International Journal of Management and Fuzzy Systems 2020; 6(2): 29-46 http://www.sciencepublishinggroup.com/j/ijmfs doi: 10.11648/j.ijmfs.20200602.12 ISSN: 2575-4939 (Print); ISSN: 2575-4947 (Online) An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process Nenad Stojanovic Faculty of Agriculture, University of Banja Luka, Banja Luka, Bosnia and Herzegovina Email address: To cite this article: Nenad Stojanovic. An Algorithm for Clustering Input Variables in a Fuzzy Model in a FLC Process. International Journal of Management and Fuzzy Systems. Vol. 6, No. 2, 2020, pp. 29-46. doi: 10.11648/j.ijmfs.20200602.12 Received: September 18, 2020; Accepted: October 6, 2020; Published: October 13, 2020 Abstract: The input and output variables in fuzzy systems are linguistic variables. The base of the fuzzy rule represents the central part of a fuzzy controller, and the fuzzy rule represents its basic part, and it has the following form: "if R then P", where R and P represent the fuzzy relation, i.e. the proposition. Complex systems described by fuzzy relations generate a large number of inference rules. Grouping the states into clusters on the basis of which we make conclusions about the value of the output variable is performed by an expert based on his or her experience and knowledge. Ideally, the number of clusters should correspond to the number of attributes by which the value of the output variable is classified, which, in reality is not the case. In the absence of experts, we perform grouping on the basis of some of the criteria. One way of grouping descriptive states into clusters is presented in this paper. It presents a construction of the method of grouping descriptive states of fuzzy models, with the aim of drawing conclusions about the value of the output variable described by a given state. The presented method of grouping descriptive states is based on defined characteristic values associated with fuzzy numbers by which the input variables of the model are evaluated. They represent the basis for defining the characteristic value of the descriptive state of the output variable of a fuzzy model. For the presented method, a mathematical logical argumentation of the application is given, as an algorithm for the application of the constructed method. The application of the algorithm is demonstrated in measuring the economic dimension of the sustainability of tourism development, measured by comparative evaluation indicators. Keywords: Data Clustering, Reduction of Inference Rules, Algorithms, Mathematical Modeling, FLC Processes 1. Introduction The meaning of a term is specified by the use of the attributes. For example, the seasonality of a visit can be high or low. Obviously, no definite value can be set in which the benefit ceases to be low. and becomes high. The boundary between these two attributes is elastic and mainly depends on a personal assessment and the circumstances in which the term is observed [14, 15]. If we want a more precise specification of this term, then we can say, for example, that the loyalty is: very low., low, medium, high, very high. Obviously a larger number of attributes contributes to the linguistic specification of the term, but the problem of limits still remains open. Fuzzy sets can play a role of elastic limits between individual attributes. We associate a fuzzy set to each attribute individually and assign it a domain that has a clear semantic meaning. Generally, we can say that a family of fuzzy sets     ,  ,  ,...,   represents a framework of cognition of term X, if each element of term X is associated with at least one fuzzy set with a non-zero degree of affiliation. In the theory of fuzzy sets, a characteristic function,   , affiliation of element x to set A,      1 , 0 , (1) is generalized by a function of affiliation, i.e.   . The degree of affiliation of element  to a fuzzy set is given by the real value from interval [0,1], i.e.   :   0,1. Fuzzy set  is completely determined with the set of ordered pairs: [0,1], i.e.   ,   |  ,     0,1, (2) where    is the degree of affiliation of element  to set , and  is a universal set. If    is greater, then there is so much more truth in the claim that element  belongs to set .