This paper presents two new types of fuzzy shortest-path network problems. We consider the edge weight of the network as uncertain, which means that it is either imprecise or unknown. Thus, the first type of fuzzy shortest-path problem uses triangular fuzzy numbers for the imprecise problem. The second type uses level (1 − β, 1 − α) interval-valued fuzzy numbers, which are based on past statist...

The aim of each company/industry is to provide a final product customers at the minimum possible cost, as well protect environment from degradation. Ensuring shortest travel distance between involved locations plays an important role in achieving company’s/industry’s objective (i) cost can be minimized by minimizing total travelled (ii) finding will require less fuel than longest locations. Thi...

Among several interesting number triangles that exist in mathematics, Pascal’s triangle is one of the best possessing rich mathematical properties. In this paper, I will introduce a containing triangular numbers arranged particular fashion. Using triangle, had proved five theorems which help us to generate Pythagorean triples as well establish bijection between whole and set all integers.

In this paper, (α,β)-interval valued set is studied. The order relation on defined. It shown that complete lattice by giving the definitions of infumum and supremum these sets. Then, negation function sets introduced. 
 With help ,(α,β)-interval intuitionistic fuzzy are fundamental algebraic properties examined. level subsets given. Some propositions examples

In this paper, the problem of measuring the degree of inclusion and similarity measure for two   interval-valued intuitionistic  fuzzy sets is considered. We propose inclusion and similarity measure by using  order on interval-valued intuitionistic fuzzy sets connected with lexicographical order. Moreover, some properties of inclusion and similarity measure and some correlation, between them an...