Optimization Techniques for Decision-making and Information Security

A New Algorithm for Solving Fully Fuzzy Linear Programming Problems using the Lexicographic Method

Author(s): Anil Kumar Nishad*, Gunjan Agarwal, S. R. Singh and Gajraj Singh

Pp: 48-61 (14)

DOI: 10.2174/9789815196320124030007

* (Excluding Mailing and Handling)

Abstract

In the current situation, ranking a general fuzzy number is a difficult task, and various ranking methods have been developed, but no perfect ranking method exists. To solve fully fuzzy linear programming problems, many ranking functions have been developed and implemented in the literature. However, all of these methods have some limitations. In this chapter, we propose a new method for comparing two triangular fuzzy numbers in a generalised form. The Ezzati method [1] has been expanded upon using the suggested approach to handle fully fuzzy linear programming issues (FFLPP). The implementation of the developed algorithm has been illustrated through numerical illustrations. The proposed algorithm has been applied to a transportation problem in light of extensive testing, and it has been discovered that it is effective and generally offers a better solution.

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      • 14. app/Models/UserAccess/UserAccess.php:784
      • 15. middleware::check_user_access:114
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      • 18. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
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      • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:206
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      • 16. app/Models/Subject.php:238
      • 17. app/Http/Controllers/ChapterController.php:1434
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 19. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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      • 14. app/Models/Subject.php:238
      • 15. app/Http/Controllers/ChapterController.php:1434
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      • 16. app/Models/Subject.php:255
      • 17. app/Http/Controllers/ChapterController.php:1435
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      • 14. app/Models/Subject.php:255
      • 15. app/Http/Controllers/ChapterController.php:1435
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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      270μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
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      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ChapterController.php:1465
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      230μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
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      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ChapterController.php:1478
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      570μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1518
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 60015499 and j.to_ip >=60015499 )) and ((j.from_date <= 1740528708 and j.to_date >= 1740528708 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 22359) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 60015499 and j.to_ip >=60015499 )) and ((j.from_date <= 1740528708 and j.to_date >= 1740528708 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 22359) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 60015499 and j.to_ip >=60015499 )) and ((j.from_date <= 1740528708 and j.to_date >= 1740528708 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 22359)
      510μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 3716 and `b`.`banner_from_date` <= 1740528708 and `b`.`banner_to_date` >= 1740528708 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.04msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 3716
