scholarly journals Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 442 ◽  
Author(s):  
Yige Xue ◽  
Yong Deng
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Decision Rules ◽  
Expected Value ◽  
Experimental Results ◽  
Numerical Examples ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Expected Values ◽  
Function Measure

Refined expected value decision rules can refine the calculation of the expected value and make decisions by estimating the expected values of different alternatives, which use many theories, such as Choquet integral, PM function, measure and so on. However, the refined expected value decision rules have not been applied to the orthopair fuzzy environment yet. To address this issue, in this paper we propose the refined expected value decision rules under the orthopair fuzzy environment, which can apply the refined expected value decision rules on the issues of decision making that is described in the orthopair fuzzy environment. Numerical examples were applied to verify the availability and flexibility of the new refined expected value decision rules model. The experimental results demonstrate that the proposed model can apply refined expected value decision rules in the orthopair fuzzy environment and solve the decision making issues with the orthopair fuzzy environment successfully.

scholarly journals Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Akram ◽  
Naveed Yaqoob ◽  
Ghous Ali ◽  
Wathek Chammam
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Ordered Weighted Averaging ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Electre I ◽  
Geometric Operator

An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.

scholarly journals Portfolio Selection Based on Distance between Fuzzy Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Weiyi Qian ◽  
Mingqiang Yin
Keyword(s):  
Mathematical Models ◽  
Portfolio Selection ◽  
Expected Value ◽  
Simple Method ◽  
Numerical Examples ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Investment Return ◽  
New Models ◽  
Different Types

This paper researches portfolio selection problem in fuzzy environment. We introduce a new simple method in which the distance between fuzzy variables is used to measure the divergence of fuzzy investment return from a prior one. Firstly, two new mathematical models are proposed by expressing divergence as distance, investment return as expected value, and risk as variance and semivariance, respectively. Secondly, the crisp forms of the new models are also provided for different types of fuzzy variables. Finally, several numerical examples are given to illustrate the effectiveness of the proposed approach.

scholarly journals Interval-Valued Intuitionistic Fuzzy Multicriteria Group Decision Making Based on VIKOR and Choquet Integral

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Chunqiao Tan ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Choquet Integral ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Problem ◽  
Multicriteria Group Decision Making ◽  
Interval Valued

An effective decision making approach based on VIKOR and Choquet integral is developed to solve multicriteria group decision making problem with conflicting criteria and interdependent subjective preference of decision makers in a fuzzy environment where preferences of decision makers with respect to criteria are represented by interval-valued intuitionistic fuzzy sets. First, an interval-valued intuitionistic fuzzy Choquet integral operator is given. Some of its properties are investigated in detail. The extended VIKOR decision procedure based on the proposed operator is developed for solving the multicriteria group decision making problem where the interactive criteria weight is measured by Shapley value. An illustrative example is given for demonstrating the applicability of the proposed decision procedure for solving the multi-criteria group decision making problem in interval-valued intuitionistic fuzzy environment.

scholarly journals Provable Guarantees on the Robustness of Decision Rules to Causal Interventions

2021 ◽  
Author(s):  
Benjie Wang ◽  
Clare Lyle ◽  
Marta Kwiatkowska
Keyword(s):  
Decision Making ◽  
Bayesian Networks ◽  
Lower Bounds ◽  
Decision Rules ◽  
Experimental Results ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Data Generating Process ◽  
Causal Bayesian Networks ◽  
Novel Model

Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical) changes in the data-generating process, whether due to natural reasons or by the action of an adversary. We consider causal Bayesian networks and formally define the interventional robustness problem, a novel model-based notion of robustness for decision functions that measures worst-case performance with respect to a set of interventions that denote changes to parameters and/or causal influences. By relying on a tractable representation of Bayesian networks as arithmetic circuits, we provide efficient algorithms for computing guaranteed upper and lower bounds on the interventional robustness probabilities. Experimental results demonstrate that the methods yield useful and interpretable bounds for a range of practical networks, paving the way towards provably causally robust decision-making systems.

scholarly journals Fuzzy Linear Physical Programming for Multiple Criteria Decision-Making Under Uncertainty

2015 ◽  
Vol 11 (1) ◽  
pp. 26 ◽  
Author(s):  
Ahmed ElSayed ◽  
Elif Kongar ◽  
Surendra M. Gupta
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Decision Maker ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Decision Making Under Uncertainty ◽  
Physical Programming ◽  
Fuzzy Environment ◽  
Linear Physical Programming ◽  
Proposed Model

