Consequences and conjectures in preordered sets

In a preordered set, or preset, consequence operators in the sense of Tarski, defined on families of subsets, are introduced. From them, the corresponding sets of conjectures, hypotheses, speculations and refutations are considered, studying the relationships between these sets and those previously defined on ortholattices. All the concepts introduced are illustrated with three particular consequence operators, whose behavior is studied in detail. The results obtained are applied to the case of fuzzy sets endowed with the usual pointwise ordering.     

A model for “crisp reasoning” with fuzzy sets

In the setting of a general type of fuzzy algebras, this paper deals with a new theoretic view on the commonsense reasoning, consisting of a kind of Popper's search for conjectures and refutations. It is supposed that the reasoning is done in natural language, but only with nonambiguous precise and imprecise terms, respectively, represented by crisp and fuzzy sets. © 2012 Wiley Periodicals, Inc.     

Electricity and telecoms reforms in the EU: Insights from the economics of federalism

The economics of federalism is a broad discipline with more than five decades of experience. It may shed light on how regulatory jurisdiction is allocated in EU electricity and telecommunications markets. The liberalization of these markets has been accompanied by gradual harmonization of national markets to overcome resistance to competitive forces. Less steps than necessary have been undertaken to promote market integration. Positive and normative reasons remain however for the participation of national or even regional/local powers. Vertical cooperation will remain a necessary condition of a sound regulatory framework, but cooperation may sometimes be inhibited by distributive considerations.     

Measures of specificity of fuzzy sets under T-indistinguishabilities

The concept of measure of specificity of fuzzy sets is extended in this paper to measure of specificity under the knowledge of T-indistinguishabilities. Four axioms of measure of specificity under T-indistinguishabilities are given. An algorithm to compute the inference independent set /spl Tfr/ from a fuzzy set and a T-indistinguishability is used to measure the specificity of fuzzy sets under T-indistinguishabilities satisfying the axioms.     

Synthesizing implications

We study some problems of synthesizing implications by using quasi-arithmetic means. By solving several functional equations some interesting characterizations are obtained.     

What Computing with Words Means to Me [Discussion Forum]

Computing with words (CWW) means different things to different people. This article is the start of a position paper, written by some of the members of the CIS Fuzzy Systems Technical Committee Task Force on CWW, that answers the question "What does CWW mean to me?"     

On contra‐symmetry and MPT conditionality in fuzzy logic

This article deals with the N‐contrapositive symmetry of fuzzy implication operators J verifying either Modus Ponens or Modus Tollens inequalities, in a similar and complementary framework to the one in which Fodor (“Contrapositive symmetry of fuzzy implications.” Fuzzy Set Syst 1995;69:141–156) did begin with the subject in fuzzy logic, that is, with the verification of J(a, b) = J(N(b), N(a)) for all a, b in [0,1] and some strong‐negation function N. This property corresponds to the classical p → q = ¬q → ¬p. The aim of this article is to study that property in relation to either Modus Ponens or Modus Tollens meta‐rules of inference when the functions J are taken among those that belong to the usual families of implications in fuzzy logic. That is, the contra‐positive of S implications, R implications, Q implications, and Mamdani–Larsen operators, verifying either Modus Ponens or Modus Tollens inequalities or both, the conditionality's aspect on which lies the complementarity with Fodor. Within this study new types of implication functions are introduced and analyzed. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 313–326, 2005.     

Conjecturing from consequences

This paper deals with a more general way of defining conjectures than that presented in Trillas et al. Here conjectures are defined once an operator of consequences in the sense of Tarski is given, and like in Trillas et al. they result classified in consequences, hypotheses and speculations. With all that, it appears for the first time the actually non-surprising idea that a formalization of deduction seems to be required previously to formalize induction and abduction.     

When QM‐operators are implication functions and conditional fuzzy relations

Some fuzzy reasoning systems base inference processes on fuzzy implication functions. Although there has been a great deal of work done on characterizing R‐ and S‐implications, little is known about QM‐implications in spite of their long history since they came to fuzzy logic by analogy with the quantum mechanic logic. This paper tackles the study of some characteristics of this type of operator. It focuses on the QM‐implication operator both as an implication function and also as a T‐conditional function, giving useful tools to characterize them. © 2000 John Wiley & Sons, Inc.