The story behind this product: Lotfi Aliasker Zadeh (February 4, 1921 – September 6, 2017) was a mathematician, computer scientist, electrical engineer, artificial intelligence researcher and professor emeritus of computer science at the University of California, Berkeley. Zadeh was best known for proposing fuzzy mathematics consisting of these fuzzy-related concepts: fuzzy sets, fuzzy logic, fuzzy algorithms, fuzzy semantics, fuzzy languages, fuzzy control, fuzzy systems, fuzzy probabilities, fuzzy events, and fuzzy information. On November 30, 2021, Google celebrated the submission of "Fuzzy Sets," a groundbreaking paper that introduced the world to his innovative mathematical framework called "fuzzy logic with a Google Doodle. This file contains 1 page of Lotfi Zadeh Word Search Puzzle with 30 Lotfi Zadeh themed Words and 1 page with its solution. The 30 words are hidden in all directions, making the word search challenging.

EPIMENIDES the Cretan, a philosopher of the 6th century BC, is said to have uttered the sentence, "All Cretans are liars". As he himself was a Cretan, this gave rise to a paradox--if he were telling the truth, then he would be a liar. Depending on how one defines a liar, the paradox is resolvable; he could have been a habitual liar who was telling the truth in this one instance. However, a stronger version of the paradox, known as the Liar paradox--"this sentence is false"--is not resolvable in conventional logic systems. Indeed, the circular loop that the sentence induces--if it is false, it must be true, and if true, false--has been used more than once in science-fiction movies to cause marauding computers to lose their sanity and explode.

Most fuzzy systems including fuzzy decision support and fuzzy control systems provide out-puts in the form of fuzzy sets that represent the inferred conclusions. Linguistic interpretation of such outputs often involves the use of linguistic approximation that assigns a linguistic label to a fuzzy set based on the predefined primary terms, linguistic modifiers and linguistic connectives. More generally, linguistic approximation can be formalized in the terms of the re-translation rules that correspond to the translation rules in ex-plicitation (e.g. simple, modifier, composite, quantification and qualification rules) in com-puting with words [Zadeh 1996]. However most existing methods of linguistic approximation use the simple, modifier and composite re-translation rules only. Although these methods can provide a sufficient approximation of simple fuzzy sets the approximation of more complex ones that are typical in many practical applications of fuzzy systems may be less satisfactory. Therefore the question arises why not use in linguistic ap-proximation also other re-translation rules corre-sponding to the translation rules in explicitation to advantage. In particular linguistic quantifica-tion may be desirable in situations where the conclusions interpreted as quantified linguistic propositions can be more informative and natu-ral. This paper presents some aspects of linguis-tic approximation in the context of the re-translation rules and proposes an approach to linguistic approximation with the use of quantifi-cation rules, i.e. quantified linguistic approxima-tion. Two methods of the quantified linguistic approximation are considered with the use of lin-guistic quantifiers based on the concepts of the non-fuzzy and fuzzy cardinalities of fuzzy sets. A number of examples are provided to illustrate the proposed approach.

This article is a sequel to an article titled "A New Direction in AI -- Toward a Computational Theory of Perceptions," which appeared in the Spring 2001 issue of AI Magazine (volume 22, No. 1, 73-84). The concept of precisiated natural language (PNL) was briefly introduced in that article, and PNL was employed as a basis for computation with perceptions. In what follows, the conceptual structure of PNL is described in greater detail, and PNL's role in knowledge representation, deduction, and concept definition is outlined and illustrated by examples. What should be understood is that PNL is in its initial stages of development and that the exposition that follows is an outline of the basic ideas that underlie PNL rather than a definitive theory. A natural language is basically a system for describing perceptions. Perceptions, such as perceptions of distance, height, weight, color, temperature, similarity, likelihood, relevance, and most other attributes of physical and mental objects are intrinsically imprecise, reflecting the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information. In this perspective, the imprecision of natural languages is a direct consequence of the imprecision of perceptions (Zadeh 1999, 2000). How can a natural language be precisiated -- precisiated in the sense of making it possible to treat propositions drawn from a natural language as objects of computation? This is what PNL attempts to do. In PNL, precisiation is accomplished through translation into what is termed a precisiation language. In the case of PNL, the precisiation language is the generalized-constraint language (GCL), a language whose elements are so-called generalized constraints and their combinations. What distinguishes GCL from languages such as Prolog, LISP, SQL, and, more generally, languages associated with various logical systems, for example, predicate logic, modal logic, and so on, is its much higher expressive power. The conceptual structure of PNL mirrors two fundamental facets of human cognition: (a) partiality and (b) granularity (Zadeh 1997). Partiality relates to the fact that most human concepts are not bivalent, that is, are a matter of degree. Thus, we have partial understanding, partial truth, partial possibility, partial certainty, partial similarity, and partial relevance, to cite a few examples. Similarly, granularity and granulation relate to clumping of values of attributes, forming granules with words as labels, for example, young, middle-aged, and old as labels of granules of age. Existing approaches to natural language processing are based on bivalent logic -- a logic in which shading of truth is not allowed. PNL abandons bivalence. By so doing, PNL frees itself from limitations imposed by bivalence and categoricity, and opens the door to new approaches for dealing with long-standing problems in AI and related fields (Novak 1991). At this juncture, PNL is in its initial stages of development. As it matures, PNL is likely to find a variety of applications, especially in the realms of world knowledge representation, concept definition, deduction, decision, search, and question answering.

This article is a sequel to an article titled "A New Direction in AI--Toward a Computational Theory of Perceptions," which appeared in the Spring 2001 issue of AI Magazine (volume 22, No. 1, 73-84). The concept of precisiated natural language (PNL) was briefly introduced in that article, and PNL was employed as a basis for computation with perceptions. In what follows, the conceptual structure of PNL is described in greater detail, and PNL's role in knowledge representation, deduction, and concept definition is outlined and illustrated by examples. What should be understood is that PNL is in its initial stages of development and that the exposition that follows is an outline of the basic ideas that underlie PNL rather than a definitive theory. A natural language is basically a system for describing perceptions.