Picture fuzzy normalized projection and extended VIKOR approach to software reliability assessment

Abstract An extended VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) method in group decision-making (GDM) setting is developed in this paper. The decision information is characterized by picture fuzzy number. A new GDM model is established and applied to software reliability assessment. First, this research finds that the current projection measure is not always reasonable in picture fuzzy setting. To solve this problem, a new normalization projection measure is developed in picture fuzzy setting. In addition, this research also finds that the most VIKOR-based GDM method requires a collective decision as a carrier to get an optimal solution. However, if a collective decision is aggregated by all the individual decisions, the positive and negative information might be canceled each other out in the decision process. To solve this problem, this paper proposes a direct VIKOR-based GDM method. The values of three VIKOR indexes are determined by the original decision matrices. The feasibility and practicability developed method in this work are illustrated by an example of software reliability assessment and some experimental analyses.

[1]  Z. Yue.  Application of the projection method to determine weights of decision makers for group decision making , 2012 .

[2]  Fuad E. Alsaadi,et al.  Projection models for multiple attribute decision making with picture fuzzy information , 2016, International Journal of Machine Learning and Cybernetics.

[3]  José Carlos Rodriguez Alcantud,et al.  Necessary and possible hesitant fuzzy sets: A novel model for group decision making , 2019, Inf. Fusion.

[4]  Hong-yu Zhang,et al.  A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection , 2016, Neural Computing and Applications.

[5]  Jianqiang Wang,et al.  Location selection of offshore wind power station by consensus decision framework using picture fuzzy modelling , 2018, Journal of Cleaner Production.

[6]  Gang Kou,et al.  An automatic procedure to create fuzzy ontologies from users' opinions using sentiment analysis procedures and multi-granular fuzzy linguistic modelling methods , 2019, Inf. Sci..

[7]  Muhammad Qiyas,et al.  Extended Version of Linguistic Picture Fuzzy TOPSIS Method and Its Applications in Enterprise Resource Planning Systems , 2019, Mathematical Problems in Engineering.

[8]  Z. Yue,et al.  A projection-based approach to intuitionistic fuzzy group decision making , 2017 .

[9]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[10]  Hoang Pham,et al.  Environmental factors analysis and comparison affecting software reliability in development of multi-release software , 2017, J. Syst. Softw..

[11]  Lin Zhong,et al.  Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions: VIKOR and TOPSIS , 2019, Inf. Sci..

[12]  Danielle Azar,et al.  A hybrid heuristic approach to optimize rule-based software quality estimation models , 2009, Inf. Softw. Technol..

[13]  Tapan Kumar Roy,et al.  Multi Attribute Decision Making Strategy on Projection and Bidirectional Projection Measures of Interval Rough Neutrosophic Sets , 2018 .

[14]  Himanshu Gupta,et al.  Evaluating service quality of airline industry using hybrid best worst method and VIKOR , 2017 .

[15]  Seyed Amin Seyed Haeri,et al.  Airports evaluation and ranking model using Taguchi loss function, best-worst method and VIKOR technique , 2017 .

[16]  Zeshui Xu,et al.  Pythagorean fuzzy VIKOR approaches based on TODIM for evaluating internet banking website quality of Ghanaian banking industry , 2019, Appl. Soft Comput..

[17]  Yuying Jia,et al.  A direct projection-based group decision-making methodology with crisp values and interval data , 2015, Soft Computing.

[18]  Z. Yue.  An intuitionistic fuzzy projection-based approach for partner selection , 2013 .

[19]  Mohammad Ghiasi,et al.  An analytical methodology for reliability assessment and failure analysis in distributed power system , 2018, SN Applied Sciences.

[20]  Chuan Yue,et al.  Entropy-based weights on decision makers in group decision-making setting with hybrid preference representations , 2017, Appl. Soft Comput..

[21]  Jian-qiang Wang,et al.  On Novel Operational Laws and Aggregation Operators of Picture 2-Tuple Linguistic Information for MCDM Problems , 2018, Int. J. Fuzzy Syst..

[22]  Elvira-Maria Arvanitou,et al.  A bibliometric assessment of software engineering scholars and institutions (2010-2017) , 2019, J. Syst. Softw..

[23]  Leila Baccour,et al.  Amended fused TOPSIS-VIKOR for classification (ATOVIC) applied to some UCI data sets , 2018, Expert Syst. Appl..

[24]  Shui Yu,et al.  Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design , 2019, Eur. J. Oper. Res..

