A note on the article “Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean” [Fuzzy Sets and Systems 161 (2010) 1604–1613]

2011 ◽  
Vol 176 (1) ◽  
pp. 76-78 ◽  
Author(s):  
Matteo Brunelli
Keyword(s):  
Fuzzy Sets ◽  
Geometric Mean ◽  
Comparison Matrix ◽  
Pair Wise Comparison ◽  
Pair Wise Comparison Matrix

Research on Fuzzy Fault Diagnosis of the Equipments

2013 ◽  
Vol 411-414 ◽  
pp. 1484-1487
Author(s):  
Ji Yang Qi ◽  
Li Na Ren ◽  
Shan Ping Ning ◽  
Yu Fu
Keyword(s):  
Fault Diagnosis ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Comparison Matrix ◽  
Fuzzy Diagnosis ◽  
The Given ◽  
Pair Wise Comparison ◽  
Pair Wise Comparison Matrix

The paper introduces a method of fault diagnosis using fuzzy set theory. In the paper, the principle that a fault symptom either exists or doesnt exist is abandoned. A crisp number between 0 and 1 is used to denote the degree of fault symptom, by which the fault symptom vector is constructed. For every kind of fault symptom, a fuzzy pair-wise comparison matrix is constructed. The elements of the pair-wise comparison matrix are triangular fuzzy numbers which denote the qualitative comparisons between the membership values of the given fault symptom with the reference to a pair of possible faults respectively. The least logarithm squares method is applied to determine the membership of the fault symptom with respect to each fault, and then the fuzzy diagnosis matrix is constructed. A simple weighted addition is used to calculate the fault vector based on the fuzzy diagnosis matrix and the fault symptom vector. Center of area is used to determine the best non-fuzzy performance value of the fuzzy number, according to which the fuzzy numbers can be ranked. The ordering of all the possible faults based on the fault symptoms is determined. At the end of the paper, an example is used to demonstrate the procedure of fuzzy fault diagnosis.

scholarly journals Selection of an optimal method for the preparation of dual loaded flavono polymeric nanoparticle using analytical hierarchy process

2014 ◽  
Vol 3 (4) ◽  
pp. 247-253 ◽  
Author(s):  
Senthil Kumar Chinnamaruthu ◽  
Mohan Sellappan
Keyword(s):  
Analytical Hierarchy Process ◽  
Polymeric Nanoparticles ◽  
Pharmaceutical Journal ◽  
Relative Importance ◽  
Optimal Method ◽  
Consistency Ratio ◽  
Comparison Matrix ◽  
Hierarchy Process ◽  
Pair Wise Comparison ◽  
Pair Wise Comparison Matrix

In this study, analytical hierarchy process was used to select an optimal method for the preparation of dual loaded flavono polymeric nanoparticles. Analytical hierarchy process involves structuring multiple choice criteria into a hierarchy, assessing the relative importance of criteria, comparing alternatives for each criterion and determining an overall ranking of the alternatives. Hierarchy model was developed with the goal in the first level, 10 criteria in the second level and methods for the preparation of polymeric nanoparticles in the third level. To assess the relative importance of criteria, all criteria were compared with each other using Saaty’s scale. To compare the methods, all the methods for the preparation of polymeric nanoparticles were compared with each other for each criterion using Saaty’s scale, which leads to the formation of pair-wise comparison matrixes and consistency ratio was calculated for the each pair-wise comparison matrix. The study result showed that the consistency ratio of each pair-wise comparison matrix were well within acceptable limits. Of 10 criteria, reproducible results received the maximum overall priority weight followed by desirable size. Of 10 methods, nanoprecipitation method received the maximum overall priority weight followed by supercritical fluid technology. Analytical hierarchy process has identified reproducible results as criteria preference and nanoprecipitation as an optimal method for the preparation of dual loaded flavono polymeric nanoparticles. The study concludes that the analytical hierarchy process has played a vital role in selecting an optimal method for the preparation of dual loaded flavono polymeric nanoparticles.DOI: http://dx.doi.org/10.3329/icpj.v3i4.18264 International Current Pharmaceutical Journal, March 2014, 3(4): 247-253 

scholarly journals DUAL HESITANT FUZZY AGGREGATION OPERATORS

2015 ◽  
Vol 22 (2) ◽  
pp. 194-209 ◽  
Author(s):  
Dejian YU ◽  
Wenyu ZHANG ◽  
George HUANG
Keyword(s):  
Human Resources ◽  
Fuzzy Sets ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Aggregation Operators ◽  
Fuzzy Arithmetic ◽  
Hesitant Fuzzy Sets ◽  
Numerical Example ◽  
Fuzzy Environment ◽  
Fuzzy Aggregation

Dual hesitant fuzzy sets (DHFSs) is a generalization of fuzzy sets (FSs) and it is typical of membership and non-membership degrees described by some discrete numerical. In this article we chiefly concerned with introducing the aggregation operators for aggregating dual hesitant fuzzy elements (DHFEs), including the dual hesitant fuzzy arithmetic mean and geometric mean. We laid emphasis on discussion of properties of newly introduced operators, and give a numerical example to describe the function of them. Finally, we used the proposed operators to select human resources outsourcing suppliers in a dual hesitant fuzzy environment.

scholarly journals An improvised similarity measure for generalized fuzzy numbers

2019 ◽  
Vol 8 (4) ◽  
pp. 1232-1238
Author(s):  
Daud Mohamad ◽  
Noorlisa Sara Adlene Ramlan ◽  
Sharifah Aniza Sayed Ahmad
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Numbers ◽  
Geometric Mean ◽  
Similarity Measures ◽  
Jaccard Index ◽  
Fuzzy Environment ◽  
Distance Methods ◽  
Generalized Fuzzy Numbers

Similarity measure between two fuzzy sets is an important tool for comparing various characteristics of the fuzzy sets. It is a preferred approach as compared to distance methods as the defuzzification process in obtaining the distance between fuzzy sets will incur loss of information. Many similarity measures have been introduced but most of them are not capable to discriminate certain type of fuzzy numbers. In this paper, an improvised similarity measure for generalized fuzzy numbers that incorporate several essential features is proposed. The features under consideration are geometric mean averaging, Hausdorff distance, distance between elements, distance between center of gravity and the Jaccard index. The new similarity measure is validated using some benchmark sample sets. The proposed similarity measure is found to be consistent with other existing methods with an advantage of able to solve some discriminant problems that other methods cannot. Analysis of the advantages of the improvised similarity measure is presented and discussed. The proposed similarity measure can be incorporated in decision making procedure with fuzzy environment for ranking purposes.

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