We introduce a composite optical lattice created by two mutually rotated square patterns and allowing observation of continuous transformation between incommensurate and completely periodic structures upon variation of the rotation angle θ. Such lattices acquire periodicity only for rotation angles cos θ = a/c, sin θ = b/c, set by Pythagorean triples of natural numbers (a, b, c). While linear e...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

This paper presents a method for determining all of the co-prime right angle triangles in the Euclidean field by looking at the intersection of the Pythagorean and Platonic right angle triangles and the corresponding lattice that this produces. The co-prime properties of each lattice point representing a unique right angle triangle are then considered. This paper proposes a conjunction between ...

With the deepening of uncertainty and fuzziness people’s understanding things, it becomes more convenient to use fuzzy decision making in evaluating schemes. These schemes not only include quantitative data but also consider evaluation information. In theory, Pythagorean set is extended, both which are less than or equal 1, increases scope application. This paper mainly studies selection green ...

ranking fuzzy numbers plays a very important role in decision making and some other fuzzy application systems. many different methods have been proposed to deal with ranking fuzzy numbers. constructing ranking indexes based on the centroid of fuzzy numbers is an important case. but some weaknesses are found in these indexes. the purpose of this paper is to give a new ranking index to rank vario...

In construction projects, a significant part of work is done by subcontractors (SCs). Therefore, their management main contractors (MCs) becomes an important issue as the density SCs created at sites. recent years, more focus on SC evaluation and selection in bidding process has been agenda whereas subject performance appraisal on-site during project execution phase untended literature. Thus, t...