Fuzzy decision making is the collection of single or multicriteria techniques aiming at selecting the best alternative in case of imprecise, incomplete, and vague data. This chapter reviews the fuzzy decision making literature and summarizes the review results by tabular and graphical illustrations. The classification is based on the new extensions of fuzzy sets: Intuitionistic, hesitant, and t...

On 2005, F. Smarandache generalized the Atanassov’s intuitionistic fuzzy setsto neutrosophic sets. Also, this author and some co-workers introduced the notion of interval neutrosophic set, which is an instance of neutrosophic set and studied various properties. The notion of neutrosophic topology on the non-standard interval is also due to Smarandache. We study in this paper relations between i...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on...

The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payoffs of TIFNs is introduced. A pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...

INTRODUCTION There have been a number of generalizations of metric spaces. One such generalization is Menger space introduced in 1942 by Menger[9] who used distribution functions instead of nonnegative real numbers as values of the metric. This space was expanded rapidly with the pioneering works of Schweizer and Sklar [11, 12]. Modifying the idea of Kramosil and Michalek [7], George and Veeram...

The author would like to thank Ioannis K. Vlachos, George D. Sergiadis [1] for providing some comments on the paper “Image thresholding using type II fuzzy sets” [2]. The main subject of the comments deals with the relationship between interval-values fuzzy sets (IVFSs) and the intuitionistic fuzzy sets (IFSs) on one side and the entropy measures introduced on the other side. Apparently, this i...

Interval-valued fuzzy sets are based on the algebra of subintervals of the unit interval [0, 1]. We study valuations as a special type of measures on this algebra. We present a description of all valuations which preserve the standard fuzzy negation and extend the identity on the elements of the form (x, x). Consequences for sublattices are formulated. Keywords— Girard algebra, interval-valued ...

In this paper, we present the interval neutrosophic logics which generalizes the fuzzy logic, paraconsistent logic, intuitionistic fuzzy logic and many other non-classical and non-standard logics. We will give the formal definition of interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. Then we give one application of interval neutrosophic logics to do appr...