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Presents fundamental results on fuzzy Mealy machines. Unlike the classical Mealy machine which requires two functions, one to describe the next state and another to describe the output, a fuzzy Mealy machine requires only one fuzzy function to characterize completely the next state and the output produced. Apart from the obvious generalization that can be obtained from corresponding results on fuzzy finite state machines by introduction of an output associated with each transition, introduces the concept of an interval partition of [0, 1] and uses it to obtain more general results.

Studies the concept of the Cartesian composition of fuzzy finite state machines. Shows that fuzzy finite state machines and their Cartesian composition share many structural properties. Some of these properties are singly generated; retrievability, connectedness, strong connectedness, commutativity, perfection and state independence. Thus a fuzzy finite state machine which is a Cartesian composition of submachines can be studied in terms of smaller machines.

In this paper, we define and examine the concept of a fuzzy recognizer. If L(M) is the language recognized by an incomplete fuzzy recognizer M, we show that there is a completion M of M such that L(M) = L(M). We also show that if A is a recognizable set of words, then there is a complete accessible fuzzy recognizer M_A such that L(M_A) = A. We lay groundwork to determine rational decompositions of recognizable sets.

The purpose of this research paper is to develop an algorithm/methodology for the reduction of a fuzzy recognizer through an algebraic concept such as homomorphism.

The approach of this research is to introduce the concepts, compatible with the purpose of this paper, and then to find a necessary and sufficient condition for the reduction of a fuzzy recognizer.

A fuzzy Σ‐recognizer M with non‐empty fuzzy initial state and the behavior A is reduced if and only if it is isomorphic to M^A.

The research proposes an algebraic method for the reduction of a fuzzy recognizer. The problem of finding dispensable fuzzy productions of a regular fuzzy grammar may be tackled by the use this algebraic method, as fuzzy recognizers and fuzzy regular grammars are equivalent.

The concepts and the methodology are original. The work is useful to the researchers in the field of fuzzy automata, fuzzy grammars and pattern recognition.

Mega construction projects (MCPs), characterized by their vast scale, numerous stakeholders and complex management, often face significant uncertainties and challenges. While existing research has explored the complexity of MCPs, it predominantly focuses on qualitative analysis and lacks systematic quantitative measurement methods. Therefore, this study aims to construct a complexity measurement model for MCPs using fuzzy comprehensive evaluation and grey relational analysis.

This study first constructs a complexity measurement framework through a systematic literature review, covering six dimensions of technical complexity, organizational complexity, goal complexity, environmental complexity, cultural complexity and information complexity and comprising 30 influencing factors. Secondly, a fuzzy evaluation matrix for complexity is constructed using a generalized bell-shaped membership function to effectively handle the fuzziness and uncertainty in the assessment. Subsequently, grey relational analysis is used to calculate the relational degree of each complexity factor, identifying their weights in the overall complexity. Finally, the weighted comprehensive evaluation results of project complexity are derived by combining the fuzzy evaluation results with the grey relational degrees.

To validate the model’s effectiveness, the 2020 Xi’an Silk Road International Conference Center construction project is used as a case study. The results indicate that the overall complexity level of the project is moderate, with goal complexity being the highest, followed by organizational complexity, environmental complexity, technical complexity, cultural complexity and informational complexity. The empirical analysis demonstrates that the model can accurately reflect the variations across different dimensions of MCP complexity and can be effectively applied in real-world projects.

This study systematically integrates research on MCPs complexity, establishing a multidimensional complexity measurement framework that addresses the limitations of previous studies focusing on partial dimensions. Moreover, the proposed quantitative measurement model combines fuzzy comprehensive evaluation and grey relational analysis, enhancing the accuracy and objectivity of complexity measurement while minimizing subjective bias. Lastly, the model has broad applicability and can be used in MCPs across different countries and regions, providing a scientific and effective basis for identifying and managing MCP complexity.