scholarly journals A Novel IVPLTS Decision Method Based on Regret Theory and Cobweb Area Model

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Peng Li ◽  
Huanhuan Peng
Keyword(s):  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Decision Makers ◽  
Regret Theory ◽  
Area Model ◽  
Decision Method ◽  
Linguistic Term ◽  
Probabilistic Linguistic Term Sets ◽  
Novel Method ◽  
Interval Valued

For the multiple criteria decision-making (MCDM) problem with interval-valued probabilistic linguistic information, we propose a novel method considering the regret theory and cobweb area model. We first propose a new score function, which can be used to compare different interval-valued probabilistic linguistic term sets (IVPLTSs) and transform the IVPLTSs into crisp numbers. Some properties of the score function are verified. Then, we utilize the regret theory to obtain the perceived utilities of decision makers (DMs), which can reflect the DMs’ bounded rationality. Furthermore, we use the cobweb area model to aggregate decision information. Finally, a real case of evaluating nursing homes is used to illustrate the effectiveness and features of our method.

scholarly journals A Mathematical Programming Model to Determine Objective Weights for the Interval Extension of TOPSIS

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Hai Shen ◽  
Lingyu Hu ◽  
Kin Keung Lai
Keyword(s):  
Mathematical Programming ◽  
Input Data ◽  
Programming Model ◽  
Multiple Criteria Decision Making ◽  
Decision Makers ◽  
Mathematical Programming Model ◽  
Topsis Method ◽  
Data Set ◽  
Interval Extension ◽  
Interval Valued

Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method has been extended in previous literature to consider the situation with interval input data. However, the weights associated with criteria are still subjectively assigned by decision makers. This paper develops a mathematical programming model to determine objective weights for the implementation of interval extension of TOPSIS. Our method not only takes into account the optimization of interval-valued Multiple Criteria Decision Making (MCDM) problems, but also determines the weights only based upon the data set itself. An illustrative example is performed to compare our results with that of existing literature.

scholarly journals Multiple Criteria Decision Making Based on Probabilistic Interval-Valued Hesitant Fuzzy Sets by Using LP Methodology

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
M. Sarwar Sindhu ◽  
Tabasam Rashid ◽  
Agha Kashif ◽  
Juan Luis García Guirao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Occurrence Probability ◽  
Hesitant Fuzzy Sets ◽  
Life Problems ◽  
Interval Valued

Probabilistic interval-valued hesitant fuzzy sets (PIVHFSs) are an extension of interval-valued hesitant fuzzy sets (IVHFSs) in which each hesitant interval value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. PIVHFSs describe the belonging degrees in the form of interval along with probabilities and thereby provide more information and can help the decision makers (DMs) to obtain precise, rational, and consistent decision consequences than IVHFSs, as the correspondence of unpredictability and inaccuracy broadly presents in real life problems due to which experts are confused to assign the weights to the criteria. In order to cope with this problem, we construct the linear programming (LP) methodology to find the exact values of the weights for the criteria. Furthermore these weights are employed in the aggregation operators of PIVHFSs recently developed. Finally, the LP methodology and the actions are then applied on a certain multiple criteria decision making (MCDM) problem and a comparative analysis is given at the end.

scholarly journals Multiple Criteria Group Decision-Making Method with Dempster–Shafer Theory and Probabilistic Linguistic Term Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Yuanwei Du ◽  
Susu Wang
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Individual Level ◽  
Preference Theory ◽  
Dempster Shafer Theory ◽  
Linguistic Term ◽  
Probabilistic Linguistic Term Sets ◽  
The Individual ◽  
Shafer Theory ◽  
Interval Valued

The motivation of this study is to propose a novel multiple criteria group decision-making (MCDGM) method based on Dempster–Shafer theory (DST) and probabilistic linguistic term sets (PLTSs) to handle the distinctions between compensatory information at the criterion level and noncompensatory information at the individual level in the process of information fusion. Initially, the information at the individual level is extracted by BPA functions. Then, they are fused with DST considering ignorance and DMs’ reliabilities. Next, the obtained BPA functions are transformed into interval-valued PLTSs with the assistance of intermediate belief and plausibility. Subsequently, the interval-valued PLTSs are converted into standard PLTSs. After normalization, the holistic PLTS is obtained with weighted addition operation and the round function is applied to determine the ultimate evaluation result. Finally, a case simulation study of evaluating the marine ranching ecological security is presented to verify and improve the validity and feasibility of the proposed method and algorithm in practical application. The proposed method and its relevant algorithm are both innovative combination of DST and PLTSs from the perspective of compensatory and noncompensatory features of information, which provides a new angle of view for the development of probabilistic preference theory and is beneficial to apply probabilistic preference theory in practice.

