Rough Truth Degrees of Formulas and Approximate Reasoning in Rough Logic

2011 ◽  
Vol 107 (1) ◽  
pp. 67-83 ◽  
Author(s):  
Yanhong She ◽  
Xiaoli He ◽  
Guojun Wang
Keyword(s):  
Approximate Reasoning ◽  
Truth Degrees

scholarly journals Truth Degrees Theory and Approximate Reasoning in 3-Valued Propositional Pre-Rough Logic

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yingcang Ma ◽  
Juanjuan Zhang ◽  
Huan Liu
Keyword(s):  
Approximate Reasoning ◽  
Logical Formula ◽  
Concept Of Truth ◽  
Truth Degrees ◽  
Truth Degree

By means of the function induced by a logical formulaA, the concept of truth degree of the logical formulaAis introduced in the 3-valued pre-rough logic in this paper. Moreover, similarity degrees among formulas are proposed and a pseudometric is defined on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in 3-value logic pre-rough logic is established.

M: AN APPROXIMATE REASONING SYSTEM

1993 ◽  
Vol 07 (03) ◽  
pp. 431-440
Author(s):  
QINPING ZHAO ◽  
BO LI
Keyword(s):  
Solution Algorithm ◽  
Approximate Reasoning ◽  
Inference Rules ◽  
Multivalued Logic ◽  
Reasoning System ◽  
Sld Resolution ◽  
Truth Value ◽  
Truth Degrees

A system of multivalued logical equations and its solution algorithm are put forward in this paper. Based on this work we generalize SLD-resolution into multivalued logic and establish the corresponding truth value calculus. As a result, M, an approximate reasoning system, is built. We present the language and inference rules of M. Furthermore, we analyse inconsistency of assignments to truth degrees and give the solving strategies of M.

Uncertainty Operators in a Many-Valued Logic

2011 ◽  
pp. 1997-2003
Author(s):  
Herman Akdag ◽  
Isis Truck
Keyword(s):  
Boolean Logic ◽  
Approximate Reasoning ◽  
Qualitative Approaches ◽  
Uncertainty Representation ◽  
Elementary Operators ◽  
Cognitive Activities ◽  
The Many ◽  
Expert Reasoning ◽  
Interval Valued ◽  
Truth Degrees

This article investigates different tools for knowledge representation and modelling in decision making problems. In this variety of AI systems the experts’ knowledge is often heterogeneous, that is, expressed in many forms: numerical, interval-valued, symbolic, linguistic, etc. Linguistic concepts (adverbs, sentences, sets of words…) are sometimes more efficient in many expertise domains rather than precise, interval-valued or fuzzy numbers. In these cases, the nature of the information is qualitative and the use of such concepts is appropriate and usual. Indeed, in the case of fuzzy logic for example, data are represented through fuzzy functions that allow an infinite number of truth values between 0 and 1. Instead, it can be more appropriate to use a finite number of qualitative symbols because, among other reasons, any arbitrary fuzzification becomes useless; because an approximation will be needed at the end anyway; etc. A deep study has been recently carried out about this subject in (Gottwald, 2007). In this article we propose a survey of different tools manipulating these symbols as well as human reasoning handles with natural linguistic statements. In order to imitate or automatize expert reasoning, it is necessary to study the representation and handling of discrete and linguistic data (Truck & Akdag, 2005; Truck & Akdag, 2006). One representation is the many-valued logic framework in which this article is situated. The many-valued logic, which is a generalization of classical boolean logic, introduces truth degrees which are intermediate between true and false and enables the partial truth notion representation. There are several many-valued logic systems (Lukasiewicz’s, Gödel’s, etc.) comprising finite-valued or infinite-valued sets of truth degrees. The system addressed in this article is specified by the use of LM = {t0,...,ti,...,tM-1} 1 a totally ordered finite set2 of truth-degrees (ti = tj ? i = j) between t0 (false) and tM-1 (true), given the operators ? (max), ? (min) and ¬ (negation or symbolic complementation, with ¬tj = tM-j-1) and the following Lukasiewicz implication ?L : ti ?L tj = min(tM-1, tM-1-(i-j)) These degrees can be seen as membership degrees: x partially belongs to a multiset3 A with a degree ti if and only if x ?ti A. The many-valued logic presented here deals with linguistic statements of the following form: x is va A where x is a variable, va a scalar adverb (such as “very”, “more or less”, etc.) and A a gradable linguistic predicate (such as “tall”, “hot”, “young”...). The predicate A is satisfiable to a certain degree expressed through the scalar adverb va. The following interpretation has been proposed (Akdag, De Glas & Pacholczyk, 1992): x is va A ? “x is A” is ta – true Qualitative degrees constitute a good way to represent uncertain and not quantified knowledge, indeed they can be associated with Zadeh’s linguistic variables (Zadeh, 2004) that model approximate reasoning well. Using this framework, several qualitative approaches for uncertainty representation have been presented in the literature. For example, in (Darwiche & Ginsberg, 1992; Seridi & Akdag, 2001) the researchers want to find a model which simulates cognitive activities, such as the management of uncertain statements of natural language that are defined in a finite totally ordered set of symbolic values. The approach consists in representing and exploiting the uncertainty by qualitative degrees, as probabilities do with numerical values. In order to manipulate these symbolic values, four elementary operators are outlined: multiplication, addition, subtraction and division (Seridi & Akdag, 2001). Then two other kinds of operators are given: modification tools based on scales and symbolic aggregators.

