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This book has eleven chapters. Chapter one describes all types of natural class of intervals and the arithmetic operations on them. Chapter two introduces the semigroup of natural class of intervals using R or Zn and study the properties…

General Mathematics · Mathematics 2011-07-05 W. B. Vasantha Kandasamy , Florentin Smarandache

This book has four chapters. In the first chapter interval bistructures (biinterval structures) such as interval bisemigroup, interval bigroupoid, interval bigroup and interval biloops are introduced. Throughout this book we work only with…

General Mathematics · Mathematics 2011-08-12 W. B. Vasantha Kandasamy , Florentin Smarandache

A new approach for uncertainty management for fuzzy, rule based decision support systems is proposed: The domain expert's knowledge is expressed by a set of rules that frequently refer to vague and uncertain propositions. The certainty of…

Artificial Intelligence · Computer Science 2013-04-10 Christoph F. Eick

Fuzzy systems have good modeling capabilities in several data science scenarios, and can provide human-explainable intelligence models with explainability and interpretability. In contrast to transaction data, which have been extensively…

Databases · Computer Science 2021-03-31 Wensheng Gan , Zilin Du , Weiping Ding , Chunkai Zhang , Han-Chieh Chao

This book has five chapters. Chapter one is introductory in nature. Fuzzy linguistic spaces are introduced in chapter two. Fuzzy linguistic vector spaces are introduced in chapter three. Chapter four introduces fuzzy linguistic models. The…

General Mathematics · Mathematics 2012-03-06 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Amal

Based on the closed operational laws in picture fuzzy numbers and strict triangular norms, we extend the Bonferroni mean (BM) operator under the picture fuzzy environment to propose the picture fuzzy interactional Bonferroni mean (PFIBM),…

General Mathematics · Mathematics 2023-01-10 Lantian Liu , Xinxing Wu , Guanrong Chen

Following the definition of intuitionistic fuzzy n-norm [ 3 ], we have introduced the definition of intuitionistic fuzzy norm (in short IFN) over a linear space and there after a few results on intuitionistic fuzzy normed linear space and…

General Mathematics · Mathematics 2015-03-13 T. K. Samanta , Iqbal H. Jebril

A new fuzzy optimization framework that extends FCM causality is proposed. This model utilizes the dynamics to map data into metrics and create a framework that examines logical implication and hierarchy of concepts using a multiplex.…

Artificial Intelligence · Computer Science 2025-12-12 Alexis Kafantaris

In the complex landscape of multivariate time series forecasting, achieving both accuracy and interpretability remains a significant challenge. This paper introduces the Fuzzy Transformer (Fuzzformer), a novel recurrent neural network…

Artificial Intelligence · Computer Science 2025-10-02 Miha Ožbot , Igor Škrjanc , Vitomir Štruc

High utility itemset mining approaches discover hidden patterns from large amounts of temporal data. However, an inescapable problem of high utility itemset mining is that its discovered results hide the quantities of patterns, which causes…

Databases · Computer Science 2022-08-29 Shicheng Wan , Zhenqiang Ye , Wensheng Gan , Jiahui Chen

Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…

Artificial Intelligence · Computer Science 2025-10-20 Mark Burgin

Fuzzy modeling has many advantages over the non-fuzzy methods, such as robustness against uncertainties and less sensitivity to the varying dynamics of nonlinear systems. Data-driven fuzzy modeling needs to extract fuzzy rules from the…

Systems and Control · Computer Science 2018-06-08 Erick de la Rosa , Wen Yu

The purpose of this paper is to point to the usefulness of applying a linear mathematical formulation of fuzzy multiple criteria objective decision methods in organising business activities. In this respect fuzzy parameters of linear…

Artificial Intelligence · Computer Science 2007-05-23 Sonja Petrovic-Lazarevic , Ajith Abraham

Several deep learning (DL) approaches have been proposed to deal with image classification tasks. However, despite their effectiveness, they lack interpretability, as they are unable to explain or justify their results. To address the…

Computer Vision and Pattern Recognition · Computer Science 2025-04-07 Georgia Sovatzidi , Michael D. Vasilakakis , Dimitris K. Iakovidis

Generative Models (GMs), particularly Large Language Models (LLMs), have garnered significant attention in machine learning and artificial intelligence for their ability to generate new data by learning the statistical properties of…

Artificial Intelligence · Computer Science 2025-12-03 Hailong Yang , Zhaohong Deng , Wei Zhang , Zhuangzhuang Zhao , Guanjin Wang , Kup-sze Choi

In keeping with the definition that biotechnology is really no more than a name given to a set of techniques and processes, the authors apply some set of fuzzy techniques to chemical industry problems such as finding the proper proportion…

General Mathematics · Mathematics 2008-07-15 W. B. Vasantha Kandasamy , Florentin Smarandache

Neutrosophic theory and applications have been expanding in all directions at an astonishing rate especially after the introduction the journal entitled Neutrosophic Sets and Systems. New theories, techniques, algorithms have been rapidly…

Artificial Intelligence · Computer Science 2016-11-28 Florentin Smarandache , Surapati Pramanik

This research concerns the estimation of latent linear or polychoric correlations from fuzzy frequency tables. Fuzzy counts are of particular interest to many disciplines including social and behavioral sciences, and are especially relevant…

Methodology · Statistics 2022-11-22 Antonio Calcagnì

The approach described here allows to use the fuzzy Object Based Representation of imprecise and uncertain knowledge. This representation has a great practical interest due to the possibility to realize reasoning on classification with a…

Artificial Intelligence · Computer Science 2012-06-13 Mohamed Nazih Omri

This paper presents a Fuzzy Cognitive Map model to quantify implicit bias in structured datasets where features can be numeric or discrete. In our proposal, problem features are mapped to neural concepts that are initially activated by…

Machine Learning · Computer Science 2022-01-14 Gonzalo Nápoles , Isel Grau , Leonardo Concepción , Lisa Koutsoviti Koumeri , João Paulo Papa