Journal of Intelligent & Fuzzy Systems - Volume 36, issue 1

Authors: Gao, Rong | Ahmadzade, Hamed | Esfahani, Mojtaba

Article Type: Research Article

Abstract: Covariance is a measure to characterize the joint variability of two complex uncertain variables. Since, calculating covariance is not easy based on uncertain measure, we present two formulas for covariance and pseudo covariance of complex uncertain variables. For calculating the covariance of complex uncertain variables, some theorems are proved and several formulas are provided by using the inverse uncertainty distribution. The main results are explained by using several examples.

Keywords: Uncertainty theory, complex uncertain variable, covariance, pseudo covariance

DOI: 10.3233/JIFS-181233

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 241-251, 2019

Authors: Jan, Naeem | Zedam, Lemnaouar | Mahmood, Tahir | Ullah, Kifayat | Ali, Zeeshan

Article Type: Research Article

Abstract: In this paper, the concept of linguistic cubic number (LCN) is introduced which further extends the concept of linguistic intuitionistic fuzzy number (LIFN). More specifically, the notions of internal (external) developed and (P-)R-order for LCN are studied. For a given LCN, some basic operational laws, score and accuracy function are proposed. Also, some generalized aggregation operators based on the operational rules are developed and their related properties are investigated. As application, a multi-attribute decision-making (MADM) method is established based in the environment of LCNs and with the help of defined aggregation operators. Finally, an illustrative example is provided to show …the effectiveness of the proposed MADM method. Show more

Keywords: Cubic set, linguistic cubic number, (P-) R-order, multi-attribute decision making

DOI: 10.3233/JIFS-181253

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 253-269, 2019

Authors: Zheng, Jing | Wang, Ying-Ming | Lin, Yang | Zhang, Kai

Article Type: Research Article

Abstract: Case retrieval is the major step in case-based reasoning (CBR). The similarity measurement between historical cases and the target case is very important in the case retrieval, and affects the results of the decision. In CBR practical application, there are hybrid attribute values for case attributes. The representation of the case and performing case retrieval with high retrieval accuracy for hybrid multiple formats of attribute values are significant challenges, but an in-depth study is lacking. The objective of this paper is to develop a new case retrieval method to hybrid multi-attribute, which contains four formats of attribute values, i.e., crisp …numbers, interval numbers, multi-granularity linguistic variables, and intuitionistic fuzzy numbers (IFNs). First, crisp numbers, interval numbers, and multi-granularity linguistic variables are transformed into IFNs and an attribute similarity measurement based on IFNs is proposed. The attribute weights are determined by an optimal matching model. This model belongs to a type of multi-objective problem and can be solved using the min-max method. Furthermore, the case similarities between historical cases and the target case are obtained by aggregating attribute similarities using evidence reasoning, and the proper historical case(s) can be retrieved according to the obtained hybrid case similarities. Finally, a case study of the gas explosion in China’s Fujian province is conducted to demonstrate the proposed approach and its potential application. Show more

Keywords: Case retrieval, intuitionistic fuzzy number, evidence reasoning, similarity measurement, gas explosion

DOI: 10.3233/JIFS-181269

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 271-282, 2019

Authors: Liu, Hui | Zhao, Bin

Article Type: Research Article

Abstract: In order to avoid combinatorial rule explosion in fuzzy reasoning, distributive laws related to fuzzy implications and aggregation functions have been widely studied in recent years. In 2017, Qiao and Hu investigated the distributivity equation I (x , O 1 (y , z )) = O 2 (I (x , y ), I (x , z )), when O 1 and O 2 are additively generated overlap functions and I is an unknown function. In this paper, this kind of distributivity equation continues to be studied at the situation that both O …1 and O 2 are multiplicatively generated overlap functions and I is a continuous function. Unfortunately, there is no continuous solution for this distributivity equation that is fuzzy implication, but a characterization for the case that I is continuous except for the point (0, 0) is given. More importantly, some solutions to the system of functional equations consisting of I (x , O 1 (y , z )) = O 2 (I (x , y ), I (x , z )) and I (x , y ) = I (N (y ), N (x )) are characterized. Finally, considered any other overlap functions, sufficient and necessary conditions, under which the previous distributivity equation holds when O 1 is an idempotent overlap function, O 2 is an Archimedean overlap function and I is an unknown function, are given. Meanwhile, some solutions to the system of functional equations are also presented. Show more

