scholarly journals INTERVAL-VALUED NEUTROSOPHIC AHP WITH POSSIBILITY DEGREE METHOD

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Eda Bolturk ◽  
Cengiz Kahraman
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Pairwise Comparison ◽  
Sensitivity Analyses ◽  
Analytic Hierarchy ◽  
Neutrosophic Sets ◽  
Interval Numbers ◽  
Possibility Degree ◽  
Definition Of ◽  
Interval Valued

The Analytic Hierarchy Process (AHP) is one of the most widely used methods in multi criteria decision making (MCDM) in many areas. The method has been extended with hesitant fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, and type -2 fuzzy sets etc. These extended methods can consider the vagueness in decision making problems through different definitions of membership functions. Each of them tries to increase the effectiveness of AHP under uncertainty. Decision makers can fully express their judgments through neutrosophic sets (NS) since NS are based on three independent parameters, truthiness (T), indeterminancy (I) and falsity (F), providing a distinction between a ‘relative truth’ and an ‘absolute truth’. In this paper, we employ the possibility degree method for ranking interval numbers in our neutrosophic AHP approach by utilizing NS’ representation power. Besides, we employ interval-valued NS since a larger domain for the definition of T, I, and F is provided. Pairwise comparison matrices can be filled in by using linguistic terms such as weakly more important, moderately more important or extremely important. Then, we obtain the relative importance degrees of criteria by using the possibility degree method. In order to show the effectiveness of our method, a MCDM application is given in energy planning. Comparative and sensitivity analyses are also presented in the paper.  

On δ-ϵ-Partitions for Finite Interval-Valued Hesitant Fuzzy Sets

2016 ◽  
Vol 24 (Suppl. 2) ◽  
pp. 145-163 ◽  
Author(s):  
Pelayo Quirós ◽  
Pedro Alonso ◽  
Irene Díaz ◽  
Susana Montes
Keyword(s):  
Image Processing ◽  
Decision Making ◽  
Fuzzy Sets ◽  
Open Problem ◽  
Finite Interval ◽  
Intuitionistic Fuzzy Sets ◽  
Hesitant Fuzzy Sets ◽  
Definition Of ◽  
Interval Valued ◽  
Atanassov’S Intuitionistic Fuzzy Sets

Hesitant fuzzy sets represent a useful tool in many areas such as decision making or image processing. Finite interval-valued hesitant fuzzy sets are a particular kind of hesitant fuzzy sets that generalize fuzzy sets, interval-valued fuzzy sets or Atanassov’s intuitionistic fuzzy sets, among others. Partitioning is a long-standing open problem due to its remarkable importance in many areas such as clustering. Thus, many different partitioning approaches have been developed for crisp and fuzzy sets. This work presents a partitioning method for the so-called finite interval-valued hesitant fuzzy sets. The definition of this partitioning method involves a definition of an ordering relation for finite interval-valued fuzzy sets membership degrees, i.e, finitely generated sets, as well as the definitions of t-norm and t-conorm for these kinds of sets.

scholarly journals Similarity Measures of Quadripartitioned Single Valued Bipolar Neutrosophic Sets and Its Application in Multi-Criteria Decision Making Problems

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1012
Author(s):  
Subhadip Roy ◽  
Jeong-Gon Lee ◽  
Anita Pal ◽  
Syamal Kumar Samanta
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measures ◽  
Distance Measures ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Decision Making Problem ◽  
Definition Of ◽  
Bipolar Fuzzy Sets

In this paper, a definition of quadripartitioned single valued bipolar neutrosophic set (QSVBNS) is introduced as a generalization of both quadripartitioned single valued neutrosophic sets (QSVNS) and bipolar neutrosophic sets (BNS). There is an inherent symmetry in the definition of QSVBNS. Some operations on them are defined and a set theoretic study is accomplished. Various similarity measures and distance measures are defined on QSVBNS. An algorithm relating to multi-criteria decision making problem is presented based on quadripartitioned bipolar weighted similarity measure. Finally, an example is shown to verify the flexibility of the given method and the advantage of considering QSVBNS in place of fuzzy sets and bipolar fuzzy sets.

