TOPSIS for Multi Criteria Decision Making in Octagonal Intuitionistic Fuzzy Environment by Using Accuracy Function

Year 2020, Issue: 31, 32 - 40, 30.06.2020

Madiha Imtıaz Muhammad Saqlaın Muhammad Saeed

Abstract

Multi Criteria Decision Making (MCDM) enables a strong valid platform in domains where choosing the best of the best among various attributes is quite complicated. This paper provides a suitable methodology for solving MCDM problems in Intuitionistic Fuzzy region. In this paper we shall be dealing with the environment of octagonal intuitionistic fuzzy numbers. These numbers are more suitable to deal with uncertainties than other generalized form of fuzzy numbers. There are ways to solve MCDM in IF environment. Many have used ∝-cuts of numbers which are complicated calculations usually ending up with deviation from the results. Despite of solving the problem using ∝-cuts, we propose a new ranking technique in the procedure. This ranking technique is called an accuracy function for octagonal intuitionistic fuzzy numbers. Octagonal Intuitionistic fuzzy numbers are introduced along with its membership and non-membership values. For application, a numerical example is solved at the end of this paper.

Keywords

Fuzzy Numbers (FN’s), Intuitionistic Fuzzy Numbers (IFN’s), Octagonal Intuitionistic Fuzzy Number (OIFN’s), Accuracy Function (AF), TOPSIS

