Multi-attribute decision making based on neutral averaging operators for intuitionistic fuzzy information
Applied Soft ComputingPublished 6 November 2014
Yingdong He, Huayou Chen, Zhen He, Ligang Zhou
Citations82
SJR quartileQ1
SJR score1.51
SNIP1.97
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
In this paper, we construct the probability sum (PS) function and the proportional distribution rules of membership function and non-membership function of intuitionistic fuzzy sets (IFSs), and give their corresponding geometric interpretations. Based on which, we present the neutrality operation and the scalar neutrality operation on intuitionistic fuzzy numbers (IFNs). We propose the intuitionistic fuzzy weighted neutral averaging (IFWNA) operator and the intuitionistic fuzzy ordered weighted neutral averaging (IFOWNA) operator. The properties of the IFWNA operator and the IFOWNA operator are investigated. The principal advantages of the proposed operators are that both the attitude of the decision makers and the interactions between different intuitionistic fuzzy numbers (IFNs) are considered. Furthermore, approaches to multi-criteria decision making based on the proposed IFWNA and IFOWNA operator are given. Finally, an example is illustrated to show the feasibility and validity of the new approaches to the application of decision making.
Keywords
Decision SciencesMathematicsEngineering
Fuzzy Sets and SystemsIntuitionistic fuzzy sets
16,153 Citations1986Krassimir Atanassov
Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
Medical Entomology and ZoologyMultiple Attribute Decision Making: Methods and Applications
8,268 Citations1981Shu-Jen J. Chen, C. L. Hwang +2 more
IEEE Transactions on Systems Man and CyberneticsOn ordered weighted averaging aggregation operators in multicriteria decisionmaking
7,125 Citations1988Ronald R. Yager
A type of operator for aggregation called an ordered weighted aggregation (OWA) operator is introduced and its performance is found to be between those obtained using the AND operator and the OR operator.
Medical Entomology and ZoologyFuzzy Sets and Fuzzy Logic: Theory and Applications
6,098 Citations1995George J. Klir, Bo Yuan
IEEE Transactions on Fuzzy SystemsIntuitionistic Fuzzy Aggregation Operators
2,660 Citations2007Zeshui Xu
Based on score function and accuracy function, a method is introduced for the comparison between two intuitionistic fuzzy values and some aggregation operators are developed, such as the intuitionism fuzzy weighted averaging operator, intuitionists fuzzy ordered weighted averaging operators, and intuitionistic fuzziness hybrid aggregation operator, for aggregating intuitionist fuzzy values.
International Journal of General SystemsSome geometric aggregation operators based on intuitionistic fuzzy sets
2,345 Citations2006Zeshui Xu, Ronald R. Yager
This paper develops some new geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionists fuzzy ordered weighted geometric(IFOWG)operator, and the intuitionism fuzzy hybrid geometric (ifHG) operators, which extend the WG and OWG operators to accommodate the environment in which the given arguments are intuitionistic fuzz sets.
Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility
2,165 Citations1980John C. Harsanyi
Fuzzy Sets and SystemsHandling multicriteria fuzzy decision-making problems based on vague set theory
1,162 Citations1994Shyi‐Ming Chen, Jiann-Mean Tan
New techniques for handling multicriteria fuzzy decision-making problems based on vague set theory can provide a useful way to efficiently help the decision-maker to make his decisions.
Fuzzy Sets and SystemsMulticriteria fuzzy decision-making problems based on vague set theory
987 Citations2000Dug Hun Hong, Chang-Hwan Choi
New functions to measure the degree of accuracy in the grades of membership of each alternative with respect to a set of criteria represented by vague values are provided.
Fuzzy Sets and SystemsNew operations defined over the intuitionistic fuzzy sets
917 Citations1994Krassimir Atanassov
The Ordered Weighted Averaging Operators: Theory and Applications
887 Citations1997Ronald R. Yager, Janusz Kacprzyk
This volume is the first in the literature on the increasingly popular Ordered Weighted Averaging (OWA) operators, making it possible to change the form of aggregation from the `pessimistic' minimum-type aggregation through all intermediate types, to the `optimistic' maximum-type aggregations.
