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...

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...

We present a solution procedure for a quadratic programming problem with some probabilistic constraints where the model parameters are either triangular fuzzy number or trapezoidal fuzzy number. Randomness and fuzziness are present in some real-life situations, so it makes perfect sense to address decision making problem by using some specified random variables and fuzzy numbers. In the present...

In this paper, we aim to extended the constraints of Tanaka’s model. Applied coefficients of the fuzzy regression by them is the symmetric triangular fuzzy numbers, while we try to replace it by more general asymmetric trapezoidal one. Possibility of two asymmetric trapezoidal fuzzy numbers is explained by possibility distribution. Two different models is presented and a numerical example is gi...

In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserv...

Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. New operators that fulfill additional requirements for the core and support of the fuzzy number are suggested. These supplementary conditions guarantee the proper interpretation of the solution even for very skew original fuzzy numbers.

Multiplicative operations for fuzzy numbers raise several problems both from the theoretical and practical point of view in fuzzy arithmetic. The multiplication based on Zadeh's extension principle and its triangular and trapezoidal approximation is used in several recent works in applications in geology. Recently, new product-type operation are introduced and studied, as e.g. the cross product...