<p>This paper presents a newly developed fuzzy linear physical programming (FLPP) model that allows the decision maker to introduce his/her preferences for multiple criteria decision making in a fuzzy environment. The major contribution of this research is to generalize the current models by accommodating an environment that is conducive to fuzzy problem solving. An example is used to evaluate, compare and discuss the results of the proposed model.</p>

Rough Set Application in Customer Classification

2011 ◽  
Vol 267 ◽  
pp. 46-49 ◽  
Author(s):  
Ju Li ◽  
Wen Bin Xu ◽  
Wei Yuan Tu ◽  
Xing Wang ◽  
Wei Zhang ◽  
...  
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Customer Relationship Management ◽  
Decision Rules ◽  
Relationship Management ◽  
Experimental Results ◽  
Customer Relationship ◽  
Decision Table ◽  
Final Decision ◽  
Customer Classification

Based on the study of customer relationship management. First, we got the data from the database, transformed the corresponding decision table, then got the data in decision-making table for further simplification, generated the final decision rules. and got good results, experimental results showed that the method provided some practical value.

An Extended TODIM Method Based on Novel Score Function and Accuracy Function under Intuitionistic Fuzzy Environment

2019 ◽  
Vol 27 (06) ◽  
pp. 905-930 ◽  
Author(s):  
Dong Zhang ◽  
Xin Bao ◽  
Chong Wu
Keyword(s):  
Decision Making ◽  
Programming Model ◽  
Choquet Integral ◽  
Score Function ◽  
Accuracy Function ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Nonlinear Programming Model ◽  
Todim Method ◽  
The Difference

Recently, multi-attribute decision making (MADM) approaches concerning decision maker’s psychological behaviors have received increasing attention, but few of them have taken all the criteria interactions (positive, negative and dependent interactions) into consideration. In this paper, we combine the TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method with the 2-additive fuzzy measure and Choquet integral theory to demonstrate how criteria interactions can be determined and further extend it into intuitionistic fuzzy environment. To begin with, we propose the novel score function and accuracy function to compare the difference among intuitionistic fuzzy sets, which have been proven to be more effective and rational than the existing measure functions. Next, we construct the nonlinear programming model based on maximum-entropy principal to obtain the optimal criteria interactions. Further, 2-additive Choquet-based dominance degree is defined whereby we put forward the 2-additive Choquet integral-based TODIM method under intuitionistic fuzzy environment to handle more challenging MADM problems. Finally, we present results of a didactic example, which concerns selection of suppliers for a manufacturing company, to evaluate the validity and rationality of proposed approach.

Weighted Fuzzy Averages in Fuzzy Environment: Part II. Generalized Weighted Fuzzy Expected Values in Fuzzy Environment

2003 ◽  
Vol 11 (02) ◽  
pp. 159-172 ◽  
Author(s):  
G. Sirbiladze ◽  
A. Sikharulidze
Keyword(s):  
Measure Space ◽  
Expected Value ◽  
Fuzzy Measure ◽  
Weighted Averages ◽  
Fuzzy Environment ◽  
Fuzzy Expected Value ◽  
Interval Extension ◽  
Finite Set ◽  
Expected Values ◽  
Iteration Processes

The weighted fuzzy expected value (WFEV) of the population for a sampling distribution was introduced in 1. In 2 the notion of WFEV is generalized for any fuzzy measure on a finite set (WFEVg). The latter paper also describes the notions of weighted fuzzy expected intervals WFEI and WFEIg which are an interval extension of WFEV and WFEVg, respectively, when due to ''scarce'' data the fuzzy expected value (FEV) 3 does not exist, but the fuzzy expected interval (FEI) 3 does. In this paper, The generalizations GWFEVg and GWFEIg of WFEVg and WFEIg, respectively, are introduced for any fuzzy measure space. Furthermore, the generalized weighted fuzzy expected value is expressed in terms of two monotone expectation (ME)4 values with respect to the Lebesgue measure on [0,1]. The convergence of iteration processes is provided by an appropriate choice of a ''weight'' function. In the interval extension (GWFEIg) the so-called combinatorial interval extension of a function 5 is successfully used, which is clearly illustrated by examples. Several examples of the use of the new weighted averages are discussed. In many cases these averages give better estimations than classical estimators of central tendencies such as mean, median or the fuzzy ''classical'' estimators FEV, FEI and ME.

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