Abstract In this paper, we consider the semidifferentiable case of an interval-valued minimization problem and establish sufficient optimality conditions Wolfe type as well Mond–Weir duality theorems under semilocal E -preinvex functions. Furthermore, present saddle-point criteria to relate optimal solution programming a saddle point Lagrangian function.

The aim of this paper is investigate the notion of a generalized interval valued intuitionistic fuzzy number (GIVIFN), which extends the interval valuedintuitionistic fuzzy number. Firstly, the concept of GIVIFNBs is introduced.Arithmetic operations and cut sets over GIVIFNBBs are investigated. Then the values and ambiguities of the membership degree and the non-membership degree and the value ...

In this paper we present a short but important summary of Pythagorean fuzzy sets. Especially we discuss several basic and important definitions of Pythagorean fuzzy sets, several operations on Pythagorean fuzzy sets, several algebraic laws of Pythagorean fuzzy sets. In the last we also present the concept of modal operators and normalization on Pythagorean fuzzy sets.

Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzyvalued, interval-valued or numeric-valued descriptive parameters using various me...

The earned value technique is a crucial and important technique in analysis and control the performance and progress of mega projects by integrating three elements of them, i.e., time, cost and scope. This paper proposes a new version of earned value analysis (EVA) to handle uncertainty in mega projects under interval-valued fuzzy (IVF)-environment. Considering that uncertainty is very common i...