We give some sufficient conditions such that a crisp, interval, triangular, trapezoidal, parametric approximation of a fuzzy number, with or without additional requirements, to have the properties of invariance to translations or scale invariance.

In this paper, we want represented a method for ranking of two exponential trapezoidal fuzzy numbers with TRD distance. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of exponential trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems.

In the present paper, a new entropy of order and type on Interval-Valued Intutionistic Fuzzy Sets (IVIFSs) along with their proofs of validity is proposed. It has been proved that the proposed entropy has monotonic decreasing behavior with respect to and . Further, a new algorithm for multiple attribute decision making method (MADM) has been provided using the benefit attributes and cost attrib...

The degree of similarity or dissimilarity between the objects under study plays an important role. In vector space, especially, the cosine similarity measure is often used in information retrieval, citation analysis, and automatic classification. However, it scarcely deals with trapezoidal fuzzy information and multicriteria decision-making problems. For this purpose, a cosine similarity measur...

To make the analysis more consistent and logical according to real life situations, in thispaper, the concept of trapezoidal vague set is extended by the idea of trapezoidal vaguesets of type-II. Also we have introduced: definition of trapezoidal vague set of type-IIand arithmetic operations between two trapezoidal vague sets of type-II. Further, a newmethod has been developed f...

Intuitionistic Fuzzy numbers each of which is characterized by the degree of membership and the degree of non-membership of an element are a very useful means to depict the decision information in the process of decision making. The aim of this article is to investigate the approach to multiple attribute group decision making with intuitionistic trapezoidal fuzzy numbers, some operational laws ...