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

Abstract

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

Advanced Computing with Words: Status and Challenges

“…It also uses the Extension Principle, but in a different way from the GEP. Moreover, it involves the challenge of choosing appropriate compatibility measures [82], and may require multiple computational methodologies for fusion of inconsistent information [84]. Much more research is needed about this approach to solving ACWW problems.…”

“…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].…”

“…It was shown in [84] that a combination rule for linguistic belief structures can be devised using an aggregation operator called Doubly Normalized Linguistic Weighted Average (DNLWA).…”

“…(b) To calculate the lower and upper probabilities of an event, choose the measures of inclusion and overlap and then use (12.28). (c) To combine several belief structures or to calculate a belief structure describing a function of variables described by several linguistic belief structures use DNLWA [84]. For inference from the combined linguistic belief structures, use (12.28) that is computed by applying the α-cut decomposition theorem and KM algorithms [52].…”

Linguistic Summarization of Processes – a research agenda

“…The idea of data summarization was strongly investigated by many researchers, e.g., Bosc [4], Dubois and Prade [11,12], Keller and his collaborators [1,2,3,31,38], Yager, Kacprzyk and their collaborators [17,19,30,41,42], Wu and Mendel [40], Marin and Sanchez [7,8], Raschia and Mouaddib [28,29], Bouchon-Meunier and her collaborators [6,24,25], Mendel [27]. There are many different approaches, but it seems the most commonly used is the one by Yager [41], that was implemented in many different applications, e.g., retail (e.g., Kacprzyk et al [14]), finance (e.g., Castillo-Ortega et al [8]), eldercare (e.g., Ros et al [31] or Wilbik et al [38,39]).…”