Consider the systems of linear interval equations whose coefficients are linear functions of interval parameters. Such systems, called parametrized systems of linear interval equations, are encountered in many practical problems, e.g in electrical engineering and structure mechanics. A direct method for computing a tight enclosure for the solution set is proposed in this paper. It is proved that for systems with real matrix and interval right-hand vector the method generates the hull of the solution set. For such systems an explicit formula for the hull is also given. Finally some numerical examples are provided to demonstrate the usefulness of the method in structure mechanics.

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Introduction: The advances in the digital era have necessitated the adoption of communication as the main channel for modern business. In the past, business negotiations, profiling, seminars, shopping, and agreements were in-person but today everything is almost digitalized. Objectives: The study aims to examine how the Internet of things (IoTs) connects text-object as part of NLP and AI responding to human needs. Also, how precipitated changes in the business environment and modern applications such as NLP and AI embedded with IoTs services have changed business settings. Problem statement: As communication takes lead in the business environment, companies have developed sophisticated applications of NLP that take human desires and fulfill them instantly with the help of text, phone calls, smart records, and chatbots. The ease of communication and interaction has shown a greater influence on customer choice, desires, and needs. Modern service providers now use email, text, phone calls, smart records, and virtual assistants as first contact points for almost all of their dealings, customer inquiries, and most preferred trading channels. Method: The study uses text content as part of NLP and AI to demonstrate how companies capture customers’ insight and how they use IoTs to influence customers’ reactions, responses, and engagement with enterprise management in industry 4.0. The “Behavior-oriented drive and influential function of IoTs on Customers in Industry 4.0” concept was used in this study to determine the influence of industry 4.0 on customers. Results: The result indicates the least score of 12 out of 15 grades for all the measurements on a behavior-oriented drive and influential function of IoTs on customers. Conclusion: The study concluded that NLP and AI are the preferred system for enterprise management in the era of industry 4.0 to understand customers’ demands and achieve customer satisfaction. Therefore, NLP and AI techniques are a necessity to attain business goals.

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Systems of linear and nonlinear equations with fuzzy parameters are relevant to many practical problems arising in structure mechanics, electrical engineering, finance, economics and physics. In this paper three methods for solving such equations are discussed: method for outer interval solution of systems of linear equations depending linearly on interval parameters, fuzzy finite element method proposed by Rama Rao and sensitivity analysis method. The performance and advantages of presented methods are described with illustrative examples. Extended version of the present paper can be downloaded from the web page of the UTEP [I. Skalna, M.V.

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