scholarly journals Trapezoidal Hesitant Intuitionistic Fuzzy Numbers and Their Applications to Multiple-Criteria Decision Making Problems

2021 ◽  
Author(s):  
Irfan Deli
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Criteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Support Set ◽  
Deviation Degree ◽  
Degree Deviation ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

Abstract In this paper, we introduce an extension theory of the trapezoidal intuitionistic fuzzy numbers under intuitionistic hesitant fuzzy sets called trapezoidal hesitant intuitionistic fuzzy number (THIF-number). This new theory provides very effectively to model uncertainties of some events by several different trapezoidal intuitionistic fuzzy numbers based on the same support set in the set of real numbers R. Also, to demonstrate the application of this theory, a new multi-criteria decision-making(MCDM) method based on THIF-numbers is presented. To do this, we first propose operations of THIF-numbers with properties. We second give score, standard deviation degree, deviation degree of THIF-numbers to compare THIF-numbers. We third develop geometric operators and arithmetic operators of THIF-number. Finally, a numerical example is presented to illustrate the application of the developed method in THIF-numbers.

scholarly journals A Value and Ambiguity-Based Ranking Method of Trapezoidal Intuitionistic Fuzzy Numbers and Application to Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xiang-tian Zeng ◽  
Deng-feng Li ◽  
Gao-feng Yu
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Implementation Process ◽  
Ranking Method ◽  
Comparison Analysis ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
A Value ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

The aim of this paper is to develop a method for ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) in the process of decision making in the intuitionistic fuzzy environment. Firstly, the concept of TrIFNs is introduced. Arithmetic operations and cut sets over TrIFNs are investigated. Then, the values and ambiguities of the membership degree and the nonmembership degree for TrIFNs are defined as well as the value-index and ambiguity-index. Finally, a value and ambiguity-based ranking method is developed and applied to solve multiattribute decision making problems in which the ratings of alternatives on attributes are expressed using TrIFNs. A numerical example is examined to demonstrate the implementation process and applicability of the method proposed in this paper. Furthermore, comparison analysis of the proposed method is conducted to show its advantages over other similar methods.

scholarly journals Decision making by the values of generalized average fuzzy functions

2012 ◽  
Vol 53 ◽  
Author(s):  
Natalja Kosareva ◽  
Aleksandras Krylovas
Keyword(s):  
Decision Making ◽  
Monte Carlo ◽  
Fuzzy Numbers ◽  
Multiple Criteria Decision Making ◽  
Monte Carlo Study ◽  
Weighted Averaging ◽  
Average Operator ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Averaging Operator

Notions of point, interval and triangular intuitionistic fuzzy numbers are introduced. The generalized weighted averaging operator is used for solving multiple criteria decision making problems. Monte Carlo study was conducted with the aim to establish for which types of intuitionistic fuzzy numbers and which exponent values of weighted generalized average operator probabilities of alternatives ranking errors are the least.

Arithmetic Behaviors of P-Norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers with Application to Circuit Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 6-58
Author(s):  
Sanhita Banerjee ◽  
Tapan Kumar Roy
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Circuit Analysis ◽  
Extension Principle ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Given ◽  
Trapezoidal Intuitionistic Fuzzy Number ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

P-norm Generalized Trapezoidal Intuitionistic Fuzzy Number is the most generalized form of Fuzzy as well as Intuitionistic Fuzzy Number. It has a huge application while solving various problems in imprecise environment. In this paper the authors have discussed some basic arithmetic operations of p-norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers using two different methods (extension principle method and vertex method) and have solved a problem of circuit analysis taking the given data as p-norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers.

scholarly journals A New Ranking Principle For Ordering Trapezoidal Intuitionistic Fuzzy Numbers

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-24 ◽  
Author(s):  
Lakshmana Gomathi Nayagam Velu ◽  
Jeevaraj Selvaraj ◽  
Dhanasekaran Ponnialagan
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Partial Ordering ◽  
Fuzzy Decision Making ◽  
Accuracy Score ◽  
Fuzzy Decision ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Area Score ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

Modelling real life (industrial) problems using intuitionistic fuzzy numbers is inevitable in the present scenario due to their efficiency in solving problems and their accuracy in the results. Particularly, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used in describing impreciseness and incompleteness of a data. Any intuitionistic fuzzy decision-making problem requires the ranking procedure for intuitionistic fuzzy numbers. Ranking trapezoidal intuitionistic fuzzy numbers play an important role in problems involving incomplete and uncertain information. The available intuitionistic fuzzy decision-making methods cannot perform well in all types of problems, due to the partial ordering on the set of intuitionistic fuzzy numbers. In this paper, a new total ordering on the class of TrIFNs using eight different score functions, namely, imprecise score, nonvague score, incomplete score, accuracy score, spread score, nonaccuracy score, left area score, and right area score, is achieved and our proposed method is validated using illustrative examples. Significance of our proposed method with familiar existing methods is discussed.

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