Distance-based Information Granularity and Hierarchical Structure for an Intuitionistic Fuzzy Granular SpaceHuang, Bing; Li, Hua-Xiong; Feng, Guo-Fu; Zhuang, Yu-Liang
2016 Fuzzy Information and Engineering
doi: 10.1016/j.fiae.2016.06.002
AbstractInformation granularity and hierarchical structures in granular computing are the two main aspects for investigating the uncertainty and structure of all types of granular spaces. This study presents a distance-based information granularity for IF and multi-granulation IF granular spaces and use it to construct a novel hierarchical structure on such spaces. First, we propose a distance and a relative distance between two IF granular structures to differentiate them and use these two distances to generalize the axiomatic approach of fuzzy information granularity to the IF context. Second, we construct a hierarchical structure based on the relative distance between two IF granular structures to organize the IF granular space hierarchically. Third, we provide the multi-granulation IF granular space and study its relative-distance based axiomatic approach of IF information granularity. Fourth, we propose a relative-distance-based hierarchical structure on multi-granulation IF granular space.
Robustness of Fuzzy Reasoning Based on Schweizer–Sklar Interval-valued t-NormsLuo, Min-Xia; Cheng, Ze
2016 Fuzzy Information and Engineering
doi: 10.1016/j.fiae.2016.06.004
AbstractIn this paper, we focus on the parametric triple I algorithms by the combination of Schweizer–Sklar interval-valued operators and triple I principles for fuzzy reasoning. Firstly, we give the interval-valued triple I solutions based on Schweizer–Sklar interval-valued operators. Then, we investigate the sensitivity of Schweizer–Sklar interval-valued fuzzy connectives. Finally, we study the robustness of the triple I algorithms based on Schweizer–Sklar interval-valued t-norms (). It shows that the quality of interval-valued fuzzy reasoning algorithms depends on the selection of interval-valued fuzzy connectives.
Complete Ranking of Intuitionistic Fuzzy NumbersGomathi Nayagam, V. Lakshmana; Jeevaraj, S.; Sivaraman, Geetha
2016 Fuzzy Information and Engineering
doi: 10.1016/j.fiae.2016.06.007
AbstractFuzzy number was introduced by Dubois and Prade [10] to handle imprecise numerical quantities. Later it was generalized to intuitionistic fuzzy number by Burillo et al. [5]. Ranking intuitionistic fuzzy numbers plays an important role in decision making and information systems. All over the world many researchers have proposed different score functions for ranking intuitionistic fuzzy numbers but unfortunately every method produces some anti-intuitive results in certain places. A complete ranking on the entire class of fuzzy numbers have been achieved by W. Wang, Z. Wang [22] using upper dense sequence defined in . But a complete ranking on the set of all intuitionistic fuzzy number remains an open problem till today. Complete ranking on the class of intuitionistic fuzzy interval number was done by Geetha et al. [13]. In this paper, total ordering on the entire class of intuitionistic fuzzy number (IFN) using upper lower dense sequence is proposed and compared with existing techniques using illustrative examples. This new total ordering on intuitionistic fuzzy numbers (IFNs) generalizes the total ordering defined in W. Wang, Z. Wang [22] for fuzzy numbers (FNs).