scholarly journals Generalized Triangular Intuitionistic Fuzzy Geometric Averaging Operator for Decision Making in Engineering

2017 ◽  
Author(s):  
Daniel O. Aikhuele ◽  
Sarah Odofin
Keyword(s):  
Decision Making ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
New Approach ◽  
Intuitionistic Fuzzy ◽  
Averaging Operator ◽  
Different Dimensions ◽  
Evaluation Information

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

ELECTRE Method Based on Interval-Valued Intuitionistic Fuzzy Number

2012 ◽  
Vol 220-223 ◽  
pp. 2308-2312 ◽  
Author(s):  
Jun Li ◽  
Min Lin ◽  
Jian Hua Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Preference Relation ◽  
Intuitionistic Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy ◽  
Electre Method ◽  
Deviation Degree ◽  
Interval Valued

A new multi-criteria decision-making method for interval-valued intuitionistic fuzzy number is proposed by the advantage of intuitionistic fuzzy set and ELECTRE method. Firstly, the possibility-degree and deviation-degree of interval number are used to establish the preference relation of interval-valued intuitionistic fuzzy number. Then, we exposit the decision theory and the steps of this method. Finally, a numerical example is given to illustrate the application of the method. The numerical results show that it is feasible and effective.

scholarly journals A Novel Method for Dynamic Multicriteria Decision Making with Hybrid Evaluation Information

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shihu Liu ◽  
Tauqir Ahmed Moughal
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Ideal Solutions ◽  
Interval Valued ◽  
Evaluation Information

How to select the most desirable pattern(s) is often a crucial step for decision making problem. By taking uncertainty as well as dynamic of database into consideration, in this paper, we construct a dynamic multicriteria decision making procedure, where the evaluation information of criteria is expressed by real number, intuitionistic fuzzy number, and interval-valued intuitionistic fuzzy number. During the process of algorithm construction, the evaluation information at all time episodes is firstly aggregated into one, and then it is transformed into the unified interval-valued intuitionistic fuzzy number representational form. Similar to most multicriteria decision making approaches, the TOPSIS method is applied in the proposed decision making algorithm. In particular, the distance between possible patterns and the ideal solutions is defined in terms of cosine similarity by considering all aspects of the unified evaluation information. Experimental results show that the proposed decision making approach can effectively select desirable pattern(s).

scholarly journals Aggregation Operators on Triangular Intuitionistic Fuzzy Numbers and its Application to Multi-Criteria Decision Making Problems

2014 ◽  
Vol 39 (3) ◽  
pp. 189-208 ◽  
Author(s):  
Changyong Liang ◽  
Shuping Zhao ◽  
Junling Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
New Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number

Abstract The aim of this work is to present some aggregation operators with triangular intuitionistic fuzzy numbers and study their desirable properties. Firstly, the score function and the accuracy function of triangular intuitionistic fuzzy number are given, the method for ranking triangular intuitionistic fuzzy numbers are developed. Then, some geometric aggregation operators for aggregating triangular intuitionistic fuzzy numbers are developed, such as triangular intuitionistic fuzzy weighted geometric (TIFWG) operator, the triangular intuitionistic fuzzy ordered weighted geometric (TIFOWG) operator and the triangular intuitionistic fuzzy hybrid geometric (TIFHG) operator. Moreover, an application of the new approach to multi-criteria decision making method was proposed based on the geometric average operator of TIFNs, and the new ranking method for TIFNs is used to rank the alternatives. Finally, an example analysis is given to verify and demonstrate the practicality and effectiveness of the proposed method.

Generalized Archimedean Intuitionistic Fuzzy Averaging Aggregation Operators and their Application to Multicriteria Decision-Making

2016 ◽  
Vol 15 (02) ◽  
pp. 311-352 ◽  
Author(s):  
Chunqiao Tan ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Multiple Criteria Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Triangular Norm ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Averaging Operator ◽  
Fuzzy Aggregation

Aggregation operators play a key role in multiple criteria decision-making (MCDM). Extensions of aggregation operators to intuitionistic fuzzy sets (IFSs) usually involve replacing the standard arithmetic operations with those defined over the membership and nonmembership of IFS, which is essentially a pair of special Archimedean triangular norm (t-norm) and triangular conorm (t-conorm), called probabilistic sum t-conorm and product t-norm, on the membership and nonmembership of IFS, respectively. In this paper, we first introduce some operations on IFSs by means of Archimedean t-norm and t-conorm. Then some generalized Archimedean intuitionistic fuzzy aggregation operators are proposed, such as generalized Archimedean intuitionistic fuzzy weighted averaging operator, generalized Archimedean intuitionistic fuzzy ordered weighted averaging (GAIFOWA) operator, and generalized Archimedean intuitionistic fuzzy hybird averaging operator. Some desirable properties of these operators are investigated. The relations between these operators and the existing intuitionistic fuzzy aggregation operators are discussed. Finally, applying these proposed operators, we develop an approach for multi-criteria decision-making with intuitionistic fuzzy information, an illustrative example is used to verify the developed approach and to demonstrate its practicality and effectiveness.

scholarly journals Distance Based Entropy Measure of Interval-Valued Intuitionistic Fuzzy Sets and Its Application in Multicriteria Decision Making

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Tabasam Rashid ◽  
Shahzad Faizi ◽  
Sohail Zafar
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Fuzzy entropy means the measurement of fuzziness in a fuzzy set and therefore plays a vital role in solving the fuzzy multicriteria decision making (MCDM) and multicriteria group decision making (MCGDM) problems. In this study, the notion of the measure of distance based entropy for uncertain information in the context of interval-valued intuitionistic fuzzy set (IVIFS) is introduced. The arithmetic and geometric average operators are firstly used to aggregate the interval-valued intuitionistic fuzzy information provided by the decision makers (DMs) or experts corresponding to each alternative, and then the fuzzy entropy of each alternative is calculated based on proposed distance measure. Several numerical examples are solved to demonstrate the application to MCDM and MCGDM problems to show the effectiveness of the proposed approach.

scholarly journals New Ranking Functions for Interval-Valued Intuitionistic Fuzzy Sets and Their Application to Multi-Criteria Decision-Making Problem

2021 ◽  
Vol 21 (1) ◽  
pp. 3-18
Author(s):  
Melda Kokoç ◽  
Süleyman Ersöz
Keyword(s):  
Decision Making ◽  
High Performance ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Score Function ◽  
Multi Criteria Decision Making ◽  
Ranking Functions ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Abstract Many authors agree that the Interval-Valued Intuitionistic Fuzzy Set (IVIFS) theory generates as realistic as possible evaluation of real-life problems. One of the real-life problems where IVIFSs are often preferred is the Multi-Criteria Decision-Making (MCDM) problem. For this problem, the ranking of values obtained by fuzzing the opinions corresponding to alternatives is an important step, as a failure in ranking may lead to the selection of the wrong alternative. Therefore, the method used for ranking must have high performance. In this article, a new score function SKE and a new accuracy function HKE are developed to overcome the disadvantages of existing ranking functions for IVIFSs. Then, two illustrative examples of MCDM problems are presented to show the application of the proposed functions and to evaluate their effectiveness. Results show that the functions proposed have high performance and they are the eligibility for the MCDM problem.

Sign in / Sign up

Export Citation Format

Share Document