A new approach for ranking of interval type-2 trapezoidal fuzzy numbers

2017 ◽  
Vol 32 (3) ◽  
pp. 1891-1902 ◽  
Author(s):  
Yanbing Gong ◽  
Shuxin Yang ◽  
Liangliang Dai ◽  
Na Hu
Keyword(s):  
Fuzzy Numbers ◽  
New Approach ◽  
Trapezoidal Fuzzy Numbers ◽  
Interval Type

scholarly journals Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
A. Srinivasan ◽  
G. Geetharamani
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Trapezoidal Fuzzy Numbers ◽  
Degree Of Satisfaction ◽  
Linear Programming Problems ◽  
Interval Type ◽  
Perfectly Normal

Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example.

Type–reduction of Interval Type–2 fuzzy numbers via the Chebyshev inequality

2021 ◽  
Author(s):  
Juan Carlos Figueroa-García ◽  
Heriberto Román-Flores ◽  
Yurilev Chalco-Cano
Keyword(s):  
Fuzzy Numbers ◽  
Chebyshev Inequality ◽  
Type Reduction ◽  
Interval Type

scholarly journals Selection of solar tracking system using extended TOPSIS technique with interval type-2 pythagorean fuzzy numbers

2021 ◽  
Author(s):  
Rimsha Umer ◽  
Muhammad Touqeer ◽  
Abdullah Hisam Omar ◽  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
...  
Keyword(s):  
Fuzzy Numbers ◽  
Tracking System ◽  
Weighted Averaging ◽  
Distance Method ◽  
Novel Approach ◽  
Solar Tracking ◽  
Interval Type ◽  
Topsis Technique ◽  
Pythagorean Fuzzy Numbers

AbstractThe Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is considered among the most frequently used techniques to deal with multi-criteria group decision-making (MCGDM) conflicts. In this article, we have presented an extended TOPSIS technique in the framework of interval type-2 trapezoidal Pythagorean fuzzy numbers (IT2TrPFN). We first projected a novel approach to evaluate the distance between them using ordered weighted averaging operator and $$(\alpha ,\beta )$$ ( α , β ) -cut. Subsequently, we widen the concept of TOPSIS method formed on the distance method with IT2TrPFNs and applied it on MCGDM dilemma by considering the attitudes and perspectives of the decision-makers. Lastly, an application of solar tracking system and numerous contrasts with the other existing techniques are presented to express the practicality and feasibility of our projected approach.

scholarly journals A New Approach for Assessing Credit Risks under Uncertainty

2020 ◽  
Author(s):  
Teimuraz Tsabadze
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Metric Space ◽  
Theoretical Basis ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Initial Part ◽  
New Approach ◽  
Trapezoidal Fuzzy Numbers ◽  
Credit Risks

The purpose of this chapter is to introduce a new approach for an assessment of the credit risks. The initial part of the chapter is to briefly discuss the existing models of assessment of the credit risks and justify the need for a new approach. Since a new approach is created for conditions of uncertainty, we cannot do without fuzzy mathematics. The proposed approach is based on group decision-making, where experts’ opinions are expressed by trapezoidal fuzzy numbers. The theoretical basis of the offered approach is laid out in the metric space of trapezoidal fuzzy numbers. The new approach is introduced and discussed, and two realization algorithms are given. The toy example of application of the introduced approach is offered as well.

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