Fundamenta Informaticae - Volume 147, issue 4

Authors: Magott, Jan | Skrobanek, Paweł

Article Type: Research Article

Abstract: Time aspects play an essential role in real-time systems. One of the most often used techniques of designing real-time systems is the timed statecharts (TSCs) technique. In this paper, new timed statecharts based on UML notation are introduced. The main difference between the UML statecharts and the TSCs presented in the paper is the pair of minimal and maximal execution times assigned to states of the TSCs. Additionally, any interaction can be characterized by its minimal and maximal duration time. Moreover, the paper presents semantics for TSCs, emphasizing time aspects rather than variable valuation. The minimal and maximal execution time …problem (MMETP) for TSCs is defined and the computational complexity of the MMETP is studied. It is proven in this paper that there is a limit between such TSCs for which there exists a polynomial algorithm for MMETP and such TSCs for which MMETP remains NP-hard. The mentioned limit is located between the AND state with any number of XOR states that are expressed by simple paths without guards and the AND state with two XOR states with no limitations. Since the MMETP is NP-hard, it is reasonable to use structural reductions of TSCs. A Theorem that is the theoretical foundation of a program loop reduction is proven. Show more

Keywords: real-time systems, performance evaluation, statecharts, computational complexity, UML

DOI: 10.3233/FI-2016-1414

Citation: Fundamenta Informaticae, vol. 147, no. 4, pp. 387-414, 2016

Authors: Peng, Xindong | Yuan, Huiyong

Article Type: Research Article

Abstract: In this paper, some new inequalities of Pythagorean fuzzy weighted averaging (PFWA) operator are explored. Later, we develop some Pythagorean fuzzy point operators and introduce generalized Pythagorean fuzzy weighed averaging (GPFWA) operator. Moreover, combining the Pythagorean fuzzy point operators with GPFWA operator, we present some generalized Pythagorean fuzzy point weighted averaging (GPFPWA) operators, which can adjust the degree of the aggregated arguments with some parameters. Based on GPFPWA operators and normal distribution, an approach to multiple attribute decision making (MADM) problem with completely unknown weight information is proposed under Pythagorean fuzzy environment. Finally, an illustrative example is given to show …the feasibility and superiority of the developed method. Show more

Keywords: Pythagorean fuzzy weighted averaging operator, Pythagorean fuzzy point operators, generalized Pythagorean fuzzy point weighed averaging operators

DOI: 10.3233/FI-2016-1415

Citation: Fundamenta Informaticae, vol. 147, no. 4, pp. 415-446, 2016

Authors: Poklukar, Darja Rupnik | Žerovnik, Janez

Article Type: Research Article

Abstract: Reliability Hosoya-Wiener polynomial for edge weighted graphs is defined, that can be used as a measure of reliability of a communication network. Each edge is assigned two weights, reliability and communication delay. Some basic properties are given and a recursive formula for the reliability Hosoya-Wiener polynomial of a rooted tree is proved that yields a linear time algorithm on weighted trees. On general graphs, the reliability Hosoya-Wiener polynomial can be computed in O (n 3 ) time.

Keywords: communication network, reliability Hosoya-Wiener polynomial

DOI: 10.3233/FI-2016-1416

Citation: Fundamenta Informaticae, vol. 147, no. 4, pp. 447-456, 2016

Authors: Zhang, Xiawei | Kong, Qingzhao

Article Type: Research Article

Abstract: The generalization of Pawlak rough sets is one of the most important directions of rough set theory. In this paper, we propose four types of multi-covering rough set (MCRS) models by combining multi-granulation rough sets with covering rough sets. In the first place, We propose two types of optimistic MCRS models and study their corresponding properties, and then propose another two types of the pessimistic MCRS models and study their corresponding properties as well. Finally, the relationships among the four types of MCRS and the interrelationships between the proposed MCRS models and the existing ones listed in [8] are further …investigated. Show more

Keywords: Rough set, multi-covering, approximation operators

DOI: 10.3233/FI-2016-1417

Citation: Fundamenta Informaticae, vol. 147, no. 4, pp. 457-476, 2016

Authors: Zhang, Yan-Lan | Li, Jinjin | Li, Changqing

Article Type: Research Article

Abstract: Rough set theory is an important tool to deal with vagueness and granularity in information systems. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough set approximations is based on equivalence relations and has been extended to relation-based generalized rough set approximations. In this paper, properties of relation-based generalized rough set approximations are examined, and topological properties of relation-based generalized rough set approximations presents. Necessary and sufficient conditions for the relation-based generalized upper (lower) approximation operators to be topological closure (interior) operators are proposed.

Keywords: approximation operator, closure operator, generalized rough set, topology

DOI: 10.3233/FI-2016-1418

Citation: Fundamenta Informaticae, vol. 147, no. 4, pp. 477-491, 2016

Article Type: Other

Citation: Fundamenta Informaticae, vol. 147, no. 4, pp. 493-494, 2016