Approximations in hypergroups and fuzzy hypergroups

AbstractThe first part of this paper represents a continuation of the study of approximations in a hypergroup. We analyse the lower and upper approximations of a subset in a hypergroup, with respect to some operators, particularly the completeness operator. In the last part, we introduce and analyse the lower and upper approximation of a subset in a fuzzy hypergroup

New Trends in Neutrosophic Theory and Applications Volume II

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Single valued neutrosophic sets have found their way into several hybrid systems, such as neutrosophic soft set, rough neutrosophic set, neutrosophic bipolar set, neutrosophic expert set, rough bipolar neutrosophic set, neutrosophic hesitant fuzzy set, etc. Successful applications of single valued neutrosophic sets have been developed in multiple criteria and multiple attribute decision making. This second volume collects original research and application papers from different perspectives covering different areas of neutrosophic studies, such as decision making, graph theory, image processing, probability theory, topology, and some theoretical papers. This volume contains four sections: DECISION MAKING, NEUTROSOPHIC GRAPH THEORY, IMAGE PROCESSING, ALGEBRA AND OTHER PAPERS. First paper (Pu Ji, Peng-fei Cheng, Hongyu Zhang, Jianqiang Wang. Interval valued neutrosophic Bonferroni mean operators and the application in the selection of renewable energy) aims to construct selection approaches for renewable energy considering the interrelationships among criteria. To do that, Bonferroni mean (BM) and geometric BM (GBM) are employed

Evaluation of the impact of the indiscernibility relation on the fuzzy-rough nearest neighbours algorithm

Fuzzy rough sets are well-suited for working with vague, imprecise or uncertain information and have been succesfully applied in real-world classification problems. One of the prominent representatives of this theory is fuzzy-rough nearest neighbours (FRNN), a classification algorithm based on the classical k-nearest neighbours algorithm. The crux of FRNN is the indiscernibility relation, which measures how similar two elements in the data set of interest are. In this paper, we investigate the impact of this indiscernibility relation on the performance of FRNN classification. In addition to relations based on distance functions and kernels, we also explore the effect of distance metric learning on FRNN for the first time. Furthermore, we also introduce an asymmetric, class-specific relation based on the Mahalanobis distance which uses the correlation within each class, and which shows a significant improvement over the regular Mahalanobis distance, but is still beaten by the Manhattan distance. Overall, the Neighbourhood Components Analysis algorithm is found to be the best performer, trading speed for accuracy

Using Granule to Search Privacy Preserving Voice in Home IoT Systems

The Home IoT Voice System (HIVS) such as Amazon Alexa or Apple Siri can provide voice-based interfaces for people to conduct the search tasks using their voice. However, how to protect privacy is a big challenge. This paper proposes a novel personalized search scheme of encrypting voice with privacy-preserving by the granule computing technique. Firstly, Mel-Frequency Cepstrum Coefficients (MFCC) are used to extract voice features. These features are obfuscated by obfuscation function to protect them from being disclosed the server. Secondly, a series of definitions are presented, including fuzzy granule, fuzzy granule vector, ciphertext granule, operators and metrics. Thirdly, the AES method is used to encrypt voices. A scheme of searchable encrypted voice is designed by creating the fuzzy granule of obfuscation features of voices and the ciphertext granule of the voice. The experiments are conducted on corpus including English, Chinese and Arabic. The results show the feasibility and good performance of the proposed scheme

Multi-Objective Modeling and Simulation for Decision Report

Modeling and simulation of various physical, environmental or socioeconomic processes is often a preliminary step for using the resulting models in decision support. With the advancements of computing technology and the methodology of decision support, it is now necessary to revise basic approaches to modeling and simulation: from the very beginning of model construction, they should aim at multi-objective analysis of the model while taking into account various optimization, sensitivity analysis and symbolic manipulation techniques treated as tools of such an analysis, not as goals. The paper illustrates how such an approach could increase the opportunities of comprehensive analysis of a model from a selected class -- as an example, the class of nonlinear dynamic discrete-time models was chosen. A user-friendly format of formulating such models is discussed together with related problems of inverse, constrained and multi-objective simulation as well as structural differentiation and sensitivity analysis, fuzzy set processing and other related issues. As a new tool for the analysis of boundaries of sets generated by such models -- for example. the a-level sets of fuzzy membership functions -- an interactive method of using an elastic "electronic pencil" is proposed

The Singular Value Decomposition over Completed Idempotent Semifields

In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD). These algebras are already complete lattices and many of their instances—the complete schedule algebra or completed max-plus semifield, the tropical algebra, and the max-times algebra—are useful in a range of applications, e.g., morphological processing. We further the task of eliciting the relation between i-SVD and the extension of Formal Concept Analysis to complete idempotent semifields (K-FCA) started in a prior work. We find out that for a matrix with entries considered in a complete idempotent semifield, the Galois connection at the heart of K-FCA provides two basis of left- and right-singular vectors to choose from, for reconstructing the matrix. These are join-dense or meet-dense sets of object or attribute concepts of the concept lattice created by the connection, and they are almost surely not pairwise orthogonal. We conclude with an attempt analogue of the fundamental theorem of linear algebra that gathers all results and discuss it in the wider setting of matrix factorization.This research was funded by the Spanish Government-MinECo project TEC2017-84395-P and the Dept. of Research and Innovation of Madrid Regional Authority project EMPATIA-CM (Y2018/TCS-5046)