Investigations of fuzzy implications satisfying generalized hypothetical syllogism

Fuzzy control theory has been extensively used in the construction of complex fuzzy inference systems. However, we argue that existing fuzzy control technologies focus mainly on the single-source fuzzy information system, disregarding the complementary nature of multi-source data. In this paper, we develop a novel Gaussian-shaped Fuzzy Inference System (GFIS) driven by multi-source fuzzy data. To this end, we first propose an interval-value normalization method to address the heterogeneity of multi-source fuzzy data. The contribution of our interval-value normalization method involves mapping heterogeneous fuzzy data to a unified distribution space by adjusting the mean and variance of data from each information source. As a result of combining the normalized descriptions from various sources for an object, we can obtain a fused representation of that object. We then derive an adaptive Gaussian-shaped membership function based on the addition law of the Gaussian distribution. GFIS uses it to dynamically granulate fusion inputs and to design inference rules. This proposed membership function has the advantage of being able to adapt to changing information sources. Finally, we integrate the normalization method and adaptive membership function to the Takagi–Sugeno (T–S) model and present a modified fuzzy inference framework. Applying our methodology to four datasets, we confirm that the data do lend support to the theory implying the improved performance and effectiveness.

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“…This is the core of an FIS. In an FIS, syllogisms [29][30][31] are commonly used to make inferences, which can be expressed as follows:…”

Section: Preliminarymentioning

confidence: 99%

A Gaussian-Shaped Fuzzy Inference System for Multi-Source Fuzzy Data

Zhang

Qin

2022

Systems

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“…Namely, they are used in approximate reasoning and/or fuzzy control. Recently, we have investigated generalized hypothetical syllogism in fuzzy logic [2] (see also [7]). This notion can be introduced from a T -transitivity in the following way T (I(x, z), I(z, y)) ≤ I(x, y), x, y, z ∈ [0, 1], (HS) where T is a t-norm and I a fuzzy implication.…”

Section: Introductionmentioning

confidence: 99%

Some Remarks on the Generalized Scheme of Reduction to Absurdity and Generalized Hypothetical Syllogism in Fuzzy Logic

Miś¹,

Baczyński²,

Helbin³

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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In this paper we investigate two generalizations, in fuzzy logic, of classical scheme of reduction to absurdity. We compare them with two possible generalizations of classical hypothetical syllogism (in fuzzy logic) and we show that generalized hypothetical syllogism is more general. We present new results concerning solutions of an inequality and an equation connected directly with generalization of scheme of reduction to absurdity in fuzzy logic.

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