Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core...

In recent work authors have proposed four new aggregation operators based on the arithmetic and geometric means of the Land Ror right side and left side apex angles for triangular [1] [2] and trapezoidal [3] [4] fuzzy numbers respectively. In this paper authors propose a new aggregation operator for TFNs in which the Land Rmembership function lines of the aggregate TFN have slopes which are the...

Two methods are proposed for correct and verifiable geometric reasoning using finite precision arithmetic. The first method, data normalization, transforms the geometric structure into a configuration for which all finite precision calculations yield correct answers. The second method, called the hidden variable method, constructs configurations that belong to objects in an infinite precision d...

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the idea of traditional arithmetic operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic weighted average (...

We present e cient representations and algorithms for accurate boundary computation on low-degree sculptured CSG solids using exact arithmetic. Previous approaches to this problem based entirely on oating-point arithmetic su er from severe robustness problems. We propose a general framework for precisely answering geometric queries on algebraic points, through the use of multivariate St urm se...