International Journal of Intelligent SystemsAn overview of methods for determining OWA weights
774 Citations2005Zeshui Xu
A novel practical method is developed for obtaining the OWA weights, which can relieve the influence of unfair arguments on the decision results by weighting these arguments with small values.
Fuzzy Sets and SystemsOn the relationship between some extensions of fuzzy set theory
759 Citations2002Glad Deschrijver, Etienne E. Kerre
The relationships between intuitionistic fuzzy sets are established and interval-valued fuzzy sets, an extension of fuzzy set theory, are established.
Aggregation operators: new trends and applications
567 Citations2002Tomasa Calvo, Gaspar Mayor +1 more
Theoretical Aspects of Aggregation Operators, Representation Models for Aggregating Linguistic Information, and Fuzzy Quantities and Their Aggregation.
Fuzzy Sets and SystemsSome operations on intuitionistic fuzzy sets
544 Citations2000Supriya Kumar De, Ranjit Biswas +1 more
Concentration, dilation and normalization of intuitionistic fuzzy sets are defined, which will be useful while dealing with various linguistic hedges like “very”, “more or less” etc. involved in the problems under intuitionism fuzzy environment.
Knowledge-Based SystemsApproaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators
462 Citations2011Zeshui Xu
This paper develops a series of operators for aggregating IFNs, establishes various properties of these power aggregation operators, and applies them to develop some approaches to multiple attribute group decision making with Atanassov's intuitionistic fuzzy information.
Information SciencesHesitant fuzzy geometric Bonferroni means
459 Citations2012Bin Zhu, Zeshui Xu +1 more
The geometric Bonferroni mean (GBM) is explored considering both the BM and the geometric mean (GM) under hesitant fuzzy environment and the proposed aggregation operators to multi-criteria decision making are applied.
Applied Mathematical ModellingMulticriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets
319 Citations2010Jun Ye
A multicriteria fuzzy decision-making method based on weighted correlation coefficients using entropy weights is proposed under interval-valued intuitionistic fuzzy environment for the some situations where the information about criteria weights for alternatives is completely unknown.
Knowledge-Based SystemsInduced generalized intuitionistic fuzzy operators
299 Citations2010Zeshui Xu, Meimei Xia
Choquet integral and Dempster-Shafer theory of evidence are applied to aggregate inuitionistic fuzzy information and some new types of aggregation operators are developed, including the induced generalized intuitionistic fuzzy Choquet integral operators and induced generalized intuistic fuzzy Dem pster-shafer operators.
Information SciencesIntuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making
209 Citations2013Yingdong He, Huayou Chen +3 more
An approach to multiple attributes decision making is given based on the proposed aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of the proposed approach.
Information SciencesArithmetic operators in interval-valued fuzzy set theory
156 Citations2007Glad Deschrijver
The addition, subtraction, multiplication and division on L^I is introduced and it is shown that using these operators the pseudo-t-representable extensions of the Lukasiewicz t- norm and the product t-norm on the unit interval to L^i and some related operators can be written in a similar way as their counterparts on ([0,1],=<).
Fuzzy Sets and SystemsOn the composition of intuitionistic fuzzy relations
150 Citations2003Glad Deschrijver, Etienne E. Kerre
This paper presents an intuitionistic fuzzy version of the triangular compositions of Bandler and Kohout and the variants of these compositions given by De Baets and Kerre, and investigates some properties ofThese compositions: containment, convertibility, monotonicity, interaction with union and intersection.
Knowledge-Based SystemsAn interpretation of intuitionistic fuzzy sets in terms of evidence theory: Decision making aspect
148 Citations2010Ludmila Dymova, Pavel Sevastjanov
The proposed approach and a new method for interval comparison based on DST allow us to solve multiple criteria decision making problem without intermediate defuzzification when not only criteria, but their weights are intuitionistic fuzzy values.
Knowledge-Based SystemsA generalization of the power aggregation operators for linguistic environment and its application in group decision making
140 Citations2011Ligang Zhou, Huayou Chen
An application of the new approach in a multiple attribute group decision making problem concerning the evaluation of university faculty for tenure and promotion is developed.
