Journal of Intelligent & Fuzzy Systems - Volume 33, issue 6

Authors: Yu, Xiaohui | Zhang, Qiang | Zhou, Zhen

Article Type: Research Article

Abstract: In this paper, a new class of games with fuzzy coalitions and fuzzy payoff value is proposed. This class of fuzzy games is based on the generalized integral form, which contains several kinds of other fuzzy games, such as fuzzy cooperative game with fuzzy payoff value, the multilinear extension game introduced by Owen, the game with proportional value proposed by Butnariu and the game with Choquet integral form given by Tsurumi et al. Also, the proposed fuzzy game is also further extension of the fuzzy game in Choquet integral form proposed by Yu et al., which is also is a …kind of fuzzy games in the condition that coalition and fuzzy payoff value are both fuzzy information. The fuzzy Shapley value for this kind of fuzzy games is represented by Shapley value of corresponding fuzzy cooperative game with fuzzy payoff value. Based on Hukuhara-difference, we give the explicit Shapley value for the proposed fuzzy game. It has been seen that most of properties hold well in the proposed fuzzy game, which are processed by cooperation game with fuzzy payoff value, and fuzzy coalition game, respectively. Finally, a practical application of the proposed model is also provided. Show more

Keywords: Cooperative game, fuzzy, coalition, payoff value, shapley value

DOI: 10.3233/JIFS-17445

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3641-3651, 2017

Authors: Li, Xiaonan | Yi, Huangjian

Article Type: Research Article

Abstract: In this paper, we will define intuitionistic fuzzy matroid and study their properties. First, we analyse the two approaches to fuzzification of matroids and decide to use an indirect approach. After some preliminaries, we define an intuitionistic fuzzy matroid as a prefect intuitionistic fuzzy pre-matroid. Second, we study two pair of classical operators imposed on intuitionistic fuzzy matroids. Finally, we induce a G-V fuzzy matroid from a given intuitionistic fuzzy matroid and study the relationship of H fuzzy matroids and intuitionistic fuzzy matroids. Besides, we introduce an approach to construction of G-V fuzzy matroids and point out the connection of …fuzzy matroids and fuzzy rough set models. Show more

Keywords: Intuitionistic fuzzy sets, matroids, rough sets

DOI: 10.3233/JIFS-17504

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3653-3663, 2017

Authors: Qin, Ya | Liu, Yi | Hong, Zhiyong

Article Type: Research Article

Abstract: Pythagorean fuzzy sets (PFSs), as an extension of intuitionistic fuzzy sets (IFSs) to deal with uncertainty, have attracted much attention since its introduction, in both theory and application aspects. The present work aims at investigating new distance measures in the PFSs and then employing them into multiple criteria decision-making application. To begin with, generalized Pythagorean fuzzy weighted averaging distance operator (GPFWAD) and generalized Pythagorean fuzzy ordered weighted averaging distance (GPFOWAD) measure are firstly introduced in the PFSs. Afterwards, probabilistic generalized Pythagorean fuzzy weighted averaging distance (P-GPFWAD) operator, probabilistic generalized Pythagorean fuzzy order weighted averaging distance (P-GPFOWAD) operator are proposed which …are new distance measures and are able to integrate the (ordered) weighted averaging operator, probabilistic weight and individual distance of two Pythagorean fuzzy numbers (PFNs) in the same formulation. These generalized weighted averaging distance measures are very suitable to deal with the situation where the input data are represented in Pythagorean fuzzy numbers (PFNs). Then we present a kind of multiple criteria decision-making method with Pythagorean fuzzy information based on the developed distance measures. Finally, a numerical example is provided to illustrate the practicality and feasibility of the developed method. Show more

Keywords: Pythagorean fuzzy set, probability, distance measures, aggregation operators, multi-criteria decision making

