Matrix Games with Interval-Valued 2-Tuple Linguistic Information
In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-09-01
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| Series: | Games |
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| Online Access: | http://www.mdpi.com/2073-4336/9/3/62 |
| _version_ | 1828770483850444800 |
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| author | Anjali Singh Anjana Gupta |
| author_facet | Anjali Singh Anjana Gupta |
| author_sort | Anjali Singh |
| collection | DOAJ |
| description | In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs. |
| first_indexed | 2024-12-11T14:07:56Z |
| format | Article |
| id | doaj.art-343b892b8e7e44479c82c1b658eddddc |
| institution | Directory Open Access Journal |
| issn | 2073-4336 |
| language | English |
| last_indexed | 2024-12-11T14:07:56Z |
| publishDate | 2018-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Games |
| spelling | doaj.art-343b892b8e7e44479c82c1b658eddddc2022-12-22T01:03:35ZengMDPI AGGames2073-43362018-09-01936210.3390/g9030062g9030062Matrix Games with Interval-Valued 2-Tuple Linguistic InformationAnjali Singh0Anjana Gupta1Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, IndiaDepartment of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, IndiaIn this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs.http://www.mdpi.com/2073-4336/9/3/622-tuple linguistic modelinterval-valued 2-tuple linguistic modellinguistic linear programming probleminterval-valued linguistic matrix game |
| spellingShingle | Anjali Singh Anjana Gupta Matrix Games with Interval-Valued 2-Tuple Linguistic Information Games 2-tuple linguistic model interval-valued 2-tuple linguistic model linguistic linear programming problem interval-valued linguistic matrix game |
| title | Matrix Games with Interval-Valued 2-Tuple Linguistic Information |
| title_full | Matrix Games with Interval-Valued 2-Tuple Linguistic Information |
| title_fullStr | Matrix Games with Interval-Valued 2-Tuple Linguistic Information |
| title_full_unstemmed | Matrix Games with Interval-Valued 2-Tuple Linguistic Information |
| title_short | Matrix Games with Interval-Valued 2-Tuple Linguistic Information |
| title_sort | matrix games with interval valued 2 tuple linguistic information |
| topic | 2-tuple linguistic model interval-valued 2-tuple linguistic model linguistic linear programming problem interval-valued linguistic matrix game |
| url | http://www.mdpi.com/2073-4336/9/3/62 |
| work_keys_str_mv | AT anjalisingh matrixgameswithintervalvalued2tuplelinguisticinformation AT anjanagupta matrixgameswithintervalvalued2tuplelinguisticinformation |