In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define exdended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm to solve decision making problems by using bipolar fuzzy soft set.

The concepts of rough and definite objects are relatively more determinate than those of granules and granulation in general rough set theory (RST) [1]. Representation of rough objects can however depend on the dialectical relation between granulation and definiteness. In this research, we make this exact in the context of RST over proto-transitive approximation spaces. This approach can be directly extended to many other types of RST. These are used for formulating an extended concept of knowledge interpretation (KI)(relative the situation for classical RST) and the problem of knowledge representation (KR) is solved. These will be of direct interest in granular KR in RST as developed by the present author [2] and of rough objects in general. In [3], these have already been used for five different semantics by the present author. This is an extended version of [4] with key examples and more results.

Fuzzy logic is an important technique for modeling uncertainty in expert systems (i.e., in cases where inferencing of conclusion from given evidence is difficult to ascertain). This paper proposes a fuzzy expert system framework that combines case-based and rule-based reasoning effectively to produce a usable tool for Type 2 Diabetes Mellitus (T2DM) management. The major targets are on combined therapies (i.e., lifestyle and pharmacologic), and the recognition of management data dynamics (trends) during reasoning. The Knowledge base (KB) is constructed using fuzzified input values which are subsequently de-fuzziffied after reasoning, to produce crisp outputs to patients in the form of low-risk advice. The extended framework features a combined reasoning approach for simplified output in the form of decision support for clinicians. With seven operational input variables and two additional pre-set variables for testing, the results of the proposed work will be compared with other methods using similarity to expert’s decision as metrics.

This paper introduces conceptual relations that synthesize utilitarian and logical concepts, extending the logics of preference of Rescher. We define first, in the context of a possible worlds model, constraint-dependent measures that quantify the relative quality of alternative solutions of reasoning problems or the relative desirability of various policies in control, decision, and planning problems. We show that these measures may be interpreted as truth values in a multi valued logic and propose mechanisms for the representation of complex constraints as combinations of simpler restrictions. These extended logical operations permit also the combination and aggregation of goal-specific quality measures into global measures of utility. We identify also relations that represent differential preferences between alternative solutions and relate them to the previously defined desirability measures. Extending conventional modal logic formulations, we introduce structures for the representation of ignorance about the utility of alternative solutions. Finally, we examine relations between these concepts and similarity based semantic models of fuzzy logic.

We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In a coherence-based setting, we study the extensions of a probability assessment defined on $n$ conditional events to their quasi conjunction, and by exploiting duality, to their quasi disjunction. The lower and upper bounds coincide with some well known t-norms and t-conorms: minimum, product, Lukasiewicz, and Hamacher t-norms and their dual t-conorms. On this basis we obtain Quasi And and Quasi Or rules. These are rules for which any finite family of conditional events p-entails the associated quasi conjunction and quasi disjunction. We examine some cases of logical dependencies, and we study the relations among coherence, inclusion for conditional events, and p-entailment. We also consider the Or rule, where quasi conjunction and quasi disjunction of premises coincide with the conclusion. We analyze further aspects of quasi conjunction and quasi disjunction, by computing probabilistic bounds on premises from bounds on conclusions. Finally, we consider biconditional events, and we introduce the notion of an $n$-conditional event. Then we give a probabilistic interpretation for a generalized Loop rule. In an appendix we provide explicit expressions for the Hamacher t-norm and t-conorm in the unitary hypercube.

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzzy sets of interpretations, each fuzzy set representing a possibility distribution describing what is known about the state of the world. A possibilistic knowledge base is then viewed as a set of possibility distributions that satisfy it. The refutation method of automated deduction in possibilistic logic, based on previously introduced generalized resolution principle is proved to be sound and complete with respect to the proposed semantics, including the case of partial inconsistency.

A reason maintenance system which extends an ATMS through Mukaidono's fuzzy logic is described. It supports a problem solver in situations affected by incomplete information and vague data, by allowing nonmonotonic inferences and the revision of previous conclusions when contradictions are detected.

This paper discusses a target tracking problem in which no dynamic mathematical model is explicitly assumed. A nonlinear filter based on the fuzzy If-then rules is developed. A comparison with a Kalman filter is made, and empirical results show that the performance of the fuzzy filter is better. Intensive simulations suggest that theoretical justification of the empirical results is possible.

In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of incidence calculus, and the belief and plausibility functions all obey the axioms of an interval structure. An interval structure can be used to synthesize the decision rules provided by the experts. An efficient algorithm to find the desirable set of rules is developed from a set of sound and complete inference axioms.

Relational models for diagnosis are based on a direct description of the association between disorders and manifestations. This type of model has been specially used and developed by Reggia and his co-workers in the late eighties as a basic starting point for approaching diagnosis problems. The paper proposes a new relational model which includes Reggia's model as a particular case and which allows for a more expressive representation of the observations and of the manifestations associated with disorders. The model distinguishes, i) between manifestations which are certainly absent and those which are not (yet) observed, and ii) between manifestations which cannot be caused by a given disorder and manifestations for which we do not know if they can or cannot be caused by this disorder. This new model, which can handle uncertainty in a non-probabilistic way, is based on possibility theory and so-called twofold fuzzy sets, previously introduced by the authors.