DOI: 10.3233/JIFS-17506

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3665-3675, 2017

Authors: Liu, Hongbin | Jiang, Le | Xu, Zeshui

Article Type: Research Article

Abstract: The hesitant fuzzy linguistic preference relations (HFLPRs) facilitate decision makers to express hesitant assessments in fuzzy decision making problems. It is important for the use of consistent HFLPRs since inconsistency leads to unreliable decision making results. This paper aims at proposing the additive and multiplicative consistency improvement processes for HFLPRs such that they reach an acceptable level. Some properties of the additive and multiplicative consistency of HFLPRs are investigated, based on which two algorithms for improving the additive consistency and multiplicative consistency are introduced. Two numerical examples are analyzed by using the algorithms and the comparative analysis between the proposed …model and other models is also given. A multi-criteria decision making model based on HFLPRs is proposed, and a practical example on performance evaluation of commercial banks is presented to show the feasibility of the proposed model. Show more

Keywords: Hesitant fuzzy linguistic preference relations, additive consistency, multiplicative consistency, envelope

DOI: 10.3233/JIFS-17519

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3677-3693, 2017

Authors: Lin, Yan-Qing | Fu, Yang-Geng | Su, Qun | Wang, Ying-Ming | Gong, Xiao-Ting

Article Type: Research Article

Abstract: The belief rules are stored out of order in the extended belief rule base (EBRB), which will weaken its reasoning performance in that all rules are visited when calculating each rule’s activation weight. This paper focuses on reducing the number of rules which are visited in the calculation of each rule’s activation weight. A new rule activation method based on VP-tree and MVP-tree is proposed to build index structure to store rules. The proposed rule activation method is based on rule similarity query, where only partial rules will be retrieved and visited while calculating each rule’s activation weight. Note that, …the performance of EBRB systems based on tree index is affected greatly by the value of query threshold. However, sometimes it is difficult to determine the value of query threshold, so this paper also proposes an approach based on the k-means clustering algorithm to choose the appropriate query threshold. Some case studies show how the use of the proposed optimization method enhances the reasoning performance of EBRB systems. The proposed method has been validated to be advantageous to visit partial suitable rules instead of all rules. Beside the work performed in the EBRB, the proposed method alone can also be used in different application areas. Show more

Keywords: Extended belief rule base, rule activation method, VP-Tree, MVP-Tree

DOI: 10.3233/JIFS-17521

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3695-3705, 2017

Authors: Zhou, Mi | Liu, Xinbao | Yang, Jianbo

Article Type: Research Article

Abstract: In a multiple attribute decision making (MADM) problem, quantitative and qualitative attributes can be assessed by numerical values and subjective judgements. Numerical value can be accurate or uncertain, while qualitative attribute can be evaluated by linguistic variables. The evidential reasoning (ER) approach provides a process for dealing with MADM problems of both a quantitative and qualitative nature under uncertainty. In the existing MADM literature, interval value is assumed to be uniformly distributed and complete in the sense that any value in the interval is equally likely and that the probabilities of values in the interval being taken sum to one. …In real life decision situations, however, interval value could be incomplete in that the sum of probabilities of values in the interval being taken can be less than one. In this paper, incomplete interval value is introduced to a decision making process, and the transformation rule of incomplete interval value to belief degrees in the frame of discernment under the ER framework is analyzed. The characteristics of the transformation rule are studied. A case study is provided to illustrate the implementation of the proposed new concept and technique and the potential in supporting MADM under uncertainty. Show more

Keywords: Evidential reasoning, belief degree, incomplete interval value, transformation rule

DOI: 10.3233/JIFS-17522

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3707-3721, 2017

Authors: Nan, Jiang-Xia | Li, Deng-Feng | An, Jing-Jing

Article Type: Research Article

Abstract: The aim of this paper is to develop a new methodology for solving bi-matrix games in which goals are regarded as intuitionistic fuzzy (IF) sets (IFSs) and payoffs are expressed with triangular IF numbers (TIFNs). In this methodology, a new ranking method of TIFNs is proposed and the concept of IF inequalities is interpreted. An IF non-linear programming model is constructed to obtain the solution for such a type of bi-matrix games. Then utilizing these IF inequalities and the ranking method of TIFNs proposed in this paper, the solution of any bi-matrix game with goals of IFSs and payoffs of …TIFNs can be transformed into a crisp non-linear programming problem. It is shown that the bi-matrix game with goals of IFSs and payoffs of TIFNs is a generalization of the bi-matrix game with goals of fuzzy sets and payoffs of triangular fuzzy numbers. The method proposed in this paper is demonstrated with a numerical example of commerce retailers’ strategy choice problem. Show more

