L.A. Zadeh. The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets Systems, 11:199--227, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... byHellend# orn s # function [6] Keywords: Triangular norm, compositional rule of inference, Lagrange s multipliers method, 1 Introduction The inference process from imprecise or vague premises isb ecoming more and more important for knowledge b#)OO systems, especially for fuzzy expert systems [9,12,13,15]. In approximate reasoning there are several kinds of inference rules, which deal with the prob#CR of deduction of conclusions in an imprecise setting. An importantprob# lem is the (approximate) computation of the memb ership function of the conclusion in these schemes [1, 4, 6, 7, 8, 10] This ....

L.A.Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems, 11(1983) 199-228.

....norm, extension principle 1 Introducti#0 During the past ten years, expert systems have drawn tremendous attention from researchers and practitioners working in the area of fuzzy information processing. At the same time, approximate reasoning gained importance, especially, after L.A. Zadeh [12]pub#kSI8S The role of fuzzy logic in the management of uncertainty in expert systems . One of the most widely used inference rule in approximate reasoning is the compositional rule of inference, which has the general form Ob#mk8 ation: X has property P Relation 1: X and Y are in relation W 1 ....

L.A.Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Set# andSyst#17 , 11(1983) 199-228.

....expert systems is the problem of imprecision and uncertainty in both data and knowledge [1] In practice, it is important to develop techniques for handling such imprecision and uncertainty to enhance the robustness and performance of medical expert systems. Fuzzy logic and fuzzy set theory [2] provide a good framework for managing uncertainty and imprecision in medicine [3] 4] 5] and have been successfully applied to a number of areas [6] 4] 7] The successful development of a fuzzy model for a particular application domain is a complex multi step process, in which the ....

L.A. Zadeh, "The role of fuzzy logic in the management of uncertainty in expert systems," Fuzzy Sets Systems, vol. 11, pp. 199--227, 1983.

.... byHellend orn s # function [6] Keywords: Triangular norm, compositional rule of inference, Lagrange s multipliers method, 1 Introduction The inference process from imprecise or vague premises isb ecoming more and more important for knowledge b)OO systems, especially for fuzzy expert systems [9,12,13,15]. In approximate reasoning there are several kinds of inference rules, which deal with theprobCR of deduction of conclusions in an imprecise setting. An importantprob lem is the (approximate) computation of the memb ership function of the conclusion in these schemes [1, 4, 6, 7, 8, 10] This paper ....

L.A.Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems, 11(1983) 199-228.

.... Compositional rule of inference, triangular norm, triangular conorm, fuzzy implication operator, generalized method of case,stab ca y 1 Introduction The inference process from imprecise premises isb ecoming more and more important for knowledge bME) systems, especially for fuzzy expert systems [5,7,8,9,11]. In Approximate Reasoning there are several kinds of fuzzy inference rules [9] e.g. entailment and conjunctive rules, the generalized modus ponens and tollens, the GMC. In this paper we will deal only with the GMC inference rule. When the predicates are crisp then the method of cases reads A OR ....

L.A.Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems, 11(1983) 199-228.

....that are words or sentences in natural language, and the concept of fuzzy logic [140, 141, 142] which extended the Lukasiewicz multi valued logic. More recently, Zadeh stated that fuzzy logic provides a systematic framework which makes it possible to deal with different types of uncertainty [144]. Fuzzy theory has generated widespread interest and the theoretical work has since been extended to show that fuzzy theory contains both classical probability theory and the Dempster Shafer belief and plausibility measures [65, 66] Fuzzy theory is probably now the most popular form of including ....

L.A. Zadeh. The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets Systems, 11:199--227, 1983.

....imperfection in a database setting into manageable chunks. Thus we will consider, in turn, storing incomplete information, which has strong links with work on non monotonic reasoning [55] imprecise information, which has been handled by various applications of fuzzy sets [168] and fuzzy logic [165, 166], and uncertain information, which has been dealt with using probability [48] possibility [40, 167] and Dempster Shafer theory [141] It should be noted, however, that the di erent forms of imperfection cannot be so cleanly seperated as this description suggests. For instance, the fact that data ....

....does not t into the relations, as well as because attribute values are not known, and the former two problems are yet to be addressed. 3. 2 Imprecise information Most of the work on the modelling of imprecise information within databases has involved the use of fuzzy sets [168] and fuzzy logic [165, 166]. Fuzzy set theory is a generalisation of normal set theory in which it is recognised that the kinds of classes of objects one encounters in the real world do not always have precisely de ned criteria of membership. Thus it is clear that the class of living things should include people, dogs and ....

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Zadeh, L. A. (1983) The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems, 11, 199-227.

