Methods for strategic decision-making problems with immediate probabilities in intuitionistic fuzzy setting
Scientia IranicaPublished 29 September 2012Open access
Guiwu Wei, José M. Merigó
Citations76
SJR quartileQ3
SJR score0.30
SNIP0.55
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.
TL;DR
Some new probability aggregation operators with intuitionistic fuzzy information are developed and applied to decision-making problem about the selection of the optimal production strategy and the developed models and procedures shall extend to solve probabilistic decision- making problems with interval-valued intuitionism fuzzy information.
Abstract
With respect to decision-making problems by using probabilities, immediate probabilities and information that can be represented with intuitionistic fuzzy information or interval-valued intuitionistic fuzzy information, some new decision analysis are proposed. Firstly, some operational laws, score function and accuracy function of intuitionistic fuzzy values or interval-valued intuitionistic fuzzy values are introduced. Then, we have developed some new probability aggregation operators with intuitionistic fuzzy information: Probability Intuitionistic Fuzzy Weighted Average (P-IFWA) operator, Immediate Probability Intuitionistic Fuzzy Ordered Weighted Average (IP-IFOWA) operator, Probability Intuitionistic Fuzzy Ordered Weighted Average (P-IFOWA) operator, Probability Intuitionistic Fuzzy Weighted Geometric (P-IFWG) operator, Immediate Probability Intuitionistic Fuzzy Ordered Weighted Geometric (IP-IFOWG) operator and Probability Intuitionistic Fuzzy Ordered Weighted Geometric (P-IFOWG) operator and applied these operators to decision-making problem about the selection of the optimal production strategy. Furthermore, we shall extend the developed models and procedures to solve probabilistic decision-making problems with interval-valued intuitionistic fuzzy information. Finally, we give an illustrative example about selection of strategies to verify the developed approach and to demonstrate its feasibility and practicality.
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.
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.
Fuzzy Sets and SystemsInterval valued intuitionistic fuzzy sets
2,842 Citations1989Krassimir Atanassov, George Gargov
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
Studies in fuzziness and soft computingInterval-Valued Intuitionistic Fuzzy Sets
1,835 Citations2019Krassimir Atanassov
In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced and the majority of the proofs below are analogous to the proofs from Chapter 1.
IEEE Transactions on Systems Man and CyberneticsVague sets
1,649 Citations1993Wen-Bing Gau, Daniel J. Buehrer
A vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of according to the inequality of the following type:
Fuzzy Sets and SystemsMore on intuitionistic fuzzy sets
1,488 Citations1989Krassimir Atanassov
Two news operators on intuitionistic fuzzy sets are defined and their basic properties are studied to introduce new results on intuitionism fuzzy sets.
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.
Elsevier eBooksOn Ordered Weighted Averaging Aggregation Operators in Multicriteria Decisionmaking
1,060 Citations1993Ronald R. Yager
IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)Induced ordered weighted averaging operators
993 Citations1999Ronald R. Yager, Dimitar Filev
A more general type of OWA operator called the Induced Ordered Weighted Averaging (IOWA) Operator is introduced, in which one component is used to induce an ordering over the second components which are then aggregated.
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.
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.
Fuzzy Sets and SystemsVague sets are intuitionistic fuzzy sets
885 Citations1996Humberto Bustince, P. Burillo
This paper recapitulates the definition given by Atanassov (1983) of intuitionistic fuzzy sets as well as the definition of vague sets given by Gau and Byehrer (1993) and sees that both definitions coincide.
Information SciencesIntuitionistic preference relations and their application in group decision making☆
838 Citations2007Zeshui Xu
This paper develops an approach to group decision making based on intuitionistic preference relations and an approach based on incomplete intuitionism preference relations respectively, in which the intuitionistic fuzzy arithmetic averaging operator and intuitionism fuzzy weighted arithmetic averagingoperator are used to aggregate intuitionistic preferences.
Fuzzy Sets and SystemsOperators over interval valued intuitionistic fuzzy sets
753 Citations1994Krassimir Atanassov
Different operators are defined over the interval valued intuitionistic fuzzy sets and their basic properties are studied.
Kongzhi yu jueceMethods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making
682 Citations2007XU Ze-shui
An approach for decision making with interval-valued intuitionistic fuzzy information is developed, and a practical example is provided to illustrate the developed approach.
