AI-Driven Decision Support System for Intuitionistic Fuzzy Assignment Problems

AI-Driven Decision Support System for Intuitionistic Fuzzy Assignment Problems

P. Senthil Kumar
Copyright: © 2024 |Pages: 47
DOI: 10.4018/979-8-3693-0639-0.ch016
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Abstract

The assignment problem (AP) is a well-known optimization problem that deals with the allocation of 'n' jobs to 'n' machines on a 1-to-1 basis. It minimizes the cost/time or maximizes the profit/production of the problem. Generally, the profit, sale, cost, and time are all called the parameters of the AP (in a traditional AP, out of these parameters, exactly one parameter will be considered a parameter of the problem). These are not at all crisp numbers due to several uncontrollable factors, which are in the form of uncertainty and hesitation. So, to solve the AP in this environment, the author proposes the software and ranking method-based PSK (P. Senthil Kumar) method. Here, plenty of theorems related to intuitionistic fuzzy assignment problems (IFAPs) are proposed and proved by the PSK. To show the superiority of his method, he presents 4 IFAPs. The computer programs for the proposed problems are presented precisely, and the results are verified with Matlab, RGui, etc. In addition, comparative results, discussion, merits and demerits of his method, and future studies are given.
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Introduction And Literature Survey

There are several methods available to solve real-world problems. Mainly, assignment problems (AP) and its solving methods are used to solve real-life problems. An AP plays an important role in assigning the following effectively:

  • •

    drivers ↔ trucks

  • •

    trucks ↔ routes

  • •

    persons ↔ jobs

  • •

    operators ↔ machines

  • •

    problems ↔ research teams, etc.

The AP is a special case of the linear programming problem (LPP). In LPP, the plan of the decision maker (DM) is to assign ‘n’ no. of jobs to ‘n’ no. of machines at a minimum cost or time. In the management science literature, to find out the solutions to assignment problems (APs), many researchers presented different methods. Some of the methods are listed in Table 1.

Table 1.
Some of the academic publications related to APs
    Authors    Aim    Methods
    Kuhn (1955)    To introduce and solve the AP    Hungarian
    Dutta and Pal (2015)    To find out the optimal solution of AP    Modified Hungarian
    Matsiy et al. (2015)    To solve the AP    Recurrent
    Shah et al. (2015)To solve the m×n AP    An alternate approach same as Hungarian
    Lee (2015)    To solve the AP    Minimum cost moving
    Betts and Vasko (2016)    To solve the unbalanced assignment problem    Hungarian
    Porchelvi and Anitha (2018)    To find out the optimal solution for AP    Average total opportunity cost
    Jamali et al. (2019)    To find out the IBFS using Modified Weighted Opportunity Cost based Least Cost Matrix (MWOC-LCM)    MWOC-LCM
    Murugesan and Esakkiammal (2020a, b)    To find the optimal solution of AP    New Method (NM), Advanced Method (NS-AVSNM), Innovative Method (TVAM), New Methodology (MAP) and TERM
    Nu’man et al. (2020)
    To find out the suitable location with the help of assignment
    method
    Assignment
    method
    Munot and Ghadle (2020)    To obtain the optimal solution of AP with congruence modulo approach    New algorithm
    Wang et al. (2020)    To solve the shortest time AP    Minimum adjustment
    Hussein and Shiker (2020)    To find a solution to the AP    Al-Saeedi's 1st method and Al-Saeedi's 2nd method
    Kaur et al. (2020)    To do the time-cost trade-off analysis of a priority based AP    Criteria based iterative algorithm
    Jayalakshmi et al., (2020)    To solve the AP    Standard method
    De Turck (2020)    To find the efficient resource allocation through ILPP    Integer linear programming
    Hu and Liu (2021)    To solve the generalized AP    Network flow algorithm
    Li et al. (2021)    To solve the multi-dimensional APs    A dual approach
    Chandrakala (2021)    To find the optimal solution of a travelling salesman and AP    Enhanced zero suffix approach
    Mondal and Tsourdos (2021)    To find the optimum task allocation    Genetic Algorithm
    Sadiq et al. (2022)    To compare the solution of AP with three different approaches    Hungarian, Alternate and New Technique
    Beirkdar and Ramesh (2022)    To find an optimal solution of APs in the complete interval    A new approach
    Shanmugasundari and Aarthi (2022)    To solve the real-world problems    The modified approach of fuzzy measures
    Gothi et al. (2023)    To find the optimal solution of AP    Median and Variable approaches
    Arora and Sharma (2023)    To solve task AP    Branch and Bound method
    Mohammed et al. (2023)    To compare the solution of AP with existing approaches    Penalty Approach

The methods mentioned in Table 1 are not all useful for solving AP with uncertain parameters.

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