The purpose of this article is to consider the notions of intuitionistic fuzzy soft matrices and some basic results. This work deals particularly with the definition of transpose of intuitionistic fuzzy soft matrices and then some properties of transpose of intuitionistic fuzzy soft matrices are studied. After that symmetric intuitionistic fuzzy matrices are also defined and some properties are discussed. Numerical examples are provided to make the concept clear.

The purpose of this article is to consider the notions of intuitionistic fuzzy soft matrices(IFSM) and to study some basic results associated with such matrices. This work deals particularly with the definition and some properties of transpose of intuitionistic fuzzy soft matrices. In the process, symmetric intuitionistic fuzzy matrix is also defined and some properties are discussed. Numerical examples are provided to make the concept clear.

In this paper, three new operations are introduced on intuitionistic fuzzy soft sets .They are based on concentration, dilatation and normalization of intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied.

In this article, we would like to revisit the existing definitions of cartesian product of fuzzy sets and the fuzzy relational matrix from the standpoint of the new definition of fuzzy sets on the basis of reference function. In the process it is observed that there are drawbacks in the current defintions and hence new definitions of terms mentioned are proposed in this article. Some numerical examples are also presented to make the matter clear and simple.

In this article, we would like to revisit and comment on the definition of complementation of fuzzy sets and also on some of the theories and formulas associated with this. Furthermore, the existing probability-possibility consistency principles are also revisited and related results are viewed from the standpoint of the Randomness-Fuzziness consistency principles. It is found that the existing definition of complementation as well as the probability – possibility consistency principles is not well defined. Consequently the results obtained from these would be inappropriate from our standpoints. Hence we would like to suggest some new definitions for some of the terms often used in the theory of fuzzy sets whenever possible.

In this paper we study fuzzy soft matrix based on reference function.Firstly, we define some new operations such as fuzzy soft complement matrix and trace of fuzzy soft matrix based on reference function.Then, we introduced some related properties, and some examples are given. Lastly, we define a new fuzzy soft matrix decision method based on reference function.

In this article, our main intention is to revisit the existing definition of complementation of fuzzy sets and thereafter various theories associated with it are also commented on. The main contribution of this paper is to suggest a new definition of complementation of fuzzy sets on the basis of reference function. Some other results have also been introduced whenever possible by using this new definition of complementation.

The main purpose of this article is to highlight the fact that there are some drawbacks in the existing definition of complementation of fuzzy sets and hence the geometrical representation of fuzzy sets on the basis of such definition which itself is defective would have no meaning. As a result the theorems or formulas which were rooted in the geometrical representation would become unacceptable and it is realized that in most cases of practical significance it is desirable to consider an additional requirement in defining fuzzy complement. It is important to mention here the fact that all these existing properties are being seen through the application of complementation of fuzzy sets which is rooted in the reference function. The current definition of complementation would infact remove those drawbacks and cosequently produce the results which seems to be logical.

In this article, we would like to revisit and comment on the widely used definition of cardinality of fuzzy sets. For this purpose we have given a brief description of the history of development of fuzzy cardinality. In the process, we can find that the existing definition fails to give a proper cardinality while dealing with complementation of fuzzy sets. So there arises the need of defining the cardinality in a different manner. Here a new definition of cardinality is proposed which is rooted in the definition of complementation of fuzzy sets on the basis of reference function. This definition of cardinality will inevitably play an important role in any problem area that involves complementation. Further, some important results are proven with the help of the proposed definition and it is found that these properties are somewhat analogus to those obtained with the help of the existing definition.

In this article, we would like to study the determinant theory of fuzzy matrices. The purpose of this article is to present a new way of expanding the determinant of fuzzy matrices and thereafter some properties of determinant are considered. Most of the properties are found to be analogus to the properties of determinant of matrices in crisp cases.

The main intention of this article is to represent fuzzy matrices with the help of reference function.Thereafter addition and multiplication of fuzzy matrices are defined keeping in pace with the newly represented fuzzy matrices. Here we study the determinant theory as well as the adjoint theory of square fuzzy matrices. The contribution of this article is to put forward a new way of expanding the determinant of fuzzy matrices and this process has led the foundation for defining the adjoint of square fuzzy matrices in a quite different way. In the process some properties of determinant as well as adjoint of fuzzy matrices are considered which are found to be almost analogus with the properties in crisp cases.

In this article, our main intention is to highlight the fact that the probable links between probability and possibility which were established by different authors at different point of time on the basis of some well known consistency principles cannot provide the desired result. That is why the paper discussed some prominent works for transformations between probability and possibility and finally aimed to suggest a new principle because none of the existing principles because none of them found the unique transformation. The new consistency principle which is suggested hereby would in turn replace all others that exist in the literature references by providing a reliable estimate of consistency between the two.Furthermore some properties of entropy of fuzzy numbers are also presented in this article.

Here at first we are going to give a brief history of the development of fuzzy entropy. Finally, new measures for entropy of fuzzy sets in continuous cases are introduced. In this article, our main purpose is to show that the entropy of fuzzy number is very much dependent on the selection of intervals. Another important thing which can be observed from the cases discussed is that the entropy of triangular fuzzy numbers is the same for the same choice of interval length and for non triangular fuzzy number this property does not hold.

Fuzzy matrices in the present form do not meet the most important requirement of matrix representatiom in the form of reference function without which no logical result can be expected. In this article, we intend to represent fuzzy matrices in which there would be the use of reference function. Our main purpose is to deal specially with complement of fuzzy matrices and some of its properties when our new definition of complementation of matrices is considered. For doing these the new definition of complementation of fuzzy sets based on reference function plays a very crucial role. Further, a new definition of trace of a fuzzy matrix is introduced in this article which is in accordance with newly defined fuzzy matrices with the help of reference function and thereby efforts have been made to establish some of the properties of trace of fuzzy matrices.