In this article, we introduce ST decomposition procedure to solve fully fuzzy linear systems. This paper mainly to discuss a decomposition of non singular fuzzy matrix, Symmetric times triangular(ST) decomposition. Every non singular fuzzy matrix can be represented as a product of symmetric matrix S and triangular matrix T in the form of trapezoidal fuzzy number matrices. By this method, we obt...

We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of interval-valued trapezoidal fuzzy numbers and, on the other hand, between the set of triangular intuitionistic fuzzy numbers and the set of triangular fuzzy numbers. Based on these main results of the paper, the methods or procedures elaborated for interval-valued trapezoidal or triangular fuzz...

In some multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. Fir...

In 2007, Zeng and Li proposed a weighted triangular approximation of a fuzzy number. Unfortunately, this approximation may fail to be a fuzzy number. In this paper, we improve this approximation and propose a generalization by the name of weighted trapezoidal approximation. Their algorithms are also presented. Finally, some examples and relevant properties are discussed. © 2009 Elsevier B.V. Al...

Methods for aggregating intuitionistic trapezoidal fuzzy information are investigated. Some operational laws of intuitionistic trapezoidal fuzzy numbers are introduced. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy ordered weighted averaging (ITFOWA) operator and intuitionistic trapezoidal fuzzy hybrid aggregation (ITFHA) operator, are p...

The aim of this paper is to investigate the multiple attribute decision making problems to deal with supplier selection with intuitionistic trapezoidal fuzzy information, in which the information about attribute weights is completely known, and the attribute values take the form of intuitionistic trapezoidal fuzzy number. We developed a multiple attribute decision making method by closeness to ...

The objective of the study is to present cosine similarity measure based multi-attribute decision making under neutrosophic environment. The assesments of alternatives over the attributes are expressed with trapezoidal fuzzy neutrosophic numbers in which the three independent components namely, truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F) ar...

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...

In some cases, our uncertainty about about a quantity can be described by an interval of its possible values. If we have two or more pieces of interval information about the same quantity, then we can conclude that the actual value belongs to the intersection of these intervals. In general, we may need a fuzzy number to represent our partial knowledge. A fuzzy number can be viewed as a collecti...

Product planning is one of four important processes in new product development (NPD) using quality function deployment (QFD), which is a widely used customer-driven approach. In our opinion, the first problem to be solved is how to incorporate both qualitative and quantitative information regarding relationships between customer requirements (CRs) and engineering characteristics (ECs) as well a...