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...

Linear programming problems with trapezoidal fuzzy numbers have recently attracted much interest. Various methods have been developed for solving these types of problems. Here, following the work of Ganesan and Veeramani and using the recent approach of Mahdavi-Amiri and Nasseri, we introduce the dual of the linear programming problem with symmetric trapezoidal fuzzy numbers and establish some ...

In this paper we introduce an approach for solving multiattribute decision-making problems in which there are several decision-makers who individually and independently elicit their preferences. The preferences of each decision-maker are imprecise and represented by an imprecise additive multiattribute utility function. We allow for incomplete information on the component utility functions and ...

2 How to Create Instances of Fuzzy Numbers 3 2.1 Arbitrary Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Definition by Side Functions . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Definition by α-cut Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Definition with Generating Functions Omitted: Shadowed Sets . . . . . . 6 2.2 Us...

There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus ...

Fuzzy Set Theory has been applied in many fields such as Operations Research, Control Theory, and Management Sciences etc. In particular, an application of this theory in Managerial Decision Making Problems has a remarkable significance. In this Paper, we consider a solution of Rectangular Fuzzy game with pay-off as imprecise numbers instead of crisp numbers viz., interval and LR-type Trapezoid...

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...

Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation o...

In this paper, Symmetric Trapezoidal Intuitionistic Fuzzy Numbers (STIFNs) have been introduced and their desirable properties are also studied. A new type of intuitionistic fuzzy arithmetic operations for STIFN have been proposed based on ( , )   -cuts. A numerical example is considered to elaborate the proposed arithmetic operations. These operations find applications in solving linear prog...