scholarly journals Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 462 ◽  
Author(s):  
Jingqian Wang ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Group Decision Making ◽  
Rough Sets ◽  
Group Decision ◽  
Multiple Criteria ◽  
Approximation Spaces ◽  
Intuitionistic Fuzzy ◽  
Definition Of ◽  
Covering Rough Set

Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) β -covering and an IF covering rough set model. In this paper, some properties of IF β -covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF β -covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.’s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model.

scholarly journals Three-Way Decisions with Interval-Valued Intuitionistic Fuzzy Decision-Theoretic Rough Sets in Group Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 281 ◽  
Author(s):  
Dajun Ye ◽  
Decui Liang ◽  
Pei Hu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Rough Sets ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Decision ◽  
Grey Correlation ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this article, we demonstrate how interval-valued intuitionistic fuzzy sets (IVIFSs) can function as extended intuitionistic fuzzy sets (IFSs) using the interval-valued intuitionistic fuzzy numbers (IVIFNs) instead of precision numbers to describe the degree of membership and non-membership, which are more flexible and practical in dealing with ambiguity and uncertainty. By introducing IVIFSs into three-way decisions, we provide a new description of the loss function. Thus, we firstly propose a model of interval-valued intuitionistic fuzzy decision-theoretic rough sets (IVIFDTRSs). According to the basic framework of IVIFDTRSs, we design a strategy to address the IVIFNs and deduce three-way decisions. Then, we successfully extend the results of IVIFDTRSs from single-person decision-making to group decision-making. In this situation, we adopt a grey correlation accurate weighted determining method (GCAWD) to compute the weights of decision-makers, which integrates the advantages of the accurate weighted determining method and grey correlation analysis method. Moreover, we utilize the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operation to count the aggregated scores and the accuracies of the expected losses. By comparing these scores and accuracies, we design a simple and straightforward algorithm to deduce three-way decisions for group decision-making. Finally, we use an illustrative example to verify our results.

scholarly journals The multicriteria group decision making FlowSort method under uncertainty

2021 ◽  
Vol 16 ◽  
pp. 122-139
Author(s):  
Fedia Daami Remad ◽  
◽  
Hela Moalla Frikha ◽  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Decision Aid ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Multiple Criteria ◽  
Multicriteria Decision Aid ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multicriteria Group Decision Making

Crisp values are insufficient to model real-life situations and imprecise ideas are frequently represented in multicriteria decision aid analysis. In fact, it is difficult to treat the evaluation criteria precisely and to fix exact preferences rating. The triangular intuitionistic fuzzy numbers succeeded to treat this kind of ambiguity in a great deal of research than other forms of fuzzy representation functions. The field of sorting issues is an active research topic in the multiple criteria decision aid (MCDA). This study extended one of the sorting methods, FLOWSORT, for solving multiple criteria group decision-making problems. This extension described the preferences rating of alternatives as linguistic terms which can be easily expressed in triangular intuitionistic fuzzy numbers. To validate our extension, an illustrative example as well as an empirical comparison with other multi-criteria decision making methods is presented. Keywords: multicriteria group decision making, sorting problematic, intuitionistic fuzzy set, FlowSort method

(α, β)-Multi-granulation bipolar fuzzified rough sets and their applications to multi criteria group decision making

2021 ◽  
pp. 1-36
Author(s):  
Rizwan Gul ◽  
Muhammad Shabir
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Group Decision Making ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Group Decision ◽  
Research Direction ◽  
New Approach ◽  
Accuracy Of Approximation

Pawlak’s rough set theory based on single granulation has been extended to multi-granulation rough set structure in recent years. Multi-granulation rough set theory has become a flouring research direction in rough set theory. In this paper, we propose the notion of (α, β)-multi-granulation bipolar fuzzified rough set ((α, β)-MGBFRSs). For this purpose, a collection of bipolar fuzzy tolerance relations has been used. In the framework of multi-granulation, we proposed two types of (α, β)-multi-granulation bipolar fuzzified rough sets model. One is called the optimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) o-MGBFRSs) and the other is called the pessimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) p-MGBFRSs). Subsequently, a number of important structural properties and results of proposed models are investigated in detail. The relationships among the (α, β)-MGBFRSs, (α, β) o-MGBFRSs and (α, β) p-MGBFRSs are also established. In order to illustrate our proposed models, some examples are considered, which are helpful for applying this theory in practical issues. Moreover, several important measures associated with (α, β)-multi-granulation bipolar fuzzified rough set like the measure of accuracy, the measure of precision, and accuracy of approximation are presented. Finally, we construct a new approach to multi-criteria group decision-making method based on (α, β)-MGBFRSs, and the validity of this technique is illustrated by a practical application. Compared with the existing results, we also expound its advantages.

DATA CONSTRUCTION PROCESS AND QUALIFLEX-BASED METHOD FOR MULTIPLE-CRITERIA GROUP DECISION MAKING WITH INTERVAL-VALUED INTUITIONISTIC FUZZY SETS

2013 ◽  
Vol 12 (03) ◽  
pp. 425-467 ◽  
Author(s):  
TING-YU CHEN
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Uncertainty Indices ◽  
Interval Valued

Based on Jacquet-Lagreze's permutation method, QUALIFLEX is an outranking model that investigates all possible permutations of alternatives with respect to the consequences of all criteria. The purpose of this paper is to develop a QUALIFLEX-based method for multiple criteria group decision making within a decision environment of interval-valued intuitionistic fuzzy sets. We conduct a statistical inference approach with finite population correction to construct interval-valued intuitionistic fuzzy numbers. In addition, we incorporate the relative importance of decision makers and fuse individual opinions to form collective ratings using a modified method with weighted interval estimations. In view of diversiform preference types (weak order, strict order, difference order, interval bound, and ratio bound), we represent multiple decision makers' various forms of preference structures and assess criterion weights under incomplete information. By means of score functions, accuracy functions, membership-uncertainty indices, and hesitation-uncertainty indices, a ranking procedure is employed to identify a criterion-wise preference of alternatives. A QUALIFLEX-based model is then established to measure the level of concordance of the complete preference order for handling multiple criteria group decisions. The feasibility of the proposed method is illustrated by a practical problem relating to the selection of a landfill site. As indicated in the application, the proposed method is useful for handling complicated group decision-making problems that involve comprehensive criteria and limited alternatives.

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