....properties as desirable, one must accept probabilities as a desirable measure of belief. These principles provide a useful framework for comparing alternative formalisms for representing uncertainty, in terms of which of the principles the formalisms reject [75] For example, fuzzy set theory [160] rejects the property of clarity, allowing linguistic imprecision in the definition of propositions. Some AI researchers have also rejected scalar continuity, arguing that a single number is insufficiently rich to represent belief [19] Dempster Shafer theory [133] rejects completeness, denying ....

.... one as the costs of representation or reasoning resources increase [69] As we mentioned in the second section of this article, analyses have been carried out in attempts to understand how alternative formalisms for reasoning under uncertainty such as nonmonotonic reasoning [46] fuzzy set theory [160], and Dempster Shafer theory [133] relate to probabilistic reasoning. See Kanal and Lemmer [86, 98] for some detailed analyses of these approaches. The application of influence diagrams in new areas is facilitated by their relatively unconstrained dependency structure at the level of relation. ....

L.A. Zadeh. The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems, 11:199--227, 1983.

....11, 265 286, 1999. 2 1 INTRODUCTION 1 Introduction Managing uncertainty in complex domains continues to remain a dicult task especially during knowledge acquisition and veri cation and validation. There are a wide variety of approaches from fuzzy logics to probabilistic networks (Nilsson 1986; Zadeh 1983; Santos Santos 1987; Pearl 1988; Thagard 1989; Dempster 1968; Shortli e Buchanan 1975; Shafer 1979; Heckerman 1991; Bacchus 1990) The diculty lies in creating a knowledge representation with the right blend of exibility and sound semantics. For the human expert and knowledge engineer, ....

Zadeh, L. A. 1983. The role of fuzzy logic in the management of uncertainty in expert systems.

....programming This work was done when I was at Database System Research Development Center in University of Florida. Especially, I thank Prof. Sharma for his support and anonymous referees for their invlauable comment. 1 1 Introduction It is well known that the fuzzy logic proposed by Zadeh [26] is a good alternative to handle uncertain knowledge in rule based expert systems [12] 14] 26] In some application domains where the uncertain knowledge is not amenable to the estimation of probabilities, the logic may be even a unique solution. FLOPS [2] and Z II [12] are the expert system ....

....in University of Florida. Especially, I thank Prof. Sharma for his support and anonymous referees for their invlauable comment. 1 1 Introduction It is well known that the fuzzy logic proposed by Zadeh [26] is a good alternative to handle uncertain knowledge in rule based expert systems [12] 14][26]. In some application domains where the uncertain knowledge is not amenable to the estimation of probabilities, the logic may be even a unique solution. FLOPS [2] and Z II [12] are the expert system shells to integrate the fuzzy logic into their reasoning process. With the powerful facility to ....

L.A. Zadeh, The role of fuzzy logic in the management of uncertainty in expert system, Fuzzy sets and Systems, 11 (1983) 199-227.

....representing some measure of confidence in input data, and intermediate propositions throughout the system to arrive at some number 15 representing a level of confidence in a conclusion. These methods include approximate Bayesian reasoning [DGH79] certainty factors [Sho76] and fuzzy logic [Zad65] A debate rages over the use of these measures. Criticisms made (which may not apply to all manifestations of the numerical approaches) include: that the numbers are often synthetic as they rely on an expert s subjective evaluation; to work properly assumptions about the independence of the ....

Lofti A. Zadeh. The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems, 11:199-- 227, 1965. 30

....) since the effect was caused by the match and its degree is expected to be proportional to the degree of the match. This interpretation can be verified by the following lemma. Lemma 4 Let r be L(E) ACT (E 0 ) where E E 0 . Then ACT (E 0 ) L (E) if L (E) 0:5 Proof According to [31], ACT (E 0 ) min( r (E) L (E) Delta Delta Delta Delta Delta Delta Delta (5:7) 25 Let s apply Lemma 3 to (5.7) then ACT (E 0 ) min(ACT (E 0 ) L (E) if L (E) 0:5 and L (E) ACT (E 0 ) Accordingly, we can get ACT (E 0 ) L (E) if L (E) 0:5 and L (E) ACT (E 0 ) ....

L.A. Zadeh, The role of fuzzy logic in the management of uncertainty in expert system, Fuzzy Sets and Systems, 11 (1983) 199-227. 30

....inference based on such models existed. Approaches to handling uncertainty which were not based strictly on probability theory were therefore developed. Two of the most well known examples of such approaches are certainty factors in rule based systems (Shortliffe and Buchanan 1975) and fuzzy logic (Zadeh 1983). Modelling of uncertainty based on probability theory has, however, experienced a remarkable renaissance in the last decade. Two factors played a key role in this successful comeback. First, a branch of statistical modelling, where emphasis on the qualitative structure is the prevailing trait, ....

