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 study two important extensions of the classical minimum cut problem, called Connectivity Preserving Minimum Cut (CPMC) problem and Threshold Minimum Cut (TMC) problem, which have important applications in largescale DDoS attacks. In CPMC problem, a minimum cut is sought to separate a of source from a destination node and meanwhile preserve the connectivity between the source a...

This paper describes a fault tree technique based on generalized fuzzy numbers to a possibility distribution of reliability indices for power systems. Due to uncertainty in the collected data, all the failure probabilities are represented by generalized trapezoidal fuzzy number. In this paper, the fault-tree incorporated with the generalized trapezoidal fuzzy number and minimal cut sets approac...

Analytical Hierarchy Process (AHP), as a multiple criteria decision making tools especially in the problems with spatial nature or GIS-based. In addition this study treats the steps AHP, its manner to apply and its weaknesses and strengths and ultimately the fuzzy modified Analytical Hierarchy Process (FAHP) which is proposed after that the concepts like of fuzziness, uncertainty and vagueness ...

A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we introduce the concepts of Rough Fuzzy Neutrosophic Sets and Fuzzy Neutrosophic Rough Sets and investigate some of their pr...

The computational complexity of multicut-like problems may vary significantly depending on whether the terminals are fixed or not. In this work we present a comprehensive study of this phenomenon in two types of cut problems in directed graphs: double cut and bicut. 1. Fixed-terminal edge-weighted double cut is known to be solvable efficiently. We show that fixed-terminal node-weighted double c...

Consider a synchronized distributed system where each node can only observe the state of its neighbors. Such a system is called selfstabilizing if it reaches a stable global state in a finite number of rounds. Allowing two different states for each node induces a cut in the network graph. In each round, every node decides whether it is (locally) satisfied with the current cut. Afterwards all un...

Many of the new MV-valued fuzzy structures, including intuitionistic, neutrosophic, or soft sets, can be transformed into so-called almost or, equivalently, sets with values in dual pair semirings (in symbols, (R,R*)-fuzzy sets). This transformation allows any construction to retransformed an analogous for these structures. In that way, approximation theories rough theories, F-transform have al...

2. Fuzzy stochastic processes First we give some mathematical notations regarding fuzzy numbers. Let (Ω,M, P ) be a probability space, where M is a σ-field and P is a non-atomic probability measure. R denotes the set of all real numbers, and let C(R) be the set of all non-empty bounded closed intervals. A ‘fuzzy number’ is denoted by its membership function ã : R → [0, 1] which is normal, upper...