Keywords: Overlap functions, fuzzy implications, distributivity equations, contrapositive symmetry equations

DOI: 10.3233/JIFS-181279

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 283-294, 2019

Authors: Gulistan, Muhammad | Beg, Ismat | Yaqoob, Naveed

Article Type: Research Article

Abstract: There are many different techniques used so for in decision making problems. Some researchers used fuzzy sets, some used soft sets and some used combination of fuzzy sets with soft sets in order to handle the imprecise information. On the other hand, matrices play very important role in handling such problems. Different researchers used fuzzy matrices and fuzzy soft matrices in decision making problems. Some others generalized tools are Molodtsov’s soft sets, presented in 1999, Smarandache’s neutrosophic sets, in 1999, Jun’s cubic sets, in 2012 and Jun’s neutrosophic cubic sets in 2017. Our aim in this paper is to combine …the above mentioned generalized tools and develop a new generalize approach namely neutrosophic cubic soft matrices. We first introduce the idea of Neutrosophic cubic soft aggregation operators with the help of neutrosophic cubic soft sets and then present the notion of neutrosophic cubic soft matrices and at the end, we present a max-min decision making problem using neutrosophic cubic soft matrices. Show more

Keywords: Neutrosophic sets, cubic sets, soft sets, neutrosophic cubic soft sets, neutrosophic cubic soft matrices

DOI: 10.3233/JIFS-181296

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 295-307, 2019

Authors: Shakeel, M. | Abdullah, Saleem | Shahzad, M. | Amin, F. | Mahmood, T. | Amin, N.

Article Type: Research Article

Abstract: The aim of this paper is to investigate information aggregation methods under Pythagorean trapezoidal fuzzy environment. Some Einstein operational laws on Pythagorean trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. Based on Einstein operations we define Pythagorean trapezoidal fuzzy Einstein weighted geometric (PTFEWG) operator, Pythagorean trapezoidal fuzzy Einstein ordered weighted geometric (PTFEOWG) operator and Pythagorean trapezoidal fuzzy Einstein hybrid geometric (PTFEHG) operator. Furthermore, we apply the proposed aggregation operators to deal with multiple attribute group decision making. In the last we construct a numerical example for multiple attribute group decision making problem and compare the result …with existing method. Show more

Keywords: Trapezoidal fuzzy numbers, pythagorean trapezoidal fuzzy numbers, Einstein operation, aggregation operation and group decision making

DOI: 10.3233/JIFS-181329

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 309-324, 2019

Authors: Zeb, Aurang | Khan, Muhammad Sajjad Ali | Ibrar, Muhammad

Article Type: Research Article

Abstract: The aim of this paper is to introduce the concept of extended Pythagorean fuzzy set (EPFS) as a generalization of extended intuitionistic fuzzy set. Further we develop credible extended Pythagorean fuzzy set (C-EPFS) and possible extended Pythagorean fuzzy set (P-EPFS). Then we explore the fundamentals operations, expressions and the selection rule of C-EPFS and P-EPFS. We propose the corresponding aggregation operators and investigate the relationship among these operators. The credible extended Pythagorean fuzzy numbers (C-EPFNs) and possible extended Pythagorean fuzzy numbers (P-EPFNs) tends to aggregate the extreme and aggregating complete information respectively. Finally to show the applicability and effectiveness of …the proposed approach a preference risk decision making problem is given. Keywords: Extended Pythagorean fuzzy set (EPFS), credible extended Pythagorean fuzzy set (C-EPFS), possible extended Pythagorean fuzzy set (P-EPFS), decision making. Show more