....beregningsmaessigt egnede inferensmetoder. Metoder til h#ndtering af usikkerhed, som ikke var baseret p# sandsynlighedsteori, blev derfor udviklet. To af de mest velkendte eksempler p# s#danne metoder er certainty factors i regelbaserede systemer (Shortliffe and Buchanan 1975) og fuzzy logik (Zadeh 1983). Modellering af usikkerhed baseret p# sandsynlighedsteori har imidlertid opn#et en bemaerkelsesvaerdig renaessance, som p#begyndtes i starten af 1980 erne. To faktorer spiller en central rolle for dette succesfulde comeback. For det frste, har den gren af statistisk modellering, hvor fokusering ....

Zadeh, L. A. (1983). The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems 11: 199--228.

....be used and what variables should be used. Fuzzy logic and fuzzy set theory provide a rich and meaningful addition to standard logic. Fuzzy quantifiers don t give the count exactly, but fuzzily in that way it can deal with fuzzy probability like not very likely , rarely, or fairly possible [9]. Even when predicted accurate the forecast is only valid for a limited time. In a couple of minutes the whole situation can be different. Uncertainty is present in most tasks that involve humans. In this case the prediction times will be uncertain, especially for trips longer then approximately ....

Zadeh, L.A. (1987), The role of fuzzy logic in the management of uncertainty in expert systems, in: Fuzzy sets and applications: Selected papers by L.A. Zadeh, Yager, R.R., Ovchinnikov, S., Nguyen, H.T.(eds), John Wiley, New York

....systems and expert systems, have been carried out. A major purpose of these previous researches is to devise data types strengthening semantic expressiveness of the uncertain information and to develop efficient methods of processing the data. It is widely conceived that Zadeh s fuzzy logic [10] provides a good tool for these purposes. Several expert system shells have been developed using the fuzzy logic to provide a quite natural interpretation of the uncertain information [11, 12] In this research, a knowledge based programming tool, namely ICOT (Integrated CObject Tool) is ....

....information, which is discussed in the next section. 4 2.2 Fuzzy logic in expert systems Processing uncertain information in expert systems have also been an important research direct, and thus a number of approaches have been proposed. It is well known that the fuzzy logic proposed by Zadeh [10] is a good alternative to handle uncertain knowledge in rule based expert systems [11, 12, 14] In general, a fuzzy inference engine tries to match uncertain knowledge with the condition part of rules. When a rule is matched to some extent, if not exact, a conclusion is derived considering the ....

L. A. ZADEH, "The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems", 11, 3 (1983) 199-227.

....and flexibility of type 2 fuzzy sets, we explicitly manage both relevance and confidence as meta descriptors of diagnostic knowledge. After an introduction to fuzzy set theory and a brief overview of CBR paradigm, we present a model for adaptive management [8] of both relevance and uncertainty [17] as information meta descriptors. Experimental results show that precision substantially improves (up to a factor of 5) for the case selection process but we also consider other the knowledge level [5] implications of explicit uncertainty management. 2 Elements of fuzzy set theory Standard set ....

L.A. Zadeh. The role of fuzzy logic in the management of uncertainty in expert systems. In Fuzzy Set and Systems, Vol. 11, North Holland, 1983.

....many ways and at different abstraction layers. Although we focused primarily on low level parameters like precision and recall, the final goal is to turn data into knowledge and it will be interesting to see how uncertainty based information bases could support classic knowledge management systems [14]. Concerning implementation aspects, efficiently manageable multiplemodal functions and patterns for optimised data access structures present interesting field of investigation. 10 6 Conclusions Uncertainty is present in many aspects of information retrieval and the process of extracting from ....

L.A. Zadeh. The role of fuzzy logic in the management of uncertainty in expert systems. In Fuzzy Set and Systems, Vol. 11, North Holland, 1983.

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L.A.Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems, 11(1983) 199-228.

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L.A. Zadeh. The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets Systems, 11:199--227, 1983.

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L.A. Zadeh, 'The role of fuzzy logic in the management of uncertainty in expert systems', Fuzzy Sets and Systems,11/3, 199-227, (1983).

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L.A. Zadeh, "The role of fuzzy logic in the management of uncertainty in expert systems," Fuzzy Sets Systems, vol. 11, pp. 199--227, 1983.

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Zadeh, L., (1983) The Role of Fuzzy Logic in the Management of Uncertainty in Expert Systems, Fuzzy Sets and Systems, 11, 199-227.

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L.A.Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems, 11(1983) 199-228.

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AAAI-86, pp. 105-112. /Zadeh 83/ L.A. Zadeh, The Role of Fuzzy Logic in the Management of Uncertainty in Expert Systems, FSS 11, 1983.

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L.A. Zadeh. The role of fuzzy logic in the management of uncertainty in expert systems. In Fuzzy Set and Systems, Vol. 11, North Holland, 1983.

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