[25]  Sebnem Yilmaz Balaman,et al.  A novel outranking based multi criteria group decision making methodology integrating ELECTRE and VIKOR under intuitionistic fuzzy environment , 2019, Expert Syst. Appl..

[26]  B. Sennaroglu,et al.  A military airport location selection by AHP integrated PROMETHEE and VIKOR methods , 2018 .

[27]  Lin Li,et al.  Picture fuzzy normalized projection-based VIKOR method for the risk evaluation of construction project , 2018, Appl. Soft Comput..

[28]  Guiwu Wei,et al.  SOME SIMILARITY MEASURES FOR PICTURE FUZZY SETS AND THEIR APPLICATIONS , 2018 .

[29]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[30]  Robert Y. Liang,et al.  Material selection for repair of structural concrete using VIKOR method , 2018 .

[31]  Chen Chen,et al.  A two-stage approach for combined heat and power economic emission dispatch: Combining multi-objective optimization with integrated decision making , 2018, Energy.

[32]  Gwo-Hshiung Tzeng,et al.  Extended VIKOR method in comparison with outranking methods , 2007, Eur. J. Oper. Res..

[33]  Zhang-peng Tian,et al.  An integrated approach for failure mode and effects analysis based on fuzzy best-worst, relative entropy, and VIKOR methods , 2018, Appl. Soft Comput..

[34]  Shouzhen Zeng,et al.  A Projection Method for Multiple Attribute Group Decision Making with Intuitionistic Fuzzy Information , 2013, Informatica.

[35]  Francisco Herrera,et al.  Large-scale group decision making model based on social network analysis: Trust relationship-based conflict detection and elimination , 2019, Eur. J. Oper. Res..

[36]  Shyi-Ming Chen,et al.  Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method , 2019, Inf. Sci..

[37]  Gwo-Hshiung Tzeng,et al.  Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS , 2004, Eur. J. Oper. Res..

[38]  Ali Fuat Guneri,et al.  Pythagorean fuzzy VIKOR-based approach for safety risk assessment in mine industry. , 2019, Journal of safety research.

[39]  Byeong Seok Ahn,et al.  Extended VIKOR method using incomplete criteria weights , 2019, Expert Syst. Appl..

[40]  F. Liu,et al.  An approach to group decision making based on interval multiplicative and fuzzy preference relations by using projection , 2013 .

[41]  Victor I. Chang,et al.  An integrated neutrosophic ANP and VIKOR method for achieving sustainable supplier selection: A case study in importing field , 2019, Comput. Ind..

[42]  Fabiano Cutigi Ferrari,et al.  The impact of Software Testing education on code reliability: An empirical assessment , 2017, J. Syst. Softw..

[43]  Peide Liu,et al.  A Novel Picture Fuzzy Linguistic Aggregation Operator and Its Application to Group Decision-making , 2018, Cognitive Computation.

[44]  Giorgio Di Natale,et al.  Computing reliability: On the differences between software testing and software fault injection techniques , 2017, Microprocess. Microsystems.

[45]  Rahul Hans,et al.  QoS based Web Service Selection and Multi-Criteria Decision Making Methods , 2019, Int. J. Interact. Multim. Artif. Intell..

[46]  R. Rakkiyappan,et al.  Interval-valued intuitionistic hesitant fuzzy entropy based VIKOR method for industrial robots selection , 2019, Expert Syst. Appl..

[47]  Chuan Yue,et al.  Projection-based approach to group decision-making with hybrid information representations and application to software quality evaluation , 2019, Comput. Ind. Eng..

[48]  Yunna Wu,et al.  Site selection decision framework using fuzzy ANP-VIKOR for large commercial rooftop PV system based on sustainability perspective , 2018, Sustainable Cities and Society.

[49]  Yanbing Ju,et al.  Study of site selection of electric vehicle charging station based on extended GRP method under picture fuzzy environment , 2019, Comput. Ind. Eng..

[50]  Muhammet Gulź,et al.  A state of the art literature review of VIKOR and its fuzzy extensions on applications , 2016 .

[51]  Juan-juan Peng,et al.  A multi-criteria decision-making framework for risk ranking of energy performance contracting project under picture fuzzy environment , 2018, Journal of Cleaner Production.

[52]  Jing Lin,et al.  Application of Bayesian Networks in Reliability Evaluation , 2019, IEEE Transactions on Industrial Informatics.

[53]  Guangyin Xu,et al.  Distributed energy system for sustainability transition: A comprehensive assessment under uncertainties based on interval multi-criteria decision making method by coupling interval DEMATEL and interval VIKOR , 2019, Energy.