scholarly journals Multicriteria Decision-Making Approach with Hesitant Interval-Valued Intuitionistic Fuzzy Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Juan-juan Peng ◽  
Jian-qiang Wang ◽  
Jing Wang ◽  
Xiao-hong Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Definition Of ◽  
Interval Valued

The definition of hesitant interval-valued intuitionistic fuzzy sets (HIVIFSs) is developed based on interval-valued intuitionistic fuzzy sets (IVIFSs) and hesitant fuzzy sets (HFSs). Then, some operations on HIVIFSs are introduced in detail, and their properties are further discussed. In addition, some hesitant interval-valued intuitionistic fuzzy number aggregation operators based ont-conorms andt-norms are proposed, which can be used to aggregate decision-makers' information in multicriteria decision-making (MCDM) problems. Some valuable proposals of these operators are studied. In particular, based on algebraic and Einsteint-conorms andt-norms, some hesitant interval-valued intuitionistic fuzzy algebraic aggregation operators and Einstein aggregation operators can be obtained, respectively. Furthermore, an approach of MCDM problems based on the proposed aggregation operators is given using hesitant interval-valued intuitionistic fuzzy information. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the developed approach, and the study is supported by a sensitivity analysis and a comparison analysis.

scholarly journals MULTIMOORA under Interval-Valued Neutrosophic Sets as the Basis for the Quantitative Heuristic Evaluation Methodology HEBIN

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 66
Author(s):  
Edmundas Kazimieras Zavadskas ◽  
Romualdas Bausys ◽  
Ingrida Lescauskiene ◽  
Ana Usovaite
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Evaluation Methodology ◽  
Heuristic Evaluation ◽  
Neutrosophic Sets ◽  
Interval Numbers ◽  
Multicriteria Decision ◽  
Decision Methods ◽  
The Impact ◽  
Interval Valued

During the last decade, researchers put a lot of effort into the development of the multi-criteria decision methods (MCDM) capable of dealing with the uncertainty and vagueness of the initial information. MCDM approaches that work under the environment of the interval-valued neutrosophic sets (IVNS) demonstrate credibility for the analysis of different opinions as well as for the inconsistency of the criteria evaluation data. The novel multicriteria decision-making approach MULTIMOORA-IVNS (multi-objective optimisation by ratio analysis under interval-valued neutrosophic sets) is presented in this paper. A novel heuristic evaluation methodology HEBIN (heuristic evaluation based on interval numbers) that exploits MULTIMOORA-IVNS for the processing of the evaluation results is also presented in this research. HEBIN is able to increase the accuracy of the checklists-based heuristic evaluation and to diminish the impact of the inconsistencies caused by the evaluators. A comparison of six e-commerce websites is introduced to reveal the practicalities of the proposed multicriteria decision-making application.

Multi-Attribute Decision Making Based on the Similarity Degree of Ternary Interval Numbers

2014 ◽  
Vol 926-930 ◽  
pp. 3092-3095
Author(s):  
Guo Feng Liu ◽  
Li Guo ◽  
Yue Bao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Calculation Formula ◽  
Topsis Method ◽  
Interval Numbers ◽  
Similarity Degree ◽  
Axiomatic Definition ◽  
Multi Attribute Decision Making ◽  
Definition Of ◽  
Theory Of Fuzzy Sets

For multi-attribute decision making problems whose attribute values are ternary interval numbers and their weights and attribute values are not fully, this paper proposes a decision-making method based on the similarity degree of ternary interval numbers. Firstly, utilizing the closeness theory of fuzzy sets, we give the corresponding axiomatic definition of ternary interval numbers and obtain the corresponding calculation formula of similarity degree. Then, according to the basic idea of traditional TOPSIS method, we establish the multi-attribute decision making and give the general steps of solving multi-attribute decision making problems. Finally, the paper demonstrates the effectiveness and practicality of the method by the example analysis.

