Fundamenta Informaticae - Volume 165, issue 2

Authors: Peng, Xindong

Article Type: Research Article

Abstract: In this paper, we initiate some new operators for Pythagorean fuzzy set and discuss their properties in detail. Then, a new score function of Pythagorean fuzzy number (PFN) is proposed for solving the failure problems when comparing two PFNs. Later, we present an algorithm for solving multi-criteria decision making (MCDM) problem based on Weighted Distance Based Approximation (WDBA). Finally, the effectiveness and feasibility of approach is demonstrated by some numerical examples. The salient features of the proposed method, compared to the existing Pythagorean fuzzy decision making methods, are (1) it can derive a ranking without the complex process; (2) it …can obtain the optimal alternative without counterintuitive phenomena; (3) it has a great power in distinguishing the optimal alternative. Show more

Keywords: Pythagorean fuzzy set, operators, Pythagorean fuzzy number, score function, multi-criteria decision making, WDBA

DOI: 10.3233/FI-2019-1778

Citation: Fundamenta Informaticae, vol. 165, no. 2, pp. 99-137, 2019

Authors: Xu, Wen-Li | Lee, Jia | Chen, Hui-Hui | Isokawa, Teijiro

Article Type: Research Article

Abstract: A Brownian cellular automaton (BCA) is an asynchronous cellular automaton (ACA) in which local configurations representing signals may move forth and back randomly, as if they were undergoing random walks. The random fluctuation offers a natural mechanism to propagate signals in the 2-dimensional cell space, and to cross signals moving in directions perpendicular to each other. As a result, the BCA in (Lee et al., 2016) employs 4 cell states and 17 transition rules to conduct universal computation, both of which are less than other equivalent ACAs in the literature. This paper aims to advance the fluctuation-based scheme one step …further, via proposing a new BCA with 4 states and 14 rules that achieves a reduction in the number of transition rules. We show that the BCA is capable of implementing any arbitrary logic circuit, thereby proving its universality in computation. We illustrate this by implementing a circuit that converts a 4-bit number to its equivalent hexadecimal digit. Show more

Keywords: cellular automaton, asynchronous circuit, universal computation, number base conversion, random fluctuation

DOI: 10.3233/FI-2019-1779

Citation: Fundamenta Informaticae, vol. 165, no. 2, pp. 139-156, 2019

Authors: Yang, Bin | Hu, Bao Qing | Qiao, Junsheng

Article Type: Research Article

Abstract: Rough membership functions in covering approximation space not only give numerical characterizations of covering-based rough set approximations, but also establish the relationship between covering-based rough sets and fuzzy covering-based rough sets. In this paper, we give a new method to discuss three-way decisions with rough membership functions in covering approximation space. Firstly, we introduce three new types of rough membership functions and study their properties. And then, relationship between a covering and its derived fuzzy β-covering is investigated by using rough membership functions. In addition, we study the relationship among the four types of rough membership functions. Finally, a novel …type of graded covering-based rough set model is proposed on the basis of rough membership function. And, as an application, its corresponding three-way decisions in incomplete decision systems are investigated. Show more

Keywords: Fuzzy β-covering, Graded covering-based rough set, Neighborhood, Rough membership function, Three-way decisions

DOI: 10.3233/FI-2019-1780

Citation: Fundamenta Informaticae, vol. 165, no. 2, pp. 157-191, 2019