Intuitionistic Fuzzy Hybrid Weighted Arithmetic Mean and Its Application in Decision Making

2019 ◽  
Vol 27 (03) ◽  
pp. 353-373
Author(s):  
Weize Wang ◽  
Jerry M. Mendel
Keyword(s):  
Decision Making ◽  
Membership Function ◽  
Arithmetic Mean ◽  
Aggregation Operators ◽  
Total Order ◽  
Intuitionistic Fuzzy ◽  
Weighted Arithmetic ◽  
Multi Attribute Decision Making ◽  
A Company ◽  
Interval Valued

Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-membership function, and a hesitancy function, is a generalization of a fuzzy set. There are various intuitionistic fuzzy hybrid weighted aggregation operators to deal with multi-attribute decision making problems which consider the importance degrees of the arguments and their ordered positions simultaneously. However, these existing hybrid weighed aggregation operators are not monotone with respect to the total order on intuitionistic fuzzy values (AIFVs), which is undesirable. Based on the Łukasiewicz triangular norm, we propose an intuitionistic fuzzy hybrid weighted arithmetic mean, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a company intends to select a project manager to illustrate the validity and applicability of the proposed aggregation operator. Moreover, we extend this kind of hybrid weighted arithmetic mean to the interval-valued intuitionistic fuzzy environments.

scholarly journals Heronian Means as Aggregation Operators for Multi-Attribute Decision Making Applications

2018 ◽  
Author(s):  
Xiaopu Shang ◽  
Jun Wang ◽  
Anupam Nanda ◽  
Weizi Li
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Novel Approach ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Heronian Mean

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

Some Interval-Valued Intuitionistic Fuzzy Zhenyuan Aggregation Operators and Their Application to Multi-Attribute Decision Making

2018 ◽  
Vol 26 (04) ◽  
pp. 633-653 ◽  
Author(s):  
Zhimin Mu ◽  
Shouzhen Zeng ◽  
Qingbing Liu
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Interval Valued

This paper develops some new decision making methods for multi-attribute decision making (MADM) problems, in which the attribute weights take the form of crisp numbers, and attribute values take the form of interval-valued intuitionistic fuzzy information. First, based on the Zhenyuan integral, an interval-valued intuitionistic fuzzy Zhenyuan averaging (IVIFZA) operator and an interval-valued intuitionistic fuzzy Zhenyuan geometric (IVIFZG) operator are introduced to facilitate aggregation of interval-valued intuitionistic fuzzy information. The proposed operators allow one to fully consider the importance of different combinations of attributes and, therefore, are highly suitable to handle problems involving inter-dependent or interactive attributes. We further proceed by exploring some desirable properties of the IVIFZA and IVIVZG operators. By employing the proposed operators, a MADM approach based on intervalvalued intuitionistic fuzzy information is proposed. Finally, an illustrative example is presented to verify the developed approach and to demonstrate its practicality and effectiveness.

scholarly journals Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 145
Author(s):  
Yun Jin ◽  
Zareena Kousar ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Nimet Yapici Pehlivan ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Evaluation Process ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

scholarly journals Hybrid Weighted Arithmetic and Geometric Aggregation Operator of Neutrosophic Cubic Sets for MADM

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 278 ◽  
Author(s):  
Lilian Shi ◽  
Yue Yuan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Geometric Average ◽  
Multi Attribute Decision Making

Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.

Additive Intuitionistic Fuzzy Aggregation Operators Based on Fuzzy Measure

2016 ◽  
Vol 24 (01) ◽  
pp. 1-12 ◽  
Author(s):  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Probability Measure ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Fuzzy Measure ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Aggregation ◽  
The World ◽  
Multi Attribute Decision Making

Intuitionistic fuzzy sets can describe the uncertainty and complexity of the world flexibly, so it has been widely used in multi-attribute decision making. Traditional intuitionistic fuzzy aggregation operators are usually based on the probability measure, namely, they consider that the attributes of objects are independent. But in actual situations, it is difficult to ensure the independence of attributes, so these operators are unsuitable in such situations. Fuzzy measure is able to depict the relationships among the attributes more comprehensively, so it can complement the traditional probability measure in dealing with the multi-attribute decision making problems. In this paper, we first analyze the existing intuitionistic fuzzy operators based on fuzzy measure, then introduce two novel additive intuitionistic fuzzy aggregation operators based on the Shapley value and the Choquet integral, respectively, and show their advantages over other ones.

scholarly journals Induced Interval-Valued Intuitionistic Fuzzy Hybrid Aggregation Operators with TOPSIS Order-Inducing Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Jun-Ling Zhang ◽  
Xiao-Wen Qi
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Special Cases ◽  
Wide Range ◽  
Induced Aggregation ◽  
Interval Valued

Two induced aggregation operators with novelly designed TOPSIS order-inducing variables are proposed: Induced Interval-valued Intuitionistic Fuzzy Hybrid Averaging (I-IIFHA) operator and Induced Interval-valued Intuitionistic Fuzzy Hybrid Geometric (I-IIFHG) operator. The merit of two aggregation operators is that they can consider additional preference information of decision maker’s attitudinal characteristics besides argument-dependent information and argument-independent information. Some desirable properties of I-IIFHA and I-IIFHG are studied and theoretical analysis also shows that they can include a wide range of aggregation operators as special cases. Further, we extend these operators to form a novel group decision-making method for selecting the most desirable alternative in multiple attribute multi-interest group decision-making problems with attribute values and decision maker’s interest values taking the form of interval-valued intuitionistic fuzzy numbers, and application research to real estate purchase selection shows its practicality.

scholarly journals Hydrogen Production Technologies Evaluation Based on Interval-Valued Intuitionistic Fuzzy Multiattribute Decision Making Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Dejian Yu
Keyword(s):  
Decision Making ◽  
Hydrogen Production ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operators ◽  
Clear Understanding ◽  
Fuzzy Approach ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Aggregation ◽  
Production Technologies ◽  
Interval Valued

We establish a decision making model for evaluating hydrogen production technologies in China, based on interval-valued intuitionistic fuzzy set theory. First of all, we propose a series of interaction interval-valued intuitionistic fuzzy aggregation operators comparing them with some widely used and cited aggregation operators. In particular, we focus on the key issue of the relationships between the proposed operators and existing operators for clear understanding of the motivation for proposing these interaction operators. This research then studies a group decision making method for determining the best hydrogen production technologies using interval-valued intuitionistic fuzzy approach. The research results of this paper are more scientific for two reasons. First, the interval-valued intuitionistic fuzzy approach applied in this paper is more suitable than other approaches regarding the expression of the decision maker’s preference information. Second, the results are obtained by the interaction between the membership degree interval and the nonmembership degree interval. Additionally, we apply this approach to evaluate the hydrogen production technologies in China and compare it with other methods.

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