[54]  P. Dey,et al.  Neutrosophic Soft Multi-Attribute Decision Making Based on Grey Relational Projection Method , 2016 .

[55]  Madhumangal Pal,et al.  Picture fuzzy Dombi aggregation operators: Application to MADM process , 2019, Appl. Soft Comput..

[56]  Bui Cong Cuong,et al.  Picture fuzzy sets , 2015 .

[57]  Chao Tian,et al.  An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method , 2019, Mathematics.

[58]  Ting-Yu Chen,et al.  A projection-based compromising method for multiple criteria decision analysis with interval-valued intuitionistic fuzzy information , 2016, Appl. Soft Comput..

[59]  Zeshui Xu,et al.  Hesitant fuzzy linguistic projection model to multi-criteria decision making for hospital decision support systems , 2018, Comput. Ind. Eng..

[60]  Ting-Yu Chen,et al.  Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis , 2018, Inf. Fusion.

[61]  Xiaohong Chen,et al.  Alternative selection of end-of-life vehicle management in China: A group decision-making approach based on picture hesitant fuzzy measurements , 2019, Journal of Cleaner Production.

[62]  Harish Garg.  Some Picture Fuzzy Aggregation Operators and Their Applications to Multicriteria Decision-Making , 2017, Arabian Journal for Science and Engineering.

[63]  Chuan Yue,et al.  An intuitionistic fuzzy projection-based approach and application to software quality evaluation , 2019, Soft Computing.

[64]  Peide Liu,et al.  Bidirectional projection measure of linguistic neutrosophic numbers and their application to multi-criteria group decision making , 2019, Comput. Ind. Eng..

[65]  Yuying Jia,et al.  A group decision making model with hybrid intuitionistic fuzzy information , 2015, Comput. Ind. Eng..

[66]  Yanbing Ju,et al.  Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting , 2013 .

[67]  Z. Yue.  Approach to group decision making based on determining the weights of experts by using projection method , 2012 .

[68]  Konstantin E. Samouylov,et al.  Carrying out consensual Group Decision Making processes under social networks using sentiment analysis over comparative expressions , 2019, Knowl. Based Syst..

[69]  Giancarlo Succi,et al.  Comparing the reliability of software systems: A case study on mobile operating systems , 2018, Inf. Sci..

[70]  Hui Gao,et al.  The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications , 2018, Informatica.

[71]  Gui-Wu Wei,et al.  Picture uncertain linguistic aggregation operators and their application to multiple attribute decision making , 2017, Int. J. Knowl. Based Intell. Eng. Syst..

[72]  Chuan Yue,et al.  Two normalized projection models and application to group decision-making , 2017, J. Intell. Fuzzy Syst..

[73]  Nikolay Pavlov,et al.  Analysis of the Chen’s and Pham’s Software Reliability Models , 2018 .

[74]  Chuan Yue,et al.  A normalized projection-based group decision-making method with heterogeneous decision information and application to software development effort assessment , 2019, Applied Intelligence.

[75]  Madjid Tavana,et al.  An extended stochastic VIKOR model with decision maker's attitude towards risk , 2018, Inf. Sci..

[76]  Yağmur Karabulut,et al.  A new group decision making approach with IF AHP and IF VIKOR for selecting hazardous waste carriers , 2019, Measurement.

[77]  Chuan Yue,et al.  An interval-valued intuitionistic fuzzy projection-based approach and application to evaluating knowledge transfer effectiveness , 2018, Neural Computing and Applications.

[78]  L. Suganthi,et al.  Multi expert and multi criteria evaluation of sectoral investments for sustainable development: An integrated fuzzy AHP, VIKOR / DEA methodology , 2018, Sustainable Cities and Society.

[79]  Zeshui Xu,et al.  Dual hesitant fuzzy VIKOR method for multi-criteria group decision making based on fuzzy measure and new comparison method , 2017, Inf. Sci..

[80]  Yixiong Feng,et al.  Environmentally friendly MCDM of reliability-based product optimisation combining DEMATEL-based ANP, interval uncertainty and Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) , 2018, Inf. Sci..

[81]  Guiwu Wei,et al.  Picture 2-Tuple Linguistic Bonferroni Mean Operators and Their Application to Multiple Attribute Decision Making , 2016, International Journal of Fuzzy Systems.

[82]  P. Dutta,et al.  Some aspects of picture fuzzy set , 2017, Transactions of A. Razmadze Mathematical Institute.