References

• C. Hwang, K. Yoon, Multiple Attribute Decision Making: Methods and Applications, A State-of-the-Art Survey, Springer (1981).
• X. Zhang, P. Liu, Method for Aggregating Triangular Fuzzy Intuitionistic Fuzzy Information and Its Application to Decision Making, Technological and Economic Development of Economy 16(2) (2010) 280-290.
• L. A. Zadeh, Fuzzy Sets, Information and Computation 8(3) (1965) 338-353.
• K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20 (1986) 87-96.
• K. T. Atanassov, More on Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 33 (1989) 37-46.
• M. Saqlain, N. Jafar, A. Riffat, Smart Phone Selection by Consumers’ İn Pakistan: FMCGDM Fuzzy Multiple Criteria Group Decision Making Approach, Gomal University Journal of Research 34(1) (2018) 27-31
• M. N. Jafar, K. Muniba, A. Saeed, S. Abbas, I. Bibi, Application of Sanchez's Approach to Disease Identification Using Trapezoidal Fuzzy Numbers, International Journal of Latest Engineering Research and Applications 4(9) (2019) 51-57.
• M. Saeed, M. Saqlain, M. Riaz, Application of Generalized Fuzzy TOPSIS in Decision Making for Neutrosophic Soft set to Predict the Champion of FIFA 2018: A Mathematical Analysis, Punjab University Journal of Mathematics 51(8) (2019) 111-126. M. Saqlain, N. Jafar, R. Hamid, A. Shahzad, Prediction of Cricket World Cup 2019 by TOPSIS Technique of MCDM-A Mathematical Analysis, International Journal of Scientific & Engineering Research 10(2) (2019) 789-792.
• M. Saqlain, M. Saeed, M. R. Ahmad, F. Smarandache, Generalization of TOPSIS for Neutrosophic Hypersoft set using Accuracy Function and its Application, Neutrosophic Sets and Systems 27 (2019) 131-137.
• P. Rajarajeswari, G. Menaka, A New Approach for Ranking of Octagonal Intuitionistic Fuzzy Numbers, International Journal of Fuzzy Logic Systems (2017), http://doi.org/ 10.5072/zenodo
• F. E. Boran, S. Genç, M. Kurt, D. Akay, A Multi-Criteria Intuitionistic Fuzzy Group Decision Making for Supplier Selection with TOPSIS Method, Expert System and Applications 36(8) (2009) 11363-11368.
• D. Bakbak, V. Uluçay, Multicriteria Decision-Making Method Using the Cosine Vector Similarity Measure Under Intuitionistic Trapezoidal Fuzzy Multi-Numbers in Architecture, 6th International Multidisciplinary Studies Congress (Multicongress’19) (2019), Gaziantep, Türkiye.
• D. Bakbak, V. Uluçay, M. Şahin, Intuitionistic Trapezoidal Fuzzy Multi-Numbers and Some Arithmetic Averaging Operators with Their Application in Architecture, 6th International Multidisciplinary Studies Congress (Multicongress’19) (2019), Gaziantep, Türkiye.
• V. Uluçay, I. Deli, M. Şahin, Intuitionistic Trapezoidal Fuzzy Multi-Numbers and Its Application to Multi-Criteria Decision-Making Problems, Complex & Intelligent Systems 5(1) (2019) 65-78.
• V. Uluçay, I. Deli, M. Şahin, Trapezoidal Fuzzy Multi-Number and Its Application to Multi-Criteria Decision-Making Problems, Neural Computing and Applications 30 (2018) 1469-1478.
• S. Broumi, F. Smarandache, Intuitionistic Fuzzy Soft Expert Sets and its Application in Decision Making, Journal of New Theory (1) (2015) 89-105.
• M. Saqlain, F. Smarandache, Octagonal Neutrosophic Number: Its Different Representations, Properties, Graphs and De-Neutrosophication, Neutrosophic Sets and Systems (2020) (Accepted).
• M. Saqlain, A. Hamza, S. Farooq, Linear and Non-Linear Octagonal Neutrosophic Number: Its Representation, 𝜶−𝑪𝒖𝒕 and Applications, International Journal of Neutrosophic Science 3 (2020) 1-17.
• A. Chakraborty, S. P. Mondal, A. Ahmadian, N. Senu, S. Alam, S. Salahshour, Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications, Symmetry 10 (8) (2018) 1-28. https://doi.org/10.3390/sym10080327
• A. Chakraborty, S. P. Mondal, A. Mahata, S. Alam, Different Linear and Non-Linear Form of Trapezoidal Neutrosophic Numbers, De-Neutrosophication Techniques and Its Application in Time Cost Optimization Technique, Sequencing Problem, Operation Research 11 (2018). https://doi.org/10.1051/ro/2019090
• A. Chakraborty, S. P. Mondal, S. Alam, A. Ahmadian, N. Senu., D. De, S. Salahshour, The Pentagonal Fuzzy Number: Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problems, Symmetry 11(2) (2019).
• S. Narayanamoorthy, S. Maheswari, The Intelligence of Octagonal Fuzzy Number to Determine the Fuzzy Critical Path: A New Ranking Method, Scientific Programming, 2016 (2016), Article ID 6158208, 8 pages.
• J. Ye, Prioritized Aggregation Operators of Trapezoidal Intuitionistic Fuzzy Sets and Their Application to Multi Criteria Decision Making, Neural Computing and Applications 25(6) (2014) 1447-1454.
• K. K. Yen, S. Ghoshray, G. Roig, G., A Linear Regression Model Using Triangular Fuzzy Number Coefficients, Fuzzy Sets and System 106(2) (1999) 167-177.
• J. Ye, Trapezoidal Neutrosophic Set and Its Application to Multiple Attribute Decision-Making, Neural Computing and Applications 26 (2015) 1157-1166.
• M. Saqlain, S. Moin, M. N. Jafar, M. Saeed, F. Smarandache, Aggregate Operators of Neutrosophic Hypersoft Set, Neutrosophic Sets and Systems 32 (2020) 294-306. https://doi.org/10.5281/zenodo.3723155
• M. Saqlain, M. N. Jafar, M. Riaz, A New Approach of Neutrosophic Soft Set with Generalized Fuzzy TOPSIS in Application of Smart Phone Selection, Neutrosophic Sets and Systems 32 (2020) 307-316 2020. https://doi.org/10.5281/zenodo.3723161
• M. Saqlain, N. Jafar, S. Moin, M. Saeed, S. Broumi, Single and Multi-valued Neutrosophic Hypersoft set and Tangent Similarity Measure of Single valued Neutrosophic Hypersoft Sets, Neutrosophic Sets and Systems 32 (2020) 317-329. https://doi.org/10.5281/zenodo.3723165
• E. Sulukan, N. Çağman, T. Aydın, Fuzzy Parameterized Intuitionistic Fuzzy Soft Sets and Their Application to a Performance-Based Value Assignment Problem, Journal of New Theory (29) (2019) 79-88. https://dergipark.org.tr/tr/download/article-file/906764
• F. Smarandache, Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set, Spherical Fuzzy Set, and q-Rung Ortho pair Fuzzy Set, while Neutrosophication is a Generalization of Regret Theory, Grey System Theory, and Three-Ways Decision (revisited), Journal of New Theory 29 (2019) 1-31. https://dergipark.org.tr/tr/download/article-file/906372