European Journal of Operational ResearchMulti-criteria decision-making methods based on intuitionistic fuzzy sets
650 Citations2006Huawen Liu, Guojun Wang
A series of new score functions are defined for multi-criteria decision-making problem based on the intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.
Fuzzy Sets and SystemsDistances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric
620 Citations2003Przemysław Grzegorzewski
New methods for measuring distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets, based on the Hausdorff metric, are suggested.
Applied Soft ComputingSome induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making
609 Citations2009Guiwu Wei
The developed models and procedures based on I-IIFOWG and IIFWG (interval-valued intuitionistic fuzzy weighted geometric) operators are extended to solve the MAGDM problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take theform of interval-valued intuistic fuzzy numbers.
International Journal of Approximate ReasoningDynamic intuitionistic fuzzy multi-attribute decision making
596 Citations2007Zeshui Xu, Ronald R. Yager
A procedure based on the DIFWA operator is developed to solve the dynamic intuitionistic fuzzy multi-attribute decision making (DIF-MADM) problems where all the decision information about attribute values takes the form of intuitionism fuzzy numbers collected at different periods.
Knowledge-Based SystemsGRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting
463 Citations2010Guiwu Wei
An optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, by which the attribute weights can be determined, and an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Information SciencesChoquet integrals of weighted intuitionistic fuzzy information
437 Citations2009Zeshui Xu
The Choquet integral is used to propose some intuitionistic fuzzy aggregation operators that not only consider the importance of the elements or their ordered positions, but also can reflect the correlations among the elements and theirordered positions.
Systems Engineering - Theory & PracticeApproach to Group Decision Making Based on Interval-Valued Intuitionistic Judgment Matrices
406 Citations2007Zeshui Xu, Jian Chen
On the basis of the arithmetic aggregation operator and hybrid aggregation operator, an approach to group decision making with interval-valued intuitionistic judgment matrices is given and some of their desirable properties are investigated in detail.
Fuzzy Sets and SystemsCorrelation of interval-valued intuitionistic fuzzy sets
379 Citations1995Humberto Bustince, P. Burillo
The concepts of correlation and correlation coefficient of interval-valued intuitionistic fuzzy sets are introduced and their first properties are studied and two decomposition theorems of the correlation are introduced.
Expert Systems with ApplicationsMulticriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment
360 Citations2008Jun Ye
A novel accuracy function for interval-valued intuitionistic fuzzy sets (IVIFS) is proposed by taking into account the unknown degree (hesitancy degree) of IVIFSs to overcome the situation of difficult decision of existing accuracy functions to the alternatives in some cases.
Journal of Computer and System SciencesMulticriteria fuzzy decision-making methods based on intuitionistic fuzzy sets
345 Citations2006Lin Lin, Xue-hai Yuan +1 more
A new method for handling multicriteria fuzzy decision-making problems based on intuitionistic fuzzy sets is presented and can provide a useful way to efficiently help the decision-maker to make his decision.
International Journal of Systems ScienceIntuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making
331 Citations2005Krassimir Atanassov, Gabriella Pasi +1 more
Intuitionistic fuzzy interpretations of the processes ofmulti-person and of multi-measurement tool multi-criteria decision makings are discussed in this paper.
Knowledge-Based SystemsMaximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting
299 Citations2008Guiwu Wei
An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established and another optimization model is established for the special situations where the information about attribute weights is completely unknown.
International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsSOME GEOMETRIC AGGREGATION FUNCTIONS AND THEIR APPLICATION TO DYNAMIC MULTIPLE ATTRIBUTE DECISION MAKING IN THE INTUITIONISTIC FUZZY SETTING
272 Citations2009Guiwu Wei
A procedure based on the DIFWG and IFWG operators is developed to solve the dynamic intuitionistic fuzzy multiple attribute decision making problems where all the decision information about attribute values takes the form of intuitionists fuzzy numbers collected at different periods.
Information SciencesCorrelation of intuitionistic fuzzy sets by centroid method
242 Citations2002Wen‐Liang Hung, Jong‐Wuu Wu
The value of the correlation coefficient between interval-valued intuitionistic fuzzy sets lies in the interval [−1,1], as computed from the formula obtained from the “centroid” method.
