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Memory-based collaborative filtering is the most popular approach to build recommender systems. Despite its success in many applications, it still suffers from several major limitations, including data sparsity. Sparse data affect the quality of the user similarity measurement and consequently the quality of the recommender system. In this paper, we propose a novel user similarity measure based on fuzzy set theory along with default voting technique aimed to provide a valid similarity measurement between users wherever the available ratings are relatively rare. The main idea of this research is to model the rating behaviour of each user by a fuzzy set, and use this model to determine the user's degree of interest on items. Experimental results on the MovieLens and Netflix datasets show the effectiveness of the proposed algorithm in handling data sparsity problem. It also outperforms some state-of-the-art collaborative filtering algorithms in terms of prediction quality.

In this paper, we introduce and study notions like state-\linebreak distinguishability, input-distinguishability and output completeness of states of a crisp deterministic fuzzy automaton. We show that for each crisp deterministic fuzzy automaton there corresponds a unique (up to isomorphism), equivalent distinguished crisp deterministic fuzzy automaton. Finally, we introduce two axioms related to output completeness of states and discuss the interrelationship between them.

The development of life time analysis started back in the $20^{textit{th}}$ century and since then comprehensive developments have been made to model life time data efficiently. Recent development in measurements shows that all continuous measurements can not be measured as precise numbers but they are more or less fuzzy. Life time is also a continuous phenomenon, and has already been shown that life time observations are not precise measurements but fuzzy. Therefore, the corresponding analysis techniques employed on the data require to consider fuzziness of the observations to obtain appropriate estimates.In this study generalized estimators for the parameters and hazard rates are proposed for bathtub failure rate distributions to model fuzzy life time data effectively.

This paper considers the problem of adaptive output feedback tracking control for a class of nonstrict-feedback nonlinear systems with unknown time-varying delays and unknown backlash-like hysteresis. Fuzzy logic systems are used to estimate the unknown nonlinear functions. Based on the Lyapunov–Krasovskii method, the control scheme is constructed by using the backstepping and adaptive technique. The proposed adaptive controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin. Finally, Simulation results further show the effectiveness of the proposed approach.

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.

In this paper, the notion of $L$-convex fuzzy sublattices is introduced and their characterizations are given. Furthermore, the notion of the degree to which an $L$-subset is an $L$-convex fuzzy sublattice is proposed and its some characterizations are given. Besides, the $L$-convex fuzzy sublattice degrees of the homomorphic image and pre-image of an $L$-subset are studied. Finally, we obtain an $L$-fuzzy convexity, which is induced by the $L$-convex fuzzy sublattice degrees, in the sense of Shi and Xiu.

The present paper has been an attempt to investigate the general fuzzy automata on the basis of complete residuated lattice-valued ($L$-GFAs). The study has been chiefly inspired from the work by Mockor cite{15, 16, 17}. Regarding this, the categorical issue of $L$-GFAs has been studied in more details. The main issues addressed in this research include: (1) investigating the relationship between the category of $L$-GFAs and the category of non-deterministic automata (NDAs); as well as the relationship between the category of generalized $L$-GFAs and the category of NDAs; (2) demonstrating the existence of isomorphism between the category of $L$-GFAs and the subcategory of generalized $L$-GFAs and between the category of $L$-GFAs and the category of sets of NDAs; (3) and further scrutinizing some specific relationship between the output $L$-valued subsets of generalized $L$-GFAs and the output $L$-valued of NDAs.

In this paper, we introduce fruitful concepts of common limit range and joint common limit range for coupled mappings on modified intuitionistic fuzzy metric spaces. An illustrations are also given to justify the notion of common limit range and joint common limit range property for coupled maps. The purpose of this paper is to prove fixed point results for coupled mappings on modified intuitionistic fuzzy metric spaces. Moreover, we extend the notion of common limit range property and E.A property for coupled maps on modified intuitionistic fuzzy metric spaces. As an application, we extend our main result to integral type contraction condition and also for finite number of mappings on modified intuitionistic fuzzy metric spaces.

Representation of a granule, relation and operation between two granules are mainly researched in granular computing. Hyperbox granular computing classification algorithms (HBGrC) are proposed based on interval analysis. Firstly, a granule is represented as the hyperbox which is the Cartesian product of $N$ intervals for classification in the $N$-dimensional space. Secondly, the relation between two hyperbox granules is measured by the novel positive valuation function induced by the two endpoints of an interval, where the operations between two hyperbox granules are designed so as to include granules with different granularity. Thirdly, hyperbox granular computing classification algorithms are designed on the basis of the operations between two hyperbox granules, the fuzzy inclusion relation between two hyperbox granules, and the granularity threshold. We demonstrate the superior performance of the proposed algorithms compared with the traditional classification algorithms, such as, Random Forest (RF), Support Vector Machines (SVMs), and Multilayer Perceptron (MLP).

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