Computers & Industrial EngineeringGeneralized power aggregation operators and their applications in group decision making
138 Citations2011Ligang Zhou, Huayou Chen +1 more
This paper investigates a generalized power average (GPA) operator and its weighted form, and develops a GPOWA operator based on the power ordered weighted average (POWA) operator, and extends these operators to uncertain environments and presents two operators to aggregate the input arguments taking the form of interval of numerical values.
Journal of Intelligent SystemsAn overview of methods for determining OWA weights: Research Articles
138 Citations2005Zeshui Xu
Fuzzy Sets and SystemsContinuous generalized OWA operator and its application to decision making
134 Citations2010Ligang Zhou, Huayou Chen
This paper presents a new class of operators called the continuous generalized ordered weighted averaging (C-GOWA) operators, which extends the continuous ordering weighted averaging operator, and generalizes the previous approaches by using Choquet integral and quasi-arithmetic means.
European Journal of Operational ResearchA robust desirability function method for multi-response surface optimization considering model uncertainty
126 Citations2012Zhen He, Pengfei Zhu +1 more
The presented method is compared with its conventional counterpart through an illustrated example from the literature and a hybrid genetic algorithm is developed to find the robust optima.
Fuzzy Sets and SystemsImplicators based on binary aggregation operators in interval-valued fuzzy set theory
110 Citations2005Glad Deschrijver, Etienne E. Kerre
This paper introduces aggregation operators on the lattice L^*, which is the underlying lattice of both interval-valued fuzzy sets and intuitionistic fuzzy sets in the sense of Atanassov.
Expert Systems with ApplicationsAn approach to group decision making with interval fuzzy preference relations based on induced generalized continuous ordered weighted averaging operator
98 Citations2011Huayou Chen, Ligang Zhou
The consistency induced generalized continuous ordered weighted averaging (C-IGCOWA) operator is presented, in which the consistency indicator is the induced ordering variable to reflect the importance of interval fuzzy preference relation.
Fuzzy Sets and SystemsA representation of t-norms in interval-valued L-fuzzy set theory
83 Citations2007Glad Deschrijver
This paper gives a representation theorem of t-norms on this lattice L^I for which the partial mappings are join-morphisms in terms ofT- norms on the underlying lattice which satisfy the residuation principle.
Expert Systems with ApplicationsGeneralized intuitionistic fuzzy geometric interaction operators and their application to decision making
80 Citations2013Yingdong He, Huayou Chen +4 more
Approaches to multiple attributes decision making are given based on the generalized aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of new approach.
Knowledge-Based SystemsOn compatibility of uncertain additive linguistic preference relations and its application in the group decision making
80 Citations2011Huayou Chen, Ligang Zhou +1 more
A mathematical model to obtain the weights of experts based on the criterion of minimizing the compatibility in the GDM is established, and the solution to the model is discussed.
Fuzzy Sets and SystemsGeneralized arithmetic operators and their relationship to t-norms in interval-valued fuzzy set theory
65 Citations2009Glad Deschrijver
This paper studies extensions of the arithmetic operators +, -, .
Expert Systems with ApplicationsUncertain generalized aggregation operators
63 Citations2011Ligang Zhou, Huayou Chen +2 more
The aim of this paper is to extend the generalized ordered weighted averaging operator and provide a new class of operators called the uncertain generalized ordering weighted averaging (UGOWA) operator, which provides a very general formulation that includes as special cases a wide range of aggregation operators and aggregates the input arguments taking the form of intervals rather than exact numbers.
Fuzzy Sets and SystemsThe Archimedean property for t-norms in interval-valued fuzzy set theory
27 Citations2006Glad Deschrijver
The relationship with the (weak) limit property is investigated and several necessary and sufficient conditions are obtained for a t-norm on L I to be Archimedean, which is the underlying lattice of interval-valued fuzzy set theory.
Fuzzy Sets and SystemsOn the representation of cardinalities of interval-valued fuzzy sets: The valuation property
3 Citations2012Glad Deschrijver, Pavol Kráľ
This paper found some basic conditions under which the valuation property, the subadditivityproperty, the complementarity rule and the Cartesian product rule are satisfied using different cardinality patterns, t-norms,t-conorms and negations on the lattice L^I (the underlying lattice of interval-valued fuzzy set theory).