Linear Programming Optimization Model for Some Extensions of Fuzzy Sets

Abstract

The linear programming (LP) technique plays a central role in optimization that provides an effective instrument in various applications. The consideration of LP technique has been fascinating in optimization for many decades due to the following foremost reasons: • Various real-life problems can be understood in LP, • LP technique can be applied to large-scale computations, • Depending upon its nature, the LP technique is easy to compute. Multiple criteria decision-making (MCDM) is a tool used by decision-makers (DMs) to choose the superior option from the multiple discordant criteria. In the MCDM process, the weights of the criteria have a lot of influence to choose the most ideal option from the indistinguishable options. Based on the expertise, sometimes, the experts or DMs feel hesitation and incommode to assign the weights to each criterion. Generally, the experts allocate weights to the criteria by their own skills that lead to a biasedness in the analysis of the underlying MCDM which is obvious as they use the specific procedures that make it hard to deal with the big data. The importance of the procedure is thus compromised as it increases the probability of the error and eventually the final outcome (decision) is not trustworthy. The fundamental aim of the contemporary study is address the shortcomings in assigning weights due to hesitation and favoritism. As a result, the major xxii research contribution is to compute the weights for each criterion using LP technique. Moreover, there are lot of real-world problems that cannot be handled by a single DM. Thereby, it is essential to allot more than one DMs in an MCDM process from diverse areas. As an example, in a MCGDM, if one has to make a decision on an educational policy matter then the educational backgrounds, skill and knowledge related to the problem etc. has to be seen in selecting the corresponding experts. Some imperative extensions of FSs are to be considered for MCDM/MCGDM procedures to reach the comprehensive decisions in the present thesis. There are three parts of the thesis which are summarized as follows: In the first part, three extensive extensions of HFSs (IVHFSs, PrIVHFSs and DHFSs) are presented. These extensions are utilized to tackle the MCDM problems with the help of extended TOPSIS (E-TOPSIS), vector SMs like Dice and Jaccard SMs, respectively. The 2 nd part tells about the establishment of a GDM model based on compatibility measure under the environment of Pg FPRs to reach the best option. The 3rd and final part is important because here three extensions of FSs like, PcFSs, SVNSs and IVSVNs are investigated with real life problems. Further, the sensitivity analysis (SA) and Spearman’s rank correlation coefficient are utilized to strengthen the outcomes attained by the proposed MCDM approaches.