scholarly journals Application of Induced Preorderings in Score Function-Based Method for Solving Decision-Making with Interval-Valued Fuzzy Soft Information

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1575
Author(s):  
Mabruka Ali ◽  
Adem Kiliçman ◽  
Azadeh Zahedi Khameneh
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Partial Solution ◽  
Soft Information ◽  
Decision Makers ◽  
Topological Spaces ◽  
Soft Sets ◽  
Fuzzy Soft Sets ◽  
Relationship Of ◽  
Interval Valued

Ranking interval-valued fuzzy soft sets is an increasingly important research issue in decision making, and provides support for decision makers in order to select the optimal alternative under an uncertain environment. Currently, there are three interval-valued fuzzy soft set-based decision-making algorithms in the literature. However, these algorithms are not able to overcome the issue of comparable alternatives and, in fact, might be ignored due to the lack of a comprehensive priority approach. In order to provide a partial solution to this problem, we present a group decision-making solution which is based on a preference relationship of interval-valued fuzzy soft information. Further, corresponding to each parameter, two crisp topological spaces, namely, lower topology and upper topology, are introduced based on the interval-valued fuzzy soft topology. Then, using the preorder relation on a topological space, a score function-based ranking system is also defined to design an adjustable multi-steps algorithm. Finally, some illustrative examples are given to compare the effectiveness of the present approach with some existing methods.

scholarly journals Interval-Valued Hesitant Fuzzy Hamacher Synergetic Weighted Aggregation Operators and Their Application to Shale Gas Areas Selection

2014 ◽  
Vol 2014 ◽  
pp. 1-25 ◽  
Author(s):  
Liang-Guo Li ◽  
Ding-Hong Peng
Keyword(s):  
Shale Gas ◽  
Multiple Criteria Decision Making ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Ordered Weighted Averaging ◽  
Essential Properties ◽  
Interval Valued ◽  
Selection Of

We investigate the multiple criteria decision making (MCDM) problem concerns on the selection of shale gas areas with interval-valued hesitant fuzzy information. First, some Hamacher operations of interval-valued hesitant fuzzy information are introduced, which generalize and extend the existing ones. Then some interval-valued hesitant fuzzy Hamacher weighted aggregation operators, especially, the interval-valued hesitant fuzzy Hamacher synergetic weighted averaging (IVHFHSWA) operators and their geometric version (IVHFHSWG) operators that weight simultaneously the argument variables themselves and their position orders and thus generalize the ideas of the weighted averaging and the ordered weighted averaging, are proposed. The distinct advantages of these operators are that they can provide more choices for the decision makers and considerably enhance or deteriorate the performance of aggregation. The essential properties of these operators are studied and their specific cases are discussed. Based on the IVHFHSWA operator, we propose a practical approach to shale gas areas selection with interval-valued hesitant fuzzy information. Finally, an illustrative example for selecting the shale gas areas is used to demonstrate the practicality and effectiveness of the proposed approach and a comparative analysis is performed with other approaches to highlight the distinctive advantages of the proposed operators.

scholarly journals A Consensus Reaching Model with Minimum Adjustments in Interval-Valued Intuitionistic MAGDM

2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Gai-li Xu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Decision Matrix ◽  
Intuitionistic Fuzzy ◽  
Novel Method ◽  
Consensus Index ◽  
Interval Valued ◽  
Consensus Reaching

This paper focuses on multiattribute group decision-making problems with interval-valued intuitionistic fuzzy values (IVIFVs) and develops a consensus reaching model with minimum adjustments to improve the consensus among decision-makers (DMs). To check the consensus, a consensus index is introduced by measuring the distance between each decision matrix and the collective one. For the group decision-making with unacceptable consensus, Consensus Rule 1 and Consensus Rule 2 are, respectively, proposed by minimizing adjustment amounts of individual decision matrices. According to these two consensus rules, two algorithms are devised to help DMs reach acceptable consensus. Moreover, the convergences of algorithms are proved. To determine weights of attributes, an interval-valued intuitionistic fuzzy program is constructed by maximizing comprehensive values of alternatives. Finally, alternatives are ranked based on their comprehensive values. Thereby, a novel method is proposed to solve MAGDM with IVIFVs. At length, a numerical example is examined to illustrate the effectiveness of the proposed method.

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