Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. Aiming to find logics that can handle inconsistency and graded truth at once, in this paper we explore the notion of paraconsistent fuzzy logic. We show that degree-preserving fuzzy logics have paraconsistency features and study them as logics of formal inc...

The lattice Lu of upper semicontinuous convex normal functions with convolution ordering arises in studies of type-2 fuzzy sets. In 2002, Kawaguchi and Miyakoshi [Extended t-norms as logical connectives of fuzzy truth values, Multiple-Valued Logic 8(1) (2002) 53–69] showed that this lattice is a complete Heyting algebra. Later, Harding et al. [Lattices of convex, normal functions, Fuzzy Sets an...

Active Learning Method (ALM) is a soft computing method used for modeling and control based on fuzzy logic. All operators defined for fuzzy sets must serve as either fuzzy S-norm or fuzzy T-norm. Despite being a powerful modeling method, ALM does not possess operators which serve as S-norms and T-norms which deprive it of a profound analytical expression/form. This paper introduces two new oper...

For two propositional fuzzy logics, we present analytic proof calculi, based on relational hypersequents. The logic considered first, called Mà L, is based on the finite ordinal sums of à Lukasiewicz t-norms. In addition to the usual connectives – the conjunction ̄, the implication →, and the constant 0 –, we use a further unary connective interpreted by the function associating with each truth...

Probability theory and fuzzy logic have been presented as quite distinct theoretical foundations for reasoning and decision making in situations of uncertainty. This paper establishes a common basis for both forms of logic of uncertainty in which a basic uncertainty logic is defined in terms of a valuation on a lattice of propositions. The (non-truth-functional) connectives for conjunction, dis...

Among the various extensions to the common [0, 1]-valued truth degrees of “traditional” fuzzy set theory, closed intervals of [0, 1] stand out as a particularly appealing and promising choice for representing imperfect information, nicely accommodating and combining the facets of vagueness and uncertainty without paying too much in terms of computational complexity. From a logical point of view...

In this chapter, we consider particular classes of infinite-valued propositional logics which are strongly related to t-norms as conjunction connectives and to the real unit interval as set of their truth degrees, and which have their implication connectives determined via an adjointness condition. Such systems have in the last ten years been of considerable interest, and the topic of important...

introduction: nowadays the necessity of the existence of a certain width of keratinized gingiva is emphasized upon to maintain periodontal health and prevent soft tissue recession around teeth and dental implants. this study was carried out to compare two gingival graft procedures including connective tissue graft and graft with a combination of collagen sponge with platelet-rich plasma and pla...

Aggregation of information represented by membership functions is a central matter in intelligent systems where fuzzy rule base and reasoning mechanism are applied. Typical examples of such systems consist of, but not limited to, fuzzy control, decision support and expert systems. Since the advent of fuzzy sets a great number of fuzzy connectives, aggregation operators have been introduced. Som...