Available online at www.sciencedirect.com Fuzzy Sets and Systems 215 (2013) 112 – 126 www.elsevier.com/locate/fss SIRMs connected fuzzy inference method adopting emphasis and suppression Hirosato Seki a , ∗ , Masaharu Mizumoto b a Department of Mathematical Sciences, Kwansei Gakuin University, 2-1 Gakuen, Sanda-shi 669-1337, Japan b Department of Engineering Informatics, Osaka Electro-Communication University, 18-8 hatsu-cho, Neyagawa-shi 572-8530, Japan Received 20 November 2011; received in revised form 4 July 2012; accepted 5 July 2012 Available online 16 July 2012 Abstract The single input rule modules connected fuzzy inference method (SIRMs method) can decrease the number of fuzzy rules drastically in comparison with the conventional fuzzy inference methods. However, the inference results obtained by the SIRMs method is generally simple compared with those of the conventional fuzzy inference methods. For example, the SIRMs method may be not equivalent to the product–sum-gravity method and fuzzy singleton-type inference method, if the fuzzy sets of the antecedent parts are limited to normal fuzzy sets. In this paper, we propose a fuzzy singleton-type SIRMs method, which weights the rules of the SIRMs method, in order to solve the above problem. This paper also clarifies the property of the fuzzy singleton-type SIRMs method, from the view point of equivalence and monotonicity. Moreover, the fuzzy singleton-type SIRMs method is shown to be superior to the conventional SIRMs method by applying to a medical diagnosis system. © 2012 Elsevier B.V. All rights reserved. Keywords: Approximate reasoning; SIRMs connected fuzzy inference method; Emphasis and suppression; Equivalence; Monotonicity 1. Introduction The single input rule modules connected type fuzzy inference method (SIRMs method) by Yubazaki, Yi et al. [1–6], which unifies the inference outputs from fuzzy rule modules of one input type “IF–THEN” form, can reduce the number of fuzzy rules drastically. The method has been applied to nonlinear function identification [1], control of first and second order lag system with dead time [1,2], stabilization control of inverted pendulum systems [3–5], anti-swing and positioning control of overhead traveling crane [6], etc., and good results are obtained. However, since the number of rules of the SIRMs method is limited compared to the traditional inference method, inference results gained by the SIRMs method are simple in general [7]. For example, the SIRMs method may not obtain the same results of the product–sum-gravity method and fuzzy singleton-type inference method, if the fuzzy sets of the antecedent parts are limited to normal fuzzy sets [8]. In this paper, we first propose a fuzzy singleton-type SIRMs method, which attaches weights to the rules of the SIRMs method, in order to solve the above problem. Second, the equivalence [7–9] and monotonicity [10–16] of the fuzzy ∗ Corresponding author. Tel.: +81 79 565 7469; fax: +81 79 565 9077. E-mail addresses: h_seki@ieee.org (H. Seki), mizumoto3003@yahoo.co.jp (M. Mizumoto). 0165-0114/$-see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fss.2012.07.004