On Moderate Fuzzy Analytic Hierarchy Process Pairwise Comparison Model With Subcriteria

2016 ◽  
Vol 2 (3) ◽  
pp. 54
Author(s):  
G. Marimuthu ◽  
G. Ramesh
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Fuzzy Ahp ◽  
Pairwise Comparison ◽  
Decision Models ◽  
Fuzzy Analytic Hierarchy Process ◽  
Analysis Method ◽  
Analytic Hierarchy ◽  
Comparison Model ◽  
Hierarchy Process

Decisions usually involve the getting the best solution, selecting the suitable experiments, most appropriate judgments, taking the quality results etc., using some techniques.  Every decision making can be considered as the choice from the set of alternatives based on a set of criteria.  The fuzzy analytic hierarchy process is a multi-criteria decision making and is dealing with decision making problems through pairwise comparisons mode [10].  The weight vectors from this comparison model are obtained by using extent analysis method.  This paper concern with an alternate method of finding the weight vectors from the original fuzzy AHP decision model (moderate fuzzy AHP model), that has the same rank as obtained in original fuzzy AHP and ideal fuzzy AHP decision models.

Multi-criteria decision-making algorithm based on aggregation operators under the complex interval-valued q-rung orthopair uncertain linguistic information

2021 ◽  
pp. 1-30
Author(s):  
Harish Garg ◽  
Zeeshan Ali ◽  
Zaoli Yang ◽  
Tahir Mahmood ◽  
Sultan Aljahdali
Keyword(s):  
Decision Making ◽  
Brain Tumors ◽  
Score Function ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Linguistic Features ◽  
Interval Numbers ◽  
Fundamental Properties ◽  
Interval Valued

The paper aims to present a concept of a Complex interval-valued q-rung orthopair uncertain linguistic set (CIVQROULS) and investigated their properties. In the presented set, the membership grades are considered in terms of the interval numbers under the complex domain while the linguistic features are added to address the uncertainties in the data. To further discuss more, we have presented the operation laws and score function for CIVQROULS. In addition to them, we present some averaging and geometric operators to aggregate the different pairs of the CIVQROULS. Some fundamental properties of the proposed operators are stated. Afterward, an algorithm for solving the decision-making problems is addressed based on the proposed operator using the CIVQROULS features. The applicability of the algorithm is demonstrated through a case study related to brain tumors and their effectiveness is compared with the existing studies.

A Novel spherical fuzzy CRITIC method and its application to prioritization of supplier selection criteria

2021 ◽  
pp. 1-8
Author(s):  
Cengiz Kahraman ◽  
Sezi Cevik Onar ◽  
Başar Öztayşi
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Supplier Selection ◽  
Selection Criteria ◽  
Business Processes ◽  
Multiple Criteria Decision Making ◽  
Decision Matrix ◽  
Neutrosophic Sets ◽  
Numerical Illustration ◽  
Picture Fuzzy Sets

Linguistic terms are quite suitable to make evaluations in multiple criteria decision making problems since humans prefer them rather than sharp evaluations. When linguistic evaluations are used in the decision matrix instead of exact numerical values, fuzzy set theory can capture the vagueness in the linguistic evaluations. Ordinary fuzzy sets have been extended to many new types of fuzzy sets such as intuitionistic fuzzy sets, neutrosophic sets, spherical fuzzy sets and picture fuzzy sets. Spherical fuzzy sets are an extension of picture fuzzy sets whose squared sum of their parameters is at most equal to one. This paper develops a novel spherical fuzzy CRiteria Importance Through Intercriteria Correlation (CRITIC) method and applies it for prioritizing supplier selection criteria. Supplier selection is one of the most critical aspects of any organization since any mistake in this process may cause poor supplier performance and inefficiencies in the business processes. Supplier selection is a multi-criteria decision making problem involving several conflicting criteria and alternatives. A numerical illustration of the proposed method is also given for this problem.

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