An Insight Into The Z-number Approach To CWW

Abstract

The Z-number is a new fuzzy-theoretic concept, proposed by Zadeh in 2011. It extends the basic philosophy of Computing With Words (CWW) to include the perception of uncertainty of the information conveyed by a natural language statement. The Z-number thus, serves as a model of linguistic summarization of natural language statements, a technique to merge human-affective perspectives with CWW, and consequently can be envisaged to play a radical role in the domain of CWW-based system design and Natural Language Processing (NLP). This article presents a comprehensive investigation of the Z-number approach to CWW. We present here: a) an outline of our understanding of the generic architecture, algorithm and challenges underlying CWW in general; b) a detailed study of the Z-number methodology -where we propose an algorithm for CWW using Z-numbers, define a Z-number based operator for the evaluation of the level of requirement satisfaction, and describe simulation experiments of CWW utilizing Z-numbers; and c) analyse the strengths and the challenges of the Z-numbers, and suggest possible solution strategies. We believe that this article would inspire research on the need for inclusion of human-behavioural aspects into CWW, as well as the integration of CWW and NLP.A system based on CWW, takes as input a set of natural language sentences that describes an event, and presents as output the corresponding response in the natural language as well.The generic architecture for a system that computes with words is hence, as is shown in Figure 1. The components of the architecture are:(i) The Encoder, processes through the two levels of CWW to translate input sentences to the corresponding antecedent constraints, i.e., the inputs are precisiated into some symbolic form (S) as is processed by the system -reminiscent of Russell's concept of philosophical logic;(ii) The Rule Base consists of the antecedent-consequent event relationships, typical to the context of discourse. The rule base may be in the form of an Explanatory Database (ED);(iii) The Inference Engine, in conjunction with the rule base is instrumental in processing the antecedent constraints to arrive at the consequent results. These results are in the symbolic form S';(iv) The Decoder translates S' into words that can be frame semantically correct natural language sentences.

Deep learning in multi-object detection and tracking: state of the art

“…provide a summary of meaning of natural language expression in terms of its qualitative aspect and embedded uncertainty. It may be used to design a framework for quantitative abstraction of information in describing the output scene of deep networks for video-object detection [3,[179][180][181]. Exploiting the merits of Z-numbers in modeling the interpret-ability of the output in natural language, therefore, constitutes another challenge.…”

Ranking of Z‐numbers based on value and ambiguity at levels of decision making

“…Aliev et al 3 introduced the arithmetic of Z-numbers. Further, its application is evident in different field of research such as multicriteria decision making problems, [4][5][6][7][8][9] computing with words, 10 linear programming problems, 11 and so forth. Zeinalova 12 used Z-value information to evaluate a decision making in a real economic problem.…”

A modified method of generating Z-number based on OWA weights and maximum entropy

“…Some other works on Z -number have been investigated, such as (1) theoretical researches of Z -number: arithmetic of discrete Z -numbers (Aliev et al 2015a), arithmetic of continuous Z -numbers (Aliev et al 2016), Z *-numbers (Banerjee and Pal 2015), derived Z -number (Liu et al 2019), modeling Z -number (Patel et al 2016), uncertainty of Z -number (Kang et al 2019a, b) and (2) applications of Z -number: Zevaluations (Yager 2012), computing with words (CWW) (Pal et al 2013), modeling in psychological research (Aliev and Memmedova 2015), Z -number-based linear programming (Aliev et al 2015b), sensor data fusion (Jiang et al 2016), dynamic plant control (Abiyev 2016), data envelopment analysis (Azadeh and Kokabi 2016), failure modes risk assessment (Mohsen and Fereshteh 2017;Jiang et al 2017b), medical diagnosis (Dong et al 2018), stable strategies analysis (Kang et al 2018b), Z -network model (Jiang et al 2019) and other decision-making models with Z -number (Jiang et al 2017a;Wang et al 2017;Peng and Wang 2017;Yang and Wang 2018;Kang et al 2016Kang et al , 2018c.…”