(a) Two definitions of the set of ‘comfortable temperatures’ on a universe of all real numbers |$\mathbb {X}$|⁠. The classical (crisp) set defines it as [20, 24], indicating a temperature value |$x$ | belonging to this interval means comfortable, i.e. |$\mu (x)=1$|⁠; otherwise not, i.e. |$\mu (x)=0$|⁠. The TFN, |$S= (12, 22, 32)$| as a special fuzzy set, defines the set of ‘comfortable temperatures’ in a more natural way, by giving the degree of membership of each temperature value |$x$|⁠, i.e. |$\mu (x)\in [0,1]$|⁠. This definition considers the diversity of how different people feel comfortable about distinct temperature. (b) Illustration of the |$\alpha $|-cut. The |$\alpha $|-cuts for |$\alpha =0.5$|⁠, |$\alpha =0.8$| and |$\alpha =1.0$| are calculated as crisp subsets |$[17,27]$|⁠, |$[20,24]$| and |$\{22\}$|⁠, respectively. (c) The main elements of an FIS. Crisp input values are converted via the fuzzifier into fuzzy values, which are then fed into the inference engine. The inference engine performs the reasoning with the fuzzy rules in the rule base and produces fuzzy output values. The defuzzifier then converts the fuzzy output values into crisp output values.