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The idea of linear Diophantine fuzzy set (LDFS) theory with its control parameters is a strong model for machine learning and optimization under uncertainty. The activity times in the critical path method (CPM) representation procedures approach are initially static, but in the Project Evaluation and Review Technique (PERT) approach, they are probabilistic. This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy (LDF) environment. The LDF expected task time, LDF variance, LDF critical path, and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network. The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT, Fuzzy PERT, and so on. The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision. We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings. When the available resources and activity times are imprecise and unpredictable, this strategy can help decision-makers make better judgments in a project. A comparison analysis of the proposed technique with the existing techniques has also been discussed. The suggested techniques are demonstrated with two suitable numerical examples. [ABSTRACT FROM AUTHOR]

A fuzzy system is a novel computing technique that accesses uncertain information by fuzzy representation. In the decision-making process, fuzzy system and soft computing are effective tools that are tolerant to imprecision, uncertainty, and partial truths. Evolutionary fuzzy systems have been developed with the appearance of interval fuzzy, dual fuzzy, hesitant fuzzy, neutrosophic, plithogenic representations, etc. Moreover, by capturing compound features and convey multi-dimensional data, complex numbers are utilized to generalize fuzzy and neutrosophic fuzzy sets. In this paper, a representation of neutrosophic soft expert systems based on the real and complex numbers in the interval form is proposed. The interval-valued neutrosophic soft expert set (I-VNSES) is defined, and the interval-valued complex neutrosophic soft expert set (I-VCNSES) is formally generalized from the concept of IVNSES. For both I-VNSES and I-VCNSES, we introduce the relevant basic theoretical operations and study their properties. Based on these new concepts, a generalized algorithm is proposed and applied to handle the imbedded indeterminacy in the two-dimensional interval data. The proposed algorithm is tested on the economic factors that affected the Malaysian economy in 2020 to see which ones are the most influential. Eventually, a comparison of three current approaches is used to back up this study. [ABSTRACT FROM AUTHOR]