The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theori...

A fuzzy rough set approach has been proposed without using any fuzzy logical connectives. By this approach, gradual decision rules are induced from a given decision table. Fuzzy-rough modus ponens and fuzzy-rough modus tollens have been formulated based on the gradual decision rules. The equivalence condition between fuzzy-rough modus ponens and fuzzy-rough modus tollens is discussed. The condi...

A new approach to normalizing fuzzy sets is introduced where it is assumed that the normalization method is compatible with a given t-norm. In this context it is proved that the most usual ways to normalize fuzzy subsets correspond to the most common t-norms. For a given fuzzy subset μ, the corresponding normalized fuzzy subset μ̂ can be viewed as the distribution of μ conditioned on the (degree...

This work presents a new methodology for ventricular premature contraction arrhythmias recognition using set of geometrical attributes recently proposed and fuzzy maximum approaching degree. Pattern models based on triangular trapezoidal membership functions are committee comprising these is composed some statistical data, beyond mechanism manual selection automatic weighting each attribute. Th...

This paper proposes a method to solve the group decision making (GDM) problems with multi-granularity linguistic assessment information. In the method, the multi-granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers. In order to make the collective opinion close to each expert’s opinion, a linear goal programming model is constructed to integra...

Smith’s article Fuzzy logic and higher-order vagueness [12] presents a solution to the problem of artificial precision, encountered in the degree-theoretical semantics of vagueness. The solution is based on fuzzy plurivaluationism, which has been discussed in more detail in Smith’s book [11]. Within the degree-theoretical framework, fuzzy plurivaluationism is certainly the appropriate treatment...

A fuzzy controller can be seen as an algorithm that, given a fuzzy set (input) and a set of linguistic rules, computes the degree of possibility of every control value. Using a valid and complete proof system for possibilistic logic, we will prove that fuzzy controllers enjoy the following property: every possibility measure that satisfies the degrees of possibility of the input and of the ling...

Received 17September 2013; accepted 5 October2013 L Baba Abstract. Finding shortest paths in graphs has been the area of interest for many researchers. Shortest paths are one of the fundamental and most widely used concepts in networks. In this paper the authors present an algorithm to find an Intuitionistic Fuzzy Shortest Path (IFSP) in a directed graph in which the cost of every edges are rep...