On Geometric Aggregation over Interval-Valued Intuitionistic Fuzzy Information
239 Citations2007Zeshui Xu, Jian Chen
This work develops some interval-valued intuitionistic fuzzy geometric operators, and applies the developed operators to solve a multiple attribute decision-making problem involving the prioritization of a set of information technology improvement projects.
Expert Systems with ApplicationsAn extended TOPSIS method with interval-valued intuitionistic fuzzy numbers for virtual enterprise partner selection
232 Citations2010Fei Ye
Results show that this extended TOPSIS method for group decision making with interval-valued intuitionistic fuzzy numbers is more suitable to cope with the partner selection problem under incomplete and uncertain information environment.
International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsMODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION
221 Citations2007Zhiping Xu
This paper investigates the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs).
International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsLINGUISTIC AGGREGATION OPERATORS FOR LINGUISTIC DECISION MAKING BASED ON THE DEMPSTER-SHAFER THEORY OF EVIDENCE
193 Citations2010José M. Merigó, Montserrat Casanovas +1 more
A new approach for decision making with Dempster-Shafer theory of evidence by using linguistic information is developed, and the belief structure — linguistic ordered weighted averaging, the BS — linguistic hybrid averaging and a wide range of particular cases are obtained.
Computers & Industrial EngineeringFuzzy decision making with immediate probabilities
180 Citations2010José M. Merigó
A new decision-making model with probabilistic information was developed and used the concept of the immediate probability to aggregate the information, which modifies the objective probability by introducing the attitudinal character of the decision maker using the ordered weighting average (OWA) operator.
Fuzzy Optimization and Decision MakingExtension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment
179 Citations2008Deng‐Feng Li
It has been proved that the methodology proposed in this article can deal with MADM problems under not only Atanassov’s IF environments but also both fuzzy and crisp environments.
Information SciencesLinear programming method for multiattribute group decision making using IF sets
178 Citations2010Deng‐Feng Li, Guohong Chen +1 more
In this methodology, IF sets are constructed to capture fuzziness in decision information and decision making process, and the group consistency and inconsistency indices are defined on the basis of pairwise comparison preference relations on alternatives given by the decision makers.
Applied Soft ComputingFractional programming methodology for multi-attribute group decision-making using IFS
176 Citations2008Deng‐Feng Li, Yongchun Wang +2 more
A new methodology for solving multi-attribute group decision-making problems using IFS, in which multiple attributes are explicitly considered, is developed.
Fuzzy Optimization and Decision MakingMulti-person multi-attribute decision making models under intuitionistic fuzzy environment
171 Citations2007Zeshui Xu
This article investigates the group decision making problems in which all the information provided by the decision makers is expressed as intuitionistic fuzzy decision matrices where each of the elements is characterized by intuitionists fuzzy number, and the information about attribute weights is partially known.
Expert Systems with ApplicationsLinear programming method for MADM with interval-valued intuitionistic fuzzy sets
170 Citations2010Deng‐Feng Li
A methodology for solving MADM problems with both ratings of alternatives on attributes and weights being expressed with IVIF sets is developed, where a weighted absolute distance between IF sets is defined using weights of IF sets.
International Journal of Intelligent Systems
166 Citations2009
An algorithm to transform a dynamic influence net (DIN) into a dynamic Bayesian network (DBN) that enables a system analyst to capture a complex situation using a DIN and pick the best COA that maximizes the likelihood of achieving the desired effect.
International Journal of Intelligent SystemsInduced aggregation operators in decision making with the Dempster-Shafer belief structure
148 Citations2009José M. Merigó, Montserrat Casanovas
This study analyzes the induced aggregation operators, focusing on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators.
International Journal of Intelligent SystemsOn the concept of immediate probabilities
133 Citations1995Ronald R. Yager, Kurt J. Engemann +1 more
It is shown how immediate probabilities allows to explain the Allais paradox, and the strategic use of these probabilities are explored as a means for effecting other people's decisions.
International Journal of General SystemsMODELLING DECISION MAKING USING IMMEDIATE PROBABILITIES
99 Citations1996Kurt J. Engemann, Dimitar Filev +1 more
Probabilistic Decision Making with the OWA Operator and its Application in Investment Management
29 Citations2009José M. Merigó
A new aggregation operator is introduced that unifies the probabilities and the ordered weighted averaging (OWA) operator in the same formulation, which provides a more complete representation of the decision problem because it is able to consider probabilistic information and the attitudinal character ofThe decision maker.