The fuzzy cross entropy of intuitionistic fuzzy sets, so-called intuitionistic cross entropy, is introduced by analogy with the cross entropy of probability distributions. This paper introduces the concepts of discrimination information and cross-entropy in the intuitionistic fuzzy sets. Based on this improved entropy measure, we add information of hesitation and reveal an intuitive and mathema...

Intuitionistic fuzzy linguistic numbers (IFLNs) are an extension of the linguistic variables and the intuitionistic fuzzy sets, which are proposed by Wang and Li (Wang J.Q., Li J.J. (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Science & Technology Information (33), 8-9.). In this paper, we introduced some operational laws of IFL...

In this paper, newly defined level operators and modal-like operators over extensional generalized intuitionistic fuzzy sets (GIFSB) are proposed. Some of the basic properties of the new operators are discussed.

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzyHv-submodules of anHv-module with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated.In particular, the connections between interval valued in...

Information theory was introduced by Shannon in 1948 and it includes the study of uncertainty measures. Analogous to information theory which is founded on probability theory, notion of fuzzy sets was established by Zadeh in 1965 which is a mechanism to manage uncertainty. The pedestal for present study is information theory with intuitionistic fuzzy sets. Atanassov (1986) devised Intuitionisti...

As an abstraction of the geometrical notion of translation, the first author has already introduced two operators T+ and T-called the intuitionistic fuzzy translation operators on the intuitionistic fuzzy sets and studied their properties and investigate theaction of these operators on intuitionistic fuzzy subgroups of a group in [11]. The concept of intuitionistic M-fuzzy subgrou...

Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets,...

in this paper we determine the sequences of join spaces and atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.