Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions
In real life, structural problems can be described in linear and nonlinear forms. This nonlinear structural problem is very challenging to solve when its all parameters are imprecise in nature. Intuitionistic fuzzy sets were proposed to manage circumstances in which experts have some membershi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Islamic Azad University, Bandar Abbas Branch
2023-11-01
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| Series: | Transactions on Fuzzy Sets and Systems |
| Subjects: | |
| Online Access: | https://tfss.journals.iau.ir/article_701915_52fa4750ae4994ff9acfefae5e99bad6.pdf |
| _version_ | 1797639344982327296 |
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| author | Sanjoy Biswas Samir Dey |
| author_facet | Sanjoy Biswas Samir Dey |
| author_sort | Sanjoy Biswas |
| collection | DOAJ |
| description | In real life, structural problems can be described in linear and nonlinear forms. This nonlinear structural problem is very challenging to solve when its all parameters are imprecise in nature. Intuitionistic fuzzy sets were proposed to manage circumstances in which experts have some membership and non-membership value to judge an option. Hesitant fuzzy sets were used to manage scenarios in which experts pause between many possible membership values while evaluating an alternative. A new growing area of a generalized fuzzy set theory called intuitionistic hesitant fuzzy set (IHFS) provides useful tools for dealing with uncertainty in structural design problem that is observed in the actual world. In this article, we have developed a procedure to solve non-linear structural problem in an intuitionistic hesitant fuzzy (IHF) environment. The concept of an intuitionistic hesitant fuzzy set is introduced to provide a computational basis to manage the situations in which experts assess an alternative in possible membership values and non-membership values. This important feature is not available in the intuitionistic fuzzy optimization technique. Here we have discussed the solution procedure of intuitionistic hesitant fuzzy optimization technique dedicatedly for linear, exponential, and hyperbolic types of membership and non-membership functions. Some theoretical development based on these functions has been discussed. A numerical illustration is given to justify the effectiveness and efficiency of the proposed method in comparison with fuzzy multi-objective nonlinear programming method and intuitionistic fuzzy multi-objective nonlinear programming method. Finally, based on the proposed work, conclusions and future research directions are addressed. |
| first_indexed | 2024-03-11T13:16:26Z |
| format | Article |
| id | doaj.art-49cc8c6a5348414a82bcea894f974728 |
| institution | Directory Open Access Journal |
| issn | 2821-0131 |
| language | English |
| last_indexed | 2024-03-11T13:16:26Z |
| publishDate | 2023-11-01 |
| publisher | Islamic Azad University, Bandar Abbas Branch |
| record_format | Article |
| series | Transactions on Fuzzy Sets and Systems |
| spelling | doaj.art-49cc8c6a5348414a82bcea894f9747282023-11-03T11:15:29ZengIslamic Azad University, Bandar Abbas BranchTransactions on Fuzzy Sets and Systems2821-01312023-11-0122396210.30495/tfss.2023.1976999.1062701915Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership FunctionsSanjoy Biswas0Samir Dey1Department of Applied Science and Humanities (Mathematics) Guru Nanak Institute of Technology, Sodepur, Kolkata 700114, West Bengal, India.Department of Mathematics JIS University, 81, Nilgunj Road, Agarpara, Kolkata 700109, West Bengal, India.In real life, structural problems can be described in linear and nonlinear forms. This nonlinear structural problem is very challenging to solve when its all parameters are imprecise in nature. Intuitionistic fuzzy sets were proposed to manage circumstances in which experts have some membership and non-membership value to judge an option. Hesitant fuzzy sets were used to manage scenarios in which experts pause between many possible membership values while evaluating an alternative. A new growing area of a generalized fuzzy set theory called intuitionistic hesitant fuzzy set (IHFS) provides useful tools for dealing with uncertainty in structural design problem that is observed in the actual world. In this article, we have developed a procedure to solve non-linear structural problem in an intuitionistic hesitant fuzzy (IHF) environment. The concept of an intuitionistic hesitant fuzzy set is introduced to provide a computational basis to manage the situations in which experts assess an alternative in possible membership values and non-membership values. This important feature is not available in the intuitionistic fuzzy optimization technique. Here we have discussed the solution procedure of intuitionistic hesitant fuzzy optimization technique dedicatedly for linear, exponential, and hyperbolic types of membership and non-membership functions. Some theoretical development based on these functions has been discussed. A numerical illustration is given to justify the effectiveness and efficiency of the proposed method in comparison with fuzzy multi-objective nonlinear programming method and intuitionistic fuzzy multi-objective nonlinear programming method. Finally, based on the proposed work, conclusions and future research directions are addressed.https://tfss.journals.iau.ir/article_701915_52fa4750ae4994ff9acfefae5e99bad6.pdfmulti objective structural problemhesitant fuzzy setintuitionistic fuzzy optimizationintuitionistic-hesitant fuzzy optimizationpareto optimal solution |
| spellingShingle | Sanjoy Biswas Samir Dey Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions Transactions on Fuzzy Sets and Systems multi objective structural problem hesitant fuzzy set intuitionistic fuzzy optimization intuitionistic-hesitant fuzzy optimization pareto optimal solution |
| title | Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions |
| title_full | Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions |
| title_fullStr | Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions |
| title_full_unstemmed | Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions |
| title_short | Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions |
| title_sort | intuitionistic hesitant fuzzy algorithm for multi objective structural model using various membership functions |
| topic | multi objective structural problem hesitant fuzzy set intuitionistic fuzzy optimization intuitionistic-hesitant fuzzy optimization pareto optimal solution |
| url | https://tfss.journals.iau.ir/article_701915_52fa4750ae4994ff9acfefae5e99bad6.pdf |
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