Fuzzy implications and inference processes

Tick, József; Fodor, János

doi:10.1109/icccyb.2005.1511558

Cited by 21 publications

(11 citation statements)

References 12 publications

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“…Journal of Control Science and Engineering 5 By substituting (22) and (23) into the last equation, the gain becomes…”

Section: The Comparison Of Cri and Irimentioning

confidence: 99%

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Reducing Computational Overhead by Improving the CRI and IRI Implication Step

Chen

2015

Journal of Control Science and Engineering

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In conventional SISO fuzzy expert systems ( -element input, -element output), the implication step requires the ( × ) operations using compositional rule-based inference (CRI) and individual rule-based inference (IRI). However, this introduces excessive complexity. This paper proposes two methods, sort compositional rule-based inference (SCRI) and sort individual rulebased inference (SIRI) aiming at reducing both temporal and spatial complexity by changing the operation of the implication step to (( + )log 2 ( + )). We also propose a divide-and-conquer technique, called Quicksort, to verify the accuracy of SCRI and SIRI algorithms deployment to easily outperform the CRI and IRI methods.

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“…Journal of Control Science and Engineering 5 By substituting (22) and (23) into the last equation, the gain becomes…”

Section: The Comparison Of Cri and Irimentioning

confidence: 99%

“…Accordingly, other researchers developed new implications, the fourth topic. Reference [22] proposed a new implication: "nilpotent minimum implication. "…”

Section: Introductionmentioning

confidence: 99%

Reducing Computational Overhead by Improving the CRI and IRI Implication Step

Chen

2015

Journal of Control Science and Engineering

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“…The aggregation operator is the minimum, the implication Io is the one defined from the nilpotent minimum Ao. For more details see [3] and [11]. Therefore, we can write Io(Ak(x), Bk(y)) 1 if Ak(X) < Bk(y), and otherwise Io (Ak (x), Bk (y)) = (1 -Ak (x)) V Bk (y) .…”

Section: A Examplesmentioning

confidence: 96%

“…Each pair (Ma, Jy)y.1 offuzzy conjunctions and implications are solutions of our system (9)-(10)- (11), satisfying also axioms Al -A8.…”

Section: A Axiomsfor Operations In Gmpmentioning

confidence: 99%

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Some classes of binary operations in approximate reasoning

Tick¹,

Fodor²

2005 IEEE International Conference on Intelligent Engineering Systems, 2005. INES '05.

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The aim ofthis paper is to study some binary operations in approximate reasoning. In the first part we summarize a former practical investigation ofthe applicability ofthe implication function based on the nilpotent minimum in that framework [1]. We also present some numerical examples to iUustrate the results. In the second part we recaU a constructive approach to the axiomatics of generalized modus ponens (GMP) published in [41. As a consequence, a system of functional equations is obtainedv Idempotent as well as non-idempotent conjunctions fufllng this system are studied& The obtained results support the use of non-commutative and non-associative conjunctions and the corresponding implications in approximate reasoning.

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Inverted Fuzzy Implications in Backward Reasoning

Suraj

Lasek

2015

Lecture Notes in Computer Science

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Fuzzy inference systems generate inference results based on fuzzy IF-THEN rules. Fuzzy implications are mostly used as a way of interpretation of the IF-THEN rules with fuzzy antecedent and fuzzy consequent. From over eight decades a number of different fuzzy implications have been described, e.g. [6-10]. This leads to the following question: how to choose the proper function among basic fuzzy implications. In our paper, we propose a new method for choosing implication. Our method allows to compare two fuzzy implications. If the truth value of the consequent and the truth value of the implication are given, by means of inverse fuzzy implications we can easily optimize the truth value of the implication antecedent. In other words, we can choose the fuzzy implication, which has the highest or the lowest truth value of the implication antecedent or which has higher or lower truth value than another implication.

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Fuzzy implications and inference processes

Cited by 21 publications

References 12 publications

Reducing Computational Overhead by Improving the CRI and IRI Implication Step

Reducing Computational Overhead by Improving the CRI and IRI Implication Step

Some classes of binary operations in approximate reasoning

Inverted Fuzzy Implications in Backward Reasoning

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