Below are shown your rules, the fuzzy sets they refer to, and an informal justification written as a dialogue between an engineer and their apprentice.
All rules combine the input variables cement_quality and water_cement_ratio , giving the result variable mix_durability .
if cement_quality be high_quality and water_cement_ratio be low_ratio then mix_durability := very_high. /* High-quality cement improves the mix's overall strength and durability, and a low water-cement ratio reduces porosity, enhancing durability. */ if cement_quality be high_quality and water_cement_ratio be medium_ratio then mix_durability := high. /* High-quality cement provides strong and durable properties, and a medium water-cement ratio balances strength and workability, maintaining good durability. */ if cement_quality be high_quality and water_cement_ratio be high_ratio then mix_durability := medium. /* While high-quality cement aids durability, a high water-cement ratio increases porosity, which can reduce durability. */ if cement_quality be medium_quality and water_cement_ratio be low_ratio then mix_durability := high. /* Medium-quality cement combined with a low water-cement ratio can still yield a durable mix by minimizing porosity. */ if cement_quality be medium_quality and water_cement_ratio be medium_ratio then mix_durability := medium. /* Medium-quality cement and a medium water-cement ratio result in average durability, suitable for general construction. */ if cement_quality be medium_quality and water_cement_ratio be high_ratio then mix_durability := low, because /* A high water-cement ratio increases porosity and reduces strength, leading to lower durability, even with medium-quality cement. */ if cement_quality be low_quality and water_cement_ratio be low_ratio then mix_durability := medium. /* Low-quality cement generally leads to less durability, but a low water-cement ratio can help improve it by reducing porosity. */ if cement_quality be low_quality and water_cement_ratio be medium_ratio then mix_durability := low. /* Low-quality cement and a medium water-cement ratio offer limited strength and durability. */ if cement_quality be low_quality and water_cement_ratio be high_ratio then mix_durability := very_low. /* Low-quality cement combined with a high water-cement ratio results in high porosity and significantly reduced durability. */
/* Fuzzy Set Definitions for Cement Quality */ low(cement_quality, 0). high(cement_quality, 5). scale(cement_quality, 'Scale of 0-5'). fuzzy_set(cement_quality, low_quality, down(0, 1, 2)). fuzzy_set(cement_quality, medium_quality, trap(1, 2, 3, 4)). fuzzy_set(cement_quality, high_quality, up(3, 4, 5)). /* Fuzzy Set Definitions for Water-Cement Ratio */ low(water_cement_ratio, 0). high(water_cement_ratio, 1). scale(water_cement_ratio, 'Scale of 0-1'). fuzzy_set(water_cement_ratio, low_ratio, down(0, 0.3, 0.4)). fuzzy_set(water_cement_ratio, medium_ratio, trap(0.3, 0.4, 0.6, 0.7)). fuzzy_set(water_cement_ratio, high_ratio, up(0.6, 0.7, 1)). /* Fuzzy Set Definitions for Mix Durability */ low(mix_durability, 0). high(mix_durability, 5). scale(mix_durability, 'Scale of 0-5'). fuzzy_set(mix_durability, very_low, down(0, 1, 2)). fuzzy_set(mix_durability, low, trap(1, 2, 3, 4)). fuzzy_set(mix_durability, medium, trap(2, 3, 4, 5)). fuzzy_set(mix_durability, high, trap(3, 4, 5, 6)). fuzzy_set(mix_durability, very_high, up(4, 5, 6)).
Apprentice: Hi, I saw you looking at some rules about concrete durability. Can you explain to me why those rules work? How do the properties of the ingredients affect the concrete's behavior?
Engineer: Of course, I'd be happy to explain. The durability of concrete is largely influenced by its physical, mechanical, and chemical properties, which in turn depend on the quality of the cement and the water-cement ratio.
Apprentice: Alright, let's start with cement quality. How does that affect durability?
Engineer: Cement quality is crucial. High-quality cement has a finer grind, better particle distribution, and fewer impurities. This leads to a more homogeneous and denser concrete mix, which in turn enhances mechanical properties such as compressive strength. It also reduces permeability.
Apprentice: So, better cement quality means stronger and less permeable concrete?
Engineer: Spot on! Less permeable concrete better resists environmental factors such as freeze-thaw cycles, chemical attacks, and corrosion of reinforcement. Now, let's talk about the water-cement ratio.
Apprentice: Yes, I was wondering about that. Why is the amount of water important?
Engineer: The water-cement ratio is fundamental in determining the concrete's strength and durability. A lower ratio means less water relative to cement. This leads to a denser and stronger concrete matrix once it hardens. Less water means fewer capillary pores and therefore lower permeability.
Apprentice: So, more water would weaken the concrete?
Engineer: Precisely. More water creates a more porous network in the hardened concrete. These pores can allow for easier entrance of harmful substances like chlorides or sulfates, which can deteriorate the concrete or corrode the reinforcement.
Apprentice: I see. So rules like "if high-quality cement and low water-cement ratio, then high durability" make sense because both factors contribute to a denser, stronger matrix.
Engineer: Right on. The interplay between cement quality and water-cement ratio defines the initial and final setting time of the concrete, its workability, and ultimately, its durability. High-quality cement with a low water-cement ratio typically yields a durable mix that can withstand harsh environmental conditions for longer.
Apprentice: What about mixes that don't meet these ideal conditions?
Engineer: Well, there, we often see a compromise in durability. For instance, medium-quality cement with a higher water-cement ratio might suffice for less demanding applications but won't provide the same durability for critical structures.
Apprentice: Splendid! This really helps me understand how the physical and chemical properties of the ingredients affect the concrete's overall performance. Thanks for explaining!