Rough Truth Degrees of Formulas and Approximate Reasoning in Rough Logic

2011 ◽  
Vol 111 (2) ◽  
pp. 223-239
Author(s):  
Yanhong She ◽  
Xiaoli He ◽  
Guojun Wang
Keyword(s):  
Approximate Reasoning ◽  
Truth Degrees

scholarly journals Approximate reasoning with fuzzy rule interpolation: background and recent advances

2021 ◽  
Author(s):  
Fangyi Li ◽  
Changjing Shang ◽  
Ying Li ◽  
Jing Yang ◽  
Qiang Shen
Keyword(s):  
Fuzzy Inference ◽  
Fuzzy Rule ◽  
Approximate Reasoning ◽  
Rule Based ◽  
Reasoning Systems ◽  
Significant Interest ◽  
Recent Developments ◽  
Rule Bases ◽  
The Given ◽  
Computing Approach

AbstractApproximate reasoning systems facilitate fuzzy inference through activating fuzzy if–then rules in which attribute values are imprecisely described. Fuzzy rule interpolation (FRI) supports such reasoning with sparse rule bases where certain observations may not match any existing fuzzy rules, through manipulation of rules that bear similarity with an unmatched observation. This differs from classical rule-based inference that requires direct pattern matching between observations and the given rules. FRI techniques have been continuously investigated for decades, resulting in various types of approach. Traditionally, it is typically assumed that all antecedent attributes in the rules are of equal significance in deriving the consequents. Recent studies have shown significant interest in developing enhanced FRI mechanisms where the rule antecedent attributes are associated with relative weights, signifying their different importance levels in influencing the generation of the conclusion, thereby improving the interpolation performance. This survey presents a systematic review of both traditional and recently developed FRI methodologies, categorised accordingly into two major groups: FRI with non-weighted rules and FRI with weighted rules. It introduces, and analyses, a range of commonly used representatives chosen from each of the two categories, offering a comprehensive tutorial for this important soft computing approach to rule-based inference. A comparative analysis of different FRI techniques is provided both within each category and between the two, highlighting the main strengths and limitations while applying such FRI mechanisms to different problems. Furthermore, commonly adopted criteria for FRI algorithm evaluation are outlined, and recent developments on weighted FRI methods are presented in a unified pseudo-code form, easing their understanding and facilitating their comparisons.

Neural networks designed on approximate reasoning architecture and their applications

1992 ◽  
Vol 3 (5) ◽  
pp. 752-760 ◽  
Author(s):  
H. Takagi ◽  
N. Suzuki ◽  
T. Koda ◽  
Y. Kojima
Keyword(s):  
Neural Networks ◽  
Approximate Reasoning
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