soft sets

DOI: 10.3233/IFS-151793

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 729-733, 2016