As we delve into the 21st century, the rapidly evolving landscape of pet care services, specifically pet sitting, has been undeniably transformed by technological advances, shifts in societal attitudes, and new market demands. This change has led us to predict novel emerging trends in the near future of pet sitting services.

Pet sitting, traditionally, involves a contracted individual caring for a pet in its own home while the owner is away. However, the digital revolution has not left this industry untouched. The advent of the internet and the resultant digital platforms have led to the creation of a shared economy in the pet sitting industry.

Platforms such as Rover and Wag have revolutionized the pet sitting scene by providing a marketplace that brings pet sitters and pet owners together. The success of these platforms lies in the theory of two-sided markets, an economic principle which posits that platforms derive value by serving two customer groups that are interdependent. In this case, pet sitters and pet owners. These platforms are using advanced algorithms to create a much more efficient matching process between pet sitters and pet owners than was previously possible.

One can even discern a parallel with the Heisenberg uncertainty principle from quantum mechanics, where the more precisely the position of a particle is determined, the less precisely its momentum can be known, and vice versa. In the context of pet sitting, the more precisely we can determine the needs of a pet owner (position), the less precisely we can predict the availability and suitability of a pet sitter (momentum), and vice versa. These digital platforms, with their advanced algorithms, are thus working to minimize this uncertainty.

More recently, pet sitting services have begun to incorporate smart technology into their services, leading us to our first prediction. In the coming years, we foresee a significant rise in the use of IoT (Internet of Things) devices in pet sitting. IoT devices such as pet cameras, automatic feeders, and GPS collars allow pet sitters to monitor and care for pets more efficiently. Simultaneously, they provide pet owners with peace of mind, knowing that they can check in on their beloved pets at any time.

However, as with any technology, there are trade-offs. Privacy concerns are a significant issue with the use of IoT devices. The use of pet cameras, for example, could lead to potential breaches of privacy if the data collected is not adequately secured.

Next, we must consider changes in societal attitudes towards pets. In many societies, pets are increasingly viewed as members of the family. This anthropomorphizing of pets has led to an increase in demand for personalized and premium pet care services.

Accordingly, our second prediction for the future of pet sitting services is towards highly personalized services. This could include personalized meal plans based on the pet's dietary needs, individualized exercise regimes, or even personalized pet entertainment. This shift towards personalization reflects broader trends in consumer behavior, with consumers increasingly seeking products and services tailored to their individual needs and preferences.

Lastly, the pet sitting industry is not immune to the increasing awareness and concern for environmental sustainability. Our third prediction, therefore, is a move towards more environmentally sustainable practices in pet sitting. This could involve using environmentally-friendly pet products, promoting adoption over buying, or implementing waste management strategies.

In conclusion, the future of pet sitting services is both exciting and challenging. The integration of digital platforms, smart technology, and changing societal attitudes towards pets are rapidly reshaping the industry. However, these developments also raise new issues and challenges that industry stakeholders must navigate. As we look to the future, it is clear that the pet sitting industry, like many others, is on the cusp of a new era of innovation and transformation.