Search Results (6)

Recent work has shown that the f-index of inclusion can serve as a foundation for modeling Generalized Modus Ponens. In this paper, we develop a novel fuzzy inference system based on this inference rule. To establish its soundness, we connect it to a Fuzzy Description Logic $\mathcal{LU}$ enriched with fuzzy modifiers (also known as fuzzy hedges). This logic background provides to the approach a strength absent in most fuzzy inference systems in the literature, which allows us to formally prove a series of results that culminate in a final correctness theorem for the proposed fuzzy inference system. This paper also presents a running example aimed at showing the potential applicability of the proposal. Full article

Reasoning is a cognitive activity that leverages knowledge to generate solutions to problems. Knowledge representations in the brain require both symbolic and graphical information since visual information is figurative and conveys a large amount of information. Consequently, graphical knowledge representation is often employed in reasoning. Distance-type fuzzy inference utilizes the distance information between the antecedent and the set of facts as the basis for inference. Compared to Mamdani inference, the distance-type fuzzy inference method not only satisfies the convexity and asymptotic properties of the inference results but also adheres to the separation rule (modus ponens), a fundamental principle in inference. This paper discusses extensions of distance-type fuzzy inference methods to handle spatial figures. In this paper, we first explain the distance-type fuzzy inference method. Then, we discuss the concept representation in the feature space and independent parameters that can completely express the characteristics of a figure in space, which are defined as “characteristic parameters”. Furthermore, we describe the correspondence between figures and vectors in the feature space, propose a new distance-type fuzzy inference method based on characteristic parameters and describe its characteristics. Finally, an example is used to demonstrate the inference results of this new distance-type fuzzy inference method. Full article

The overlap function, a particular kind of binary aggregate function, has been extensively utilized in decision-making, image manipulation, classification, and other fields. With regard to overlap function theory, many scholars have also obtained many achievements, such as pseudo-overlap function, quasi-overlap function, semi-overlap function, etc. The above generalized overlap functions contain commutativity and continuity, which makes them have some limitations in practical applications. In this essay, we give the definition of pseudo-quasi overlap functions by removing the commutativity and continuity of overlap functions, and analyze the relationship of pseudo-t-norms and pseudo-quasi overlap functions. Moreover, we present a structure method for pseudo-quasi overlap functions. Then, we extend additive generators to pseudo-quasi overlap functions, and we discuss additive generators of pseudo-quasi overlap functions. The results show that, compared with the additive generators generated by overlap functions, the additive generators generated by pseudo-quasi overlap functions have fewer restraint conditions. In addition, we also provide a method for creating quasi-overlap functions by utilizing pseudo-t-norms and pseudo automorphisms. Finally, we introduce the idea of left-continuous pseudo-quasi overlap functions, and we study fuzzy inference triple I methods of residual implication operators induced by left-continuous pseudo-quasi overlap functions. On the basis of the above, we give solutions of pseudo-quasi overlap function fuzzy inference triple I methods based on FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems. Full article

Generalized modus ponens (GMP) is a basic model of approximate reasoning. GMP in fuzzy propositions is called fuzzy modus ponen (FMP) and it is called intuitionistic fuzzy modus ponens (IFMP) when fuzzy propositions are generalized to intuitionistic fuzzy propositions. In this paper, we aim to investigate fuzzy reasoning methods for GMP with mixture of fuzzy/intuitionistic fuzzy information. For mixed types of GMP, we present two basic methods to solve GMP problems based on the triple I method (TIM). One is to transform the GMP problem into two FMP problems by decomposition and aggregate the solutions of TIM for FMP problems to obtain the solution for GMP problem. The other is to transform the GMP problem into the IFMP problem by expansion and aggregate the solutions of TIM for the IFMP problem to obtain the solution for the GMP problem. These two methods are called the decomposition triple I method (DTIM) and expansion triple I method (ETIM), respectively. We analyze the relationship between DTIM and ETIM. Furthermore, we discuss the reversibility of DTIM and ETIM. Full article

Two important basic inference models of fuzzy reasoning are Fuzzy Modus Ponens (FMP) and Fuzzy Modus Tollens (FMT). In order to solve FMP and FMT problems, the full implication triple I algorithm, the reverse triple I algorithm and the Subsethood Inference Subsethood (SIS for short) algorithm are proposed, respectively. Furthermore, the existing reasoning algorithms are extended to intuitionistic fuzzy sets and interval-valued fuzzy sets according to different needs. The purpose of this paper is to study the relationship between intuitionistic fuzzy reasoning algorithms and interval-valued fuzzy reasoning algorithms. It is proven that there is a bijection between the solutions of intuitionistic fuzzy triple I algorithm and the interval-valued fuzzy triple I algorithm. Then, there is a bijection between the solutions of intuitionistic fuzzy reverse triple I algorithm and the interval-valued fuzzy reverse triple I algorithm. At the same time, it is shown that there is also a bijection between the solutions of intuitionistic fuzzy SIS algorithm and interval-valued fuzzy SIS algorithm. Full article

As a generalization of intuitionistic fuzzy sets, single-valued neutrosophic sets have certain advantages for solving indeterminate and inconsistent information. In this paper, we study the fuzzy inference full implication method based on a single-valued neutrosophic t-representable t-norm. Firstly, single-valued neutrosophic fuzzy inference triple I principles for fuzzy modus ponens and fuzzy modus tollens are shown. Then, single-valued neutrosophic $ℛ$-type triple I solutions for fuzzy modus ponens and fuzzy modus tollens are given. Finally, the robustness of the full implication of the triple I method based on a left-continuous single-valued neutrosophic t-representable t-norm is investigated. As a special case in the main results, the sensitivities of full implication triple I solutions, based on three special single-valued neutrosophic t-representable t-norms, are given. Full article