Novel Weighted Averages versus Normalized Sums in Computing with Words

Rajati, Mohammad Reza; Mendel, Jerry M.

doi:10.1016/j.ins.2012.12.022

Cited by 28 publications

(12 citation statements)

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“…For ICWW and ACWW, many other mathematical tools may be needed in the computations, such as antonyms and negations [13,100], syllogisms [74,84,94,141], and aggregation operators [35,86,125,127].…”

Section: Computing Solutions To Acww Problemsmentioning

confidence: 99%

“…In this section, we explain a syllogistic approach to solving ACWW problems [82-84, 88, 89]. Those solutions use the Extension Principle in a different way, namely by applying it to the calculation of Novel Weighted Averages (NWAs) 10 [68,86]. To begin, we need to translate the ACWW problems into a form suitable for NWAs.The following syllogism [151] is used for handling the probability words and linguistic quantifiers in the ACWW problems:…”

Section: A Syllogistic Approach To Acww Problemsmentioning

confidence: 99%

“…[the lower and upper probability that χ is B (e.g., John is short)] from B, the following normalized sums [86], which are extensions of (12.25), have to be calculated: Given the statement "The probability that χ is A is P", one can infer a belief structure like the one in (12.23), and then apply (12.27) to calculate the probability that χ is B. It was shown in [86, pp.…”

Section: G {(T All Probable) (Not T All I Mprobable)}) In Order mentioning

confidence: 99%

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Advanced Computing with Words: Status and Challenges

Mendel

Rajati

2015

Towards the Future of Fuzzy Logic

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In this chapter, we focus on the status of Advanced Computing with Words (ACWW) and the challenges that it may encounter in the future. First, we elaborate on the notion of Computing with Words (CWW) and its various subareas. Then we present some non-engineering ACWW problems and connect them to more realistic engineering problems, after which we provide a roadmap for solving ACWW problems, and show how the Generalized Extension Principle (GEP) can be used to formulate their solutions. We also propose a syllogistic approach to solving ACWW problems that also uses the Extension Principle but in a different way. Finally, we discuss present and future challenges to ACWW, i.e. we explain what challenges ACWW encounters given the current trend of data abundance and widespread use of Internet for dealing with questions posed in natural languages. Introduction: Computing with Words and Advanced Computing with WordsComputing with Words (CWW or CW) [11,29,34,66,69,70,75,91,104,109,142,144,147,154] was probably conceived as the main area of application of fuzzy logic [132] when the field was originated. It is a methodology of computation whose objects are words rather than numbers, although those words are linked to numbers and classical calculations that can be carried out by computing machinery, via membership functions of fuzzy sets associated with words. To do that, a process called precisiation of meaning [152] is essential, which, in a nutshell, is determining membership functions of the fuzzy sets that model the words. Zadeh distinguishes two subareas for CWW:1. Basic Computing with Words (BCWW), which mainly deals with descriptions of complex systems in terms of fuzzy IF-THEN rules [134]. Soft constraints are generally possibilistic, i.e. they describe (physical) attributes like speed, temperature,

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Section: Computing Solutions To Acww Problemsmentioning

confidence: 99%

Section: A Syllogistic Approach To Acww Problemsmentioning

confidence: 99%

Section: G {(T All Probable) (Not T All I Mprobable)}) In Order mentioning

confidence: 99%

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Advanced Computing with Words: Status and Challenges

Mendel

Rajati

2015

Towards the Future of Fuzzy Logic

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“…It was shown [34] that constraints of the same form as D may make the optimization problem associated with the Extension Principle have no solution, especially when models of the probability words are synthesized using collecting data about words from subjects. To avoid this, one can use the Doubly Normalized Linguistic Weighted Average (DNLWA) operator, which is the extension of the following function to IT2 FSs :…”

Section: Our Solution To the Plpmentioning

confidence: 99%

“…Unfortunately, the above optimization problems may have no solutions [34], and instead, one can use Fuzzy Weighted Averages (FWAs) represented by the following expressive formulas [37]: 9 {…”

Section: Our Solution To the Plpmentioning

confidence: 99%

Advanced computing with words using syllogistic reasoning and arithmetic operations on linguistic belief structures

Rajati

Mendel

2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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In this paper, we present solutions to an Advanced Computing with Words problem that is equivalent to one of Zadeh's challenge problems on linguistic probabilities. We use a syllogism based on the entailment principle to interpret the problem so that it yields two linguistic belief structures. Then we perform an addition of those linguistic belief structures to obtain a belief structure on the variable about which linguistic probabilities have to be inferred. We show that pessimistic (lower) and optimistic (upper) probabilities can be inferred from such a belief structure using Linguistic Weighted Averages and pessimistic and optimistic compatibility measures. Then, we choose vocabularies for linguistic attributes (lifetimes of products) and linguistic probabilities that are involved in the problem statement. The vocabularies are modeled using interval type-2 fuzzy sets. We calculate optimistic (upper) and pessimistic (lower) probabilities, and map them into words present in the vocabulary of linguistic probabilities, so that the results can be comprehended by a human.Index Terms-advanced computing with words, belief structures, compatibility measures, interval type-2 fuzzy sets, linguistic weighted average, lower and upper probabilities, operations on belief structures

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Type-1 Fuzzy Sets and Fuzzy Logic

Mendel

2024

Explainable Uncertain Rule-Based Fuzzy Systems

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Novel Weighted Averages versus Normalized Sums in Computing with Words

Cited by 28 publications

References 30 publications

Advanced Computing with Words: Status and Challenges

Advanced Computing with Words: Status and Challenges

Advanced computing with words using syllogistic reasoning and arithmetic operations on linguistic belief structures

Type-1 Fuzzy Sets and Fuzzy Logic

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