      • 3: 1740528708
      • 4: 1740528708
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='031013d9c6b5c7d15c6de7d8c13f299b'
      220μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        ZALfFhzE6aKWA1qnxqDabwhPtsDbAHKwsSjEknmW
        uc_cart_id
        031013d9c6b5c7d15c6de7d8c13f299b
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/22359" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/22359
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6IldPNXdpYm5ZVEtFUDkxL3UrM09PQ3c9PSIsInZhbHVlIjoiTllDak94bDB3c1l4ci9INFh5am5pRVJHUTJqZzB4MGZEN29LTHovanFBYz0iLCJtYWMiOiIzNWMwNTlhOGQwNzQ0YTk5MTA4Y2VjNzZmOTQ0MzJhM2MwNGJhY2M2NGUzNDI0ZWU3M2Q1MGRiZGZjNzQwMWY0IiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6IldPNXdpYm5ZVEtFUDkxL3UrM09PQ3c9PSIsInZhbHVlIjoiTllDak94bDB3c1l4ci9INFh5am5pRVJHUTJqZzB4MGZEN29LTHovanFBYz0iLCJtYWMiOiIzNWMwNTlhOGQwNzQ0" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:1 [ "wayfindertarget" => null ]
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Wed, 26 Feb 2025 00:11:48 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InlBL2JSWHRZZ0Faek16YzJUZDlzQmc9PSIsInZhbHVlIjoiUDA5ZGlmRmxpZFlQM0IydnZqS1VUaVhHbzZYbURkSU5aTVJOL1BMcy9TeFM2RHpjSzNiS0s2eDh4OEtCWEw5V1hESVBTdWl6aHpTTFJ6dG5HU3JEUnh6UWJPdEprWmx5RmliQXRJUnV6MzB3VzYwVDJoZk5QOTM3djNYeHVDRzUiLCJtYWMiOiI4ZjJmNTJhY2YxMjI4NzY2YmEzZjg4ZDUyMzkyMjUxNGY2ODc3OWY1ODNmYjkzNTM5NjQ4NmQ3MTMwYjI1ZDk1IiwidGFnIjoiIn0%3D; expires=Fri, 28 Feb 2025 12:11:48 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6InlBL2JSWHRZZ0Faek16YzJUZDlzQmc9PSIsInZhbHVlIjoiUDA5ZGlmRmxpZFlQM0IydnZqS1VUaVhHbzZYbURkSU5aTVJOL1BMcy9TeFM2RHpjSzNiS0s2eDh4OEtCWEw5V1hESVBTd" 1 => "alphaeurekaselectnet_session=eyJpdiI6IlFEdmd0Z1pQLytSaVUxbzEybzBLVXc9PSIsInZhbHVlIjoiMGRpZ1BmQVB3elRiby9hNXN6T01FbHVKaGRXL0dHSEZJbEhyK0M0MVJnTk10N1VIdk1TSWFJSzB3djUyWVRuZjJpalVsZFJTald0RFUxR29BUkhwZG9HT0tVVGs5SUdjL2FlUmJrbHFIbFp3cEdYTUFtVWNyY09hMHFxbEVOQ2MiLCJtYWMiOiIxMzNjYjhlYWRjMDdjM2U4YTZlOGFlMDhmZDEwNGEyZDkxN2VmZGY2OGYwYzYyNTY4MTVkYmMzMmUyMDAyYTRiIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6IlFEdmd0Z1pQLytSaVUxbzEybzBLVXc9PSIsInZhbHVlIjoiMGRpZ1BmQVB3elRiby9hNXN6T01FbHVKaGRXL0dHSEZJbEhyK0M0MVJnTk10N1VIdk1TSWFJSzB" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InlBL2JSWHRZZ0Faek16YzJUZDlzQmc9PSIsInZhbHVlIjoiUDA5ZGlmRmxpZFlQM0IydnZqS1VUaVhHbzZYbURkSU5aTVJOL1BMcy9TeFM2RHpjSzNiS0s2eDh4OEtCWEw5V1hESVBTdWl6aHpTTFJ6dG5HU3JEUnh6UWJPdEprWmx5RmliQXRJUnV6MzB3VzYwVDJoZk5QOTM3djNYeHVDRzUiLCJtYWMiOiI4ZjJmNTJhY2YxMjI4NzY2YmEzZjg4ZDUyMzkyMjUxNGY2ODc3OWY1ODNmYjkzNTM5NjQ4NmQ3MTMwYjI1ZDk1IiwidGFnIjoiIn0%3D; expires=Fri, 28-Feb-2025 12:11:48 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6InlBL2JSWHRZZ0Faek16YzJUZDlzQmc9PSIsInZhbHVlIjoiUDA5ZGlmRmxpZFlQM0IydnZqS1VUaVhHbzZYbURkSU5aTVJOL1BMcy9TeFM2RHpjSzNiS0s2eDh4OEtCWEw5V1hESVBTd" 1 => "alphaeurekaselectnet_session=eyJpdiI6IlFEdmd0Z1pQLytSaVUxbzEybzBLVXc9PSIsInZhbHVlIjoiMGRpZ1BmQVB3elRiby9hNXN6T01FbHVKaGRXL0dHSEZJbEhyK0M0MVJnTk10N1VIdk1TSWFJSzB3djUyWVRuZjJpalVsZFJTald0RFUxR29BUkhwZG9HT0tVVGs5SUdjL2FlUmJrbHFIbFp3cEdYTUFtVWNyY09hMHFxbEVOQ2MiLCJtYWMiOiIxMzNjYjhlYWRjMDdjM2U4YTZlOGFlMDhmZDEwNGEyZDkxN2VmZGY2OGYwYzYyNTY4MTVkYmMzMmUyMDAyYTRiIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6IlFEdmd0Z1pQLytSaVUxbzEybzBLVXc9PSIsInZhbHVlIjoiMGRpZ1BmQVB3elRiby9hNXN6T01FbHVKaGRXL0dHSEZJbEhyK0M0MVJnTk10N1VIdk1TSWFJSzB" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "ZALfFhzE6aKWA1qnxqDabwhPtsDbAHKwsSjEknmW" "uc_cart_id" => "031013d9c6b5c7d15c6de7d8c13f299b" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/22359" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-26 00:11:48GET/chapter/22359112192