Keywords: Intuitionistic fuzzy set, intuitionistic fuzzy number, ranking method, bi-matrix game, intuitionistic fuzzy optimization

DOI: 10.3233/JIFS-17595

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3723-3732, 2017

Authors: Zhu, Xi | Yang, Jiang | Saeid, Arsham Borumand

Article Type: Research Article

Abstract: In this paper, using a special family of extreme fuzzy filters F on a BL -algebra L , we construct a uniform structure ( L , K ) , and then the part K induce a uniform topology T F in L . Also, we prove that the pair ( L , T F ) is a topological BL -algebra, and some properties of ( L , T F ) …are investigated. In particular, we show that ( L , T F ) is a first-countable, zero-dimensional, disconnected and completely regular space. At the same time, we give some characterizations of topological properties of ( L , T F ) , for example, ( L , T F ) is a discrete space if and only if g 1  = {1}, and ( L , T F ) is a Hausdorff space if and only if g 1  = {1}, where g = ∩ F . Finally, we naturally contact the relationship between isomorphism (algebraic invariant) and homeomorphism (topological invariant) in topological BL -algebras. Show more

Keywords: Extreme fuzzy filter, uniform space, topological BL-algebra, BL-morphism

DOI: 10.3233/JIFS-17597

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3733-3741, 2017

Authors: Yang, Eunsuk

Article Type: Research Article

Abstract: This paper investigates a non-associative generalization, more exactly, a weak t -associative (wta) generalization, of continuous t-norm-based logics. First, the wta-uninorm logic WAt BL and its axiomatic extensions WAt Ł , WAt Π , and WAt G are introduced as [0, e ]-continuous wta-uninorm-based analogues of the most famous continuous t-norm-based logics, BL (Basic fuzzy logic), Ł (Łukasiewicz logic), Π (Product logic), and G (Gödel logic), respectively. Their corresponding algebraic structures and algebraic completeness results are considered. Next, completeness with respect to the algebras whose lattice reduct is …[0, 1], known as standard completeness , is established for these systems by a construction in the style of Jenei–Montagna. Show more

Keywords: Fuzzy logic, micanorm, wta-uninorm, uninorm, t-norm

DOI: 10.3233/JIFS-17623

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3743-3752, 2017

Authors: Khan, Fadia Ali | Ahmed, Jameel | Khan, Jan Sher | Ahmad, Jawad | Khan, Muazzam A.

Article Type: Research Article

Abstract: Internet is used as the main source of communication throughout the world. However due to public nature of internet data are always exposed to different types of attacks. To address this issue many researchers are working in this area and proposing data encryption techniques. Recently a new substitution box has been proposed for image encryption using many interesting properties like gingerbread-man chaotic map and S 8 permutation. But there are certain weaknesses in aforesaid technique which does not provide sufficient security. To resolve the security issue an enhanced version of existing technique is proposed in this paper. Lorenz chaotic …map based confusion and diffusion processes in existing technique are employed. Lorenz map is used to remove strong correlation among the plain text image pixels. In diffusion stage a random matrix is generated through lorenz chaotic map and XORed with shuffled image. It the end, existing gingerbread-man chaotic map based S-box is applied to extract the final cipher text image. The proposed enhanced scheme is analysed by statistical analysis, key space analysis, information entropy analysis and differential analysis. In order to ensure the robustness and higher security of proposed scheme, results via Number of Pixel Rate Change (NPRC) and Unified Average Change Intensity (UACI) tests are also validated. Show more

Keywords: Lorenz equation, S-Box, Gingerbreadman chaotic map, confusion, diffusion.

DOI: 10.3233/JIFS-17656

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3753-3765, 2017