Formal Rules for Fuzzy Causal Analyses and Fuzzy Inferences

Formal Rules for Fuzzy Causal Analyses and Fuzzy Inferences

Yingxu Wang (International Institute of Cognitive Informatics and Cognitive Computing (ICIC), University of Calgary, Calgary, Canada)
DOI: 10.4018/jssci.2012100105
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Abstract

Causal inference is one of the central capabilities of the natural intelligence that plays a crucial role in thinking, perception, and problem solving. Fuzzy inferences are an extended form of formal inferences that provide a denotational mathematical means for rigorously dealing with degrees of matters, uncertainties, and vague semantics of linguistic variables, as well as for rational reasoning the semantics of fuzzy causalities. This paper presents a set of formal rules for causal analyses and fuzzy inferences such as those of deductive, inductive, abductive, and analogical inferences. Rules and methodologies for each of the fuzzy inferences are formally modeled and illustrated with real-world examples and cases of applications. The formalization of fuzzy inference methodologies enables machines to mimic complex human reasoning mechanisms in cognitive informatics, cognitive computing, soft computing, abstract intelligence, and computational intelligence.
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1. Introduction

A causation is a relationship between a sole or multiple causes and a single or multiple effects. The cause in a causation is a premise state such as an event, phenomenon, action, behavior, or existence; while the effect is a consequent or conclusive state such as an event, phenomenon, action, behavior, or existence.

An inference is a cognitive process that deduces a conclusion, particularly a causation, based on evidences and reasoning. Causal inference is one of the central capabilities of human brains that plays a crucial role in thinking, perception, and problem solving (BISC, 2008; Sternberg, 1998; Payne & Wenger, 1998; Zadeh, 1975, 1998, 1999; Smith, 2001; Wang, 2002a, 2007b, 2008b, 2009a; Wang et al., 2006, 2009). The framework of causal inferences can be classified into four categories known as the intuitive, empirical, heuristic, and rational causalities (Wang, 2011a, 2011c, 2012c). Therefore, a causal inference can be conducted based on empirical observations, formal inferences, and/or statistical regulations (Bender, 1996; Wilson and Keil, 2001; Wang, 2007a, 2007b, 2008a, 2011a, 2011c, 2012c).

Formal logic inferences may be classified as deductive, inductive, abductive, and analogical inferences (Schoning, 1989; Sperschneider & Antoniou, 1991; Rose, 1995; Hurley, 1997; van Heijenoort, 1997; Tomassi, 1999; Smith, 2001; Wilson & Keil, 2001; Wang, 2007b; Wang et al., 2006, 2009, 2011xx). Although logic inferences can be carried out on the basis of abstraction and symbolic reasoning with crisp sets and Boolean logic, more human inference mechanisms and rules such as those of intuitive, empirical, heuristic, and perceptive inferences are fuzzy and uncertain, which are yet to be studied by fuzzy inferences on the basis of fuzzy sets and fuzzy logic (Zadeh, 1965, 1971, 1975, 1983, 2004, 2006, 2008; Wang, 2008a) in the context of denotational mathematics (Wang, 2002b, 2007d, 2008a, 2008c, 2009c, 2011a, 2011c, 2012a, 2012b, 2012c, 2012h; Wang & Chiew, 2011) and cognitive computing (Wang, 2002a, 2003, 2007c, 2007e, 2008d, 2008e, 2009b, 2009d, 2009e, 2010a, 2010b, 2011b, 2011d, 2012d, 2012e, 2012f, 2012g, 2012i, 2012j, 2012k, 2012l, 2013a, 2013b, 2013c; Wang & Wang, 2006; Wang & Fariello, 2012; Wang et al., 2006, 2009, 2010a, 2010b, 2012).

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