Pythagorean triples can be represented by points of the unit circle with rational coordinates. These form an abelian group, and we describe its structure. This structural description yields enumeration normalized a given hypotenuse. It also gives rise to effective method for producing all such triples, this seems new.This paper is intended general mathematical audience, including undergraduate ...

in this paper, a novel method for ranking of fuzzy numbers are proposed. in this method, decision maker is defined based on the center of mass at some cuts of a pair of fuzzy numbers in discreet version and center of mass on all of cuts of a pair of fuzzy numbers in continuous version. our method can rank more than two fuzzy numbers simultaneously. also, some properties of methods are described...

Fuzzy set theory has much application in different fields; therefore several scholars are working in this area. In fuzzy set theory the most important topic for research is aggregation operators. Therefore in this notes we present the concept of Pythagorean fuzzy ordered weighted geometric aggregation operator, and also discuss many basic and important properties of the propose operator. At the...

Pythagorean fuzzy sets (PyFSs) are an essential tool for characterizing data in decision-making processes. In contrast to normal structures, PyFSs feature a sum of squares membership grades that is near unit interval, which increases uncertainty. Within environment, we intend build unique operational rules and aggregation operators (AOs) this proposed work. The work presents; notions, rules, pr...

in this paper, by using a new approach on distance between two fuzzy numbers, we construct a new ranking system for fuzzy number which is very realistic and also matching our intuition as the crisp ranking system on r.

fuzzy measures are suitable in analyzing human subjective evaluation processes. several different strategies have been proposed for distance of fuzzy numbers. the distances introduced for fuzzy numbers can be categorized in two groups:1. the crisp distances which explain crisp values for the distance between two fuzzy numbers.2. the fuzzy distance which introduce a fuzzy distance for normal fuz...

We address the question of the “partition regularity” of the Pythagorean equation a+b = c; in particular, can the natural numbers be assigned a 2-coloring, so that no Pythagorean triple (i.e., a solution to the equation) is monochromatic? We prove that the hypergraph of Pythagorean triples can contain no Steiner triple systems, a natural obstruction to 2-colorability. Then, after transforming t...