Keywords: Extended Pythagorean fuzzy set (EPFS), credible extended Pythagorean fuzzy set (C-EPFS), possible extended Pythagorean fuzzy set (P-EPFS), decision making

DOI: 10.3233/JIFS-181385

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 325-335, 2019

Authors: Kutlu Gündoğdu, Fatma | Kahraman, Cengiz

Article Type: Research Article

Abstract: All the extensions of ordinary fuzzy sets with three dimensional membership functions such as intuitionistic fuzzy sets (IFS), intuitionistic fuzzy sets of second type (IFS2), and neutrosophic fuzzy sets (NFS) aim at defining the judgments of decision makers/ experts with a more detailed description. Introduction of generalized three dimensional spherical fuzzy sets (SFS) including some essential differences from the other fuzzy sets is presented in this paper. The new type of fuzzy sets is based on the spherical fuzzy distances which have been already defined in the literature. Arithmetic operations involving addition, subtraction and multiplication are presented together with their …proofs. Aggregation operators, score and accuracy functions are developed. The multi-criteria decision making method TOPSIS is extended to spherical fuzzy TOPSIS and an illustrative example is presented. Additionally, a comparative analysis with intuitionistic fuzzy TOPSIS (IF-TOPSIS) is given. Show more

Keywords: IFS, IFS2, NFS, spherical fuzzy sets, decision making, TOPSIS, distance measurement, ideal solution

DOI: 10.3233/JIFS-181401

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 337-352, 2019

Authors: Gu, Yujie | Hao, Qingwei | Shen, Jie | Zhang, Xiang | Yu, Liying

Article Type: Research Article

Abstract: Variance in fuzzy set theory, generally applied in investment decision, risk evaluation, and so on, can be described as a measurement that gauges the deviation of a fuzzy number. In this paper, in order to extend the application range and enrich the research area of variance, the concepts of variance bounds and semi-variances are defined and discussed from a theoretical point of view. With respect to some frequently-used fuzzy intervals, four relatively simple calculation formulas for upper and lower bounds of variance, and upside and downside semi-variances are put forward respectively, with the aid of which several correlation inequalities are …subsequently presented and proved. Besides, in order to depict the concepts and inequalities more distinctly, plenty of examples are introduced to make some numerical illustration. Show more

Keywords: Fuzzy interval, bounds of variance, semi-variance, inequalities

DOI: 10.3233/JIFS-181467

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 353-369, 2019

Authors: Fan, Jianping | Lan, Jinrong | Zhang, Jing | Wang, Zhan | Wu, Meiqin

Article Type: Research Article

Abstract: In the cross-efficiency model, when the decision making unit (DMU) self-evaluation efficiency value is optimal, the sets of input and output weights exhibit non-uniqueness, and the choice among alternative optimal solutions results in different peer- evaluation values, consequently leading to different cross-efficiency scores and rankings. In addition, the interval value constitutes the cross-efficiency value, which increases the uncertainty of the decision- making due to the information fuzziness. To solve this problem, a group decision-making method for cross-efficiency is proposed on the basis of hesitant fuzzy sets (HFSs). This method selects five optimal solutions. Moreover, given that the attitudes of decision-makers …range from pessimistic to optimistic, this method introduces HFSs to the cross-efficiency matrix, and obtains the multi-objective optimization method to rank the alternatives based on the relative closeness degree. Finally, a classical numerical example is provided to illustrate the potential applications of the proposed method and its effectiveness in ranking DMUs. Show more

Keywords: cross-efficiency, group decision-making, hesitant fuzzy set, attribute weight, relative closeness degree

DOI: 10.3233/JIFS